{"id":2159,"date":"2017-10-07T23:22:01","date_gmt":"2017-10-07T23:22:01","guid":{"rendered":"http:\/\/www.cientificos.pe\/?p=2159"},"modified":"2018-04-09T19:07:13","modified_gmt":"2018-04-09T19:07:13","slug":"qualifiers-to-the-world-cup-russia-2018-an-introduction-to-the-theory-of-probability","status":"publish","type":"post","link":"https:\/\/www.cientificos.pe\/?p=2159","title":{"rendered":"Qualifiers to the World Cup Russia 2018: An introduction to the theory of probability"},"content":{"rendered":"<p style=\"text-align: justify;\"><strong>November\u00a015<sup>th<\/sup>,\u00a02017<\/strong><\/p>\n<p style=\"text-align: justify;\">Argentina, Colombia, and Peru qualified to the World Cup Russia 2018. The latter qualified beating New Zealanad 2-0 in the interconfederation play-off.<\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 12pt;\"><strong>October 7<sup>th<\/sup>,\u00a02017<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\">In the <a href=\"http:\/\/www.cientificos.pe\/index.php\/2017\/10\/07\/qualifiers-to-the-world-cup-russia-2018-an-introduction-to-the-theory-of-probability\/3\/\">first part of this article<\/a>, published on September 11<sup>th<\/sup>, we elaborated a mathematical analysis to predict the Conmebol teams that will qualify to the World Cup Russia 2018. The analysis was done before Matchday 17 and Matchday 18, we assumed that Colombia was not going to lose against Paraguay, but for ironies of soccer Paraguay defeated Colombia, scoring 2 goals in the last 5 minutes. This outcome radically changed the results discussed in the analysis. We considered a positive result of Colombia because, by doing\u00a0so, the possible combinations were reduced from <strong>2187<\/strong> to <strong>243<\/strong> (refer to the <a href=\"http:\/\/www.cientificos.pe\/index.php\/2017\/10\/07\/qualifiers-to-the-world-cup-russia-2018-an-introduction-to-the-theory-of-probability\/3\/\">first part of the article<\/a>), the latter being an easy-to-handle number. In this second part, we are going to develop a similar analysis considering the results of Matchday 17. The standings are as follow:<\/p>\n<p><img loading=\"lazy\" class=\"wp-image-2286 aligncenter\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/tablelast-300x140.png\" alt=\"\" width=\"500\" height=\"234\" srcset=\"https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/tablelast-300x140.png 300w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/tablelast-768x360.png 768w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/tablelast-696x326.png 696w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/tablelast-897x420.png 897w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/tablelast.png 959w\" sizes=\"(max-width: 500px) 100vw, 500px\" \/><\/p>\n<p style=\"text-align: justify;\">To begin with, we are going to consider that in Matchday 18, Uruguay vs Bolivia is an irrelevant game; therefore, we have 4 games left, giving us:<\/p>\n<ul>\n<li style=\"text-align: justify;\">Possible combinations in Matchday 18: 3 x 3 x 3 x 3 =\u00a0<strong>81.<\/strong><\/li>\n<\/ul>\n<p style=\"text-align: justify;\">This means that there are 81 ways in which the standings\u00a0can be left (<a href=\"http:\/\/www.cientificos.pe\/index.php\/2017\/10\/07\/qualifiers-to-the-world-cup-russia-2018-an-introduction-to-the-theory-of-probability\/2\/\">click here<\/a> to see the 81 possible ways). Of all of them only one will represent the end of the Qualifiers. In this analysis we have two qualified teams: Brazil and Uruguay. The candidates for the other three places are Chile, Argentina, Peru, Colombia, and Paraguay (in this article, a &#8220;qualified team&#8221; includes the team that\u00a0advances to the inter-confederation play-offs). Their games\u00a0are as follow:<\/p>\n<p style=\"text-align: center;\">&#8212;&#8212;&#8212;&#8211; vs Argentina<img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>Peru vs\u00a0Colombia\u00a0<img loading=\"lazy\" class=\"alignnone wp-image-2277\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag.png\" alt=\"\" width=\"24\" height=\"16\" srcset=\"https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag.png 200w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag-100x70.png 100w\" sizes=\"(max-width: 24px) 100vw, 24px\" \/><br \/>\n&#8212;&#8212;&#8212;&#8211; vs Chile<img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-2278\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/paraguayflag.png\" alt=\"\" width=\"27\" height=\"15\" \/>Paraguay vs &#8212;&#8212;&#8212;&#8211;<\/p>\n<p>As it can be seen, in Matchday 18 it does not matter against which teams Argentina, Chile, and Paraguay play because the only ones who can alter the standings\u00a0are them and not their rivals. Now we will use the theory of probability&#8230;<\/p>\n<p>Based in mathematics we can answer the following questions:<\/p>\n<p style=\"text-align: justify;\">1<em>.<span style=\"text-decoration: underline;\"><strong>How many points is likely to have the last qualified team?<\/strong><\/span><strong><span style=\"text-decoration: underline;\"><br \/>\n<\/span><\/strong><\/em>Considering the tree diagram (explained in the <a href=\"http:\/\/www.cientificos.pe\/index.php\/2017\/10\/07\/qualifiers-to-the-world-cup-russia-2018-an-introduction-to-the-theory-of-probability\/3\/\">first part of this article<\/a>) we obtain:<\/p>\n<p style=\"text-align: center;\">P(28) = 6\/81<br \/>\nP(27) = 27\/81<br \/>\nP(26) = 42\/81<br \/>\nP(25) = 6\/81<\/p>\n<p style=\"text-align: justify;\">P(X) indicates the probability of obtaining X points in the last qualifying spot. Therefore, it is\u00a0likely that <strong>the 5<sup>th<\/sup>\u00a0place in the Conmebol Qualifiers will have\u00a026 points<\/strong>, P(26) = 42\/81 = 51.9%. Additionally, we see that the highest score possible\u00a0is 28 points. Uruguay to date has 28 points with a goal difference of +10; consequently, to be eliminated her rivals must win 9-0 at least. In these circumstances, it is feasible to assume that Uruguay is already qualified.<\/p>\n<p style=\"text-align: justify;\">2<em>.\u00a0<strong><span style=\"text-decoration: underline;\">In how many cases the last qualified team\u00a0and the best eliminated team\u00a0are tied in\u00a0points?<\/span><\/strong><\/em><\/p>\n<p>Using the results given in the <a href=\"http:\/\/www.cientificos.pe\/index.php\/2017\/10\/07\/qualifiers-to-the-world-cup-russia-2018-an-introduction-to-the-theory-of-probability\/2\/\">supplementary information<\/a> we have:<\/p>\n<p style=\"text-align: center;\">TOTAL PROBABILITY: 27\/81 = 33.3%<\/p>\n<p style=\"text-align: center;\">PROBABILITY (If Brazil beats Chile) = 15\/27 = 55.5%<br \/>\nPROBABILITY (If Chile ties\u00a0Brazil) = 6\/27 = 22.2%<br \/>\nPROBABILITY (Si Chile beats\u00a0Brasil) = 6\/27 = 22.2%<\/p>\n<p style=\"text-align: justify;\">This means that in\u00a027 cases out of 81, the 5<sup>th<\/sup> and 6<sup>th<\/sup> place in the standings are settled by goal difference. For the particular case in which Chile loses against Brazil, this situation happens in 15 out of 27 cases.<\/p>\n<p style=\"text-align: justify;\">3<i>.\u00a0<\/i><span style=\"text-decoration: underline;\"><i><em><strong>Which teams will qualify?<\/strong><\/em><\/i><\/span><\/p>\n<p style=\"text-align: justify;\">In this\u00a0analysis, Brazil and Uruguay are already qualified. There are 3 spots left to reach the World Cup. Based on the results shown in the <a href=\"http:\/\/www.cientificos.pe\/index.php\/2017\/10\/07\/qualifiers-to-the-world-cup-russia-2018-an-introduction-to-the-theory-of-probability\/2\/\">supplementary information<\/a> we have for the teams that are still competing:<\/p>\n<table>\n<caption>Total qualifying probability\u00a0<\/caption>\n<tbody>\n<tr>\n<td style=\"text-align: center;\">With the best goal difference<\/td>\n<td style=\"text-align: center;\">With the worst goal difference<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">\n<h4><strong>P(<img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>) = 78\/81 = \u00a096.3%<\/strong><\/h4>\n<h4><strong>P(<img loading=\"lazy\" class=\"alignnone wp-image-2277\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag.png\" alt=\"\" width=\"24\" height=\"16\" srcset=\"https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag.png 200w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag-100x70.png 100w\" sizes=\"(max-width: 24px) 100vw, 24px\" \/>) =\u00a070\/81 = \u00a086.4%<\/strong><\/h4>\n<h4><strong>P(<img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>) = 54\/81 = \u00a066.6%<\/strong><\/h4>\n<h5>P(<img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>) = 49\/81 = \u00a060.5%<\/h5>\n<h6>P(<img loading=\"lazy\" class=\"alignnone wp-image-2278\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/paraguayflag.png\" alt=\"\" width=\"27\" height=\"15\" \/>) =\u00a0NOT APPLICABLE<\/h6>\n<\/td>\n<td style=\"text-align: center;\">\n<h4><strong>P(<img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>) = 65\/81 = \u00a080.2%<\/strong><\/h4>\n<h4><strong>P(<img loading=\"lazy\" class=\"alignnone wp-image-2277\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag.png\" alt=\"\" width=\"24\" height=\"16\" srcset=\"https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag.png 200w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag-100x70.png 100w\" sizes=\"(max-width: 24px) 100vw, 24px\" \/>) = 60\/81 = \u00a074.1%<\/strong><\/h4>\n<h4><strong>\u00a0P(<img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>) = 33\/81 = 40.1%<\/strong><\/h4>\n<h5>\u00a0P(<img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>) = 33\/81 = 40.1%<\/h5>\n<h6>\u00a0 \u00a0 \u00a0P(<img loading=\"lazy\" class=\"alignnone wp-image-2278\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/paraguayflag.png\" alt=\"\" width=\"27\" height=\"15\" \/>) = 21\/81 = 25.9%<\/h6>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">The interesting thing is that although Peru and Argentina have the same amount of points before playing their matches, once\u00a0they finish them, the qualifying probability of Argentina\u00a0is higher. The reason is because Peru plays against a direct rival that is Colombia. For the analysis of Paraguay we omitted the case with best goal difference because for this to happen Paraguay must thrash Venezuela 7-0. <strong>If these results would be\u00a0relevant, the 3 qualified\u00a0teams would be\u00a0Chile, Colombia, and Argentina<\/strong>.<br \/>\nHowever, it is important to note that although Paraguay has\u00a0the lowest probability, she\u00a0has the most accessible game, facing Venezuela in Asuncion. In contrast, although Chile has the best qualifying probability, she\u00a0faces Brazil in Sao Paulo. Therefore, we can perform a similar analysis taking these data into account. That is to say, if we assume that Paraguay beats\u00a0Venezuela, and Chile as much ties Brazil, the qualifying probability becomes:<\/p>\n<table>\n<caption>Total qualifying probability\u00a0<\/caption>\n<tbody>\n<tr>\n<td style=\"text-align: center;\">With the best goal difference<\/td>\n<td style=\"text-align: center;\">With the worst\u00a0goal difference<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">\n<h4><strong>P(<\/strong><strong><img loading=\"lazy\" class=\"alignnone wp-image-2278\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/paraguayflag.png\" alt=\"\" width=\"27\" height=\"15\" \/>) =\u00a0NOT APPLICABLE<\/strong><\/h4>\n<h4><strong>P(<\/strong><strong><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/><\/strong><strong>) = 15\/18 = \u00a083.3%<\/strong><\/h4>\n<h4><strong>P(<\/strong><strong><img loading=\"lazy\" class=\"alignnone wp-image-2277\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag.png\" alt=\"\" width=\"24\" height=\"16\" srcset=\"https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag.png 200w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag-100x70.png 100w\" sizes=\"(max-width: 24px) 100vw, 24px\" \/><\/strong><strong>) = 14\/18 = \u00a077.8%<\/strong><\/h4>\n<h5>P(<strong><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/><\/strong>) = 9\/18 = \u00a050.0%<\/h5>\n<h6>P(<img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>) =\u00a08\/18 = 44.4%<\/h6>\n<\/td>\n<td style=\"text-align: center;\">\n<h4><strong>P(<\/strong><strong><img loading=\"lazy\" class=\"alignnone wp-image-2278\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/paraguayflag.png\" alt=\"\" width=\"27\" height=\"15\" \/>) = 15\/18 = \u00a083.3%<\/strong><\/h4>\n<h4><strong>P(<\/strong><strong><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/><\/strong><strong>) = 10\/18 = \u00a055.6%<\/strong><\/h4>\n<h4><strong>\u00a0P(<\/strong><strong><img loading=\"lazy\" class=\"alignnone wp-image-2277\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag.png\" alt=\"\" width=\"24\" height=\"16\" srcset=\"https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag.png 200w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag-100x70.png 100w\" sizes=\"(max-width: 24px) 100vw, 24px\" \/><\/strong><strong>) = 12\/18 = 66.7%<\/strong><\/h4>\n<h5>\u00a0P(<strong><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/><\/strong>) = 6\/18 = 33.3%<\/h5>\n<h6>\u00a0 \u00a0 \u00a0P(<img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>) = 6\/18\u00a0= 33.3%<\/h6>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">From the Table above we can conclude\u00a0the following:<\/p>\n<ul>\n<li style=\"text-align: justify;\"><strong>Paraguay,<\/strong>\u00a0beating Venezuela 1-0 reaches a qualifying probability of 83.3%.<\/li>\n<li style=\"text-align: justify;\"><strong>Chile<\/strong> is the second team most likely to qualify; nevertheless, her qualifying probability strongly depends in goal difference (goes from 55.6% to 83.3%). The advantage that Chile has with respect to the other teams is that even if losing against Brazil her qualifying probability remains latent. A curious fact that can be seen by paying attention to\u00a0the <a href=\"http:\/\/www.cientificos.pe\/index.php\/2017\/10\/07\/qualifiers-to-the-world-cup-russia-2018-an-introduction-to-the-theory-of-probability\/2\/\">supplementary information<\/a> is that for Chile, a draw or a win against Brazil gives the same outcome, that is, it does not modify her qualifying probability\u00a0nor it harms the other teams. With this, Chile could calmly play defense against Brazil.<\/li>\n<li style=\"text-align: justify;\"><strong>Colombia<\/strong> is the third team with more chances to qualify, her qualifying\u00a0probability remains similar with best or worst goal difference. Colombia has the advantage that if she ties Peru, her chances to qualify remain latent. That is, Colombia could calmly play defense\u00a0against Peru.<\/li>\n<li style=\"text-align: justify;\"><strong>Argentina<\/strong>\u00a0and\u00a0<strong>Peru<\/strong>\u00a0have the lowest qualifying probabilities, they must\u00a0win their matches so as to not depend on many variables. Therefore, they must play offense in Matchday 18.<\/li>\n<\/ul>\n<p style=\"text-align: justify;\">Finally, it is worth mentioning that the unexpected triumph of Paraguay greatly benefited Chile and seriously damaged Peru, as evidenced by comparing these calculations with those made in the <a href=\"http:\/\/www.cientificos.pe\/index.php\/2017\/10\/07\/qualifiers-to-the-world-cup-russia-2018-an-introduction-to-the-theory-of-probability\/3\/\">first part of the article<\/a>&#8230; Who will take their songs to the World Cup? Will Argentina and Peru give the surprise? Will Paraguay lose her\u00a0great option? Will Chile, being favorite, be eliminated? Or Colombia, being third, will remember her match against Paraguay and realize that they lost their chances to qualify in the 5 last minutes? On October 10<sup>th<\/sup>, everything will be revealed&#8230;<\/p>\n<p style=\"text-align: justify;\">Christian Ortiz, PhD.<\/p>\n<p style=\"text-align: justify;\"><!--nextpage--><\/p>\n<h4 style=\"text-align: justify;\"><span style=\"font-family: verdana, geneva, sans-serif; font-size: 12pt;\"><strong>October 7<sup>th<\/sup>,\u00a02017<\/strong><\/span><\/h4>\n<h3 style=\"text-align: justify;\"><strong><span style=\"text-decoration: underline;\">Supplementary information<\/span><\/strong>\u00a0(2<sup>nd<\/sup> part of the article)<\/h3>\n<p style=\"text-align: justify;\">There are 81\u00a0configurations in which the standings can be arranged at the end of the competition (considering the results of Matchday 17) for the teams disputing the last qualifying spots.<\/p>\n<ul>\n<li style=\"text-align: justify;\">In Tables 1, 2, and 3, we show the standings. We have grouped 9 standing tables for each sub-group (Table 1 refers to the case where Ecuador beats Argentina, Table 2 refers to the case where they tie, and Table 3 to the case where Argentina beats Ecuador). For each one, Chile has 3 values depending on the match against Brazil (giving a total of 27 possible configurations for each sub-group). The first two places\u00a0qualify directly to the World Cup, the third\u00a0place advances to the inter-confederation play-offs.<\/li>\n<\/ul>\n<p style=\"text-align: center;\"><strong><span style=\"text-decoration: underline;\">1) Ecuador beats\u00a0Argentina\u00a0<\/span><\/strong><\/p>\n<table>\n<caption>Table 1<\/caption>\n<tbody>\n<tr>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 28<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 26 (27) (29)<\/li>\n<li><strong><img loading=\"lazy\" class=\"alignnone wp-image-2277\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag.png\" alt=\"\" width=\"24\" height=\"16\" srcset=\"https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag.png 200w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag-100x70.png 100w\" sizes=\"(max-width: 24px) 100vw, 24px\" \/><\/strong>= 26<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 25<\/li>\n<li><strong><img loading=\"lazy\" class=\"alignnone wp-image-2278\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/paraguayflag.png\" alt=\"\" width=\"27\" height=\"15\" \/><\/strong>= 24<\/li>\n<\/ol>\n<\/td>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 28<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 26 (27) (29)<\/li>\n<li><strong><img loading=\"lazy\" class=\"alignnone wp-image-2277\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag.png\" alt=\"\" width=\"24\" height=\"16\" srcset=\"https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag.png 200w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag-100x70.png 100w\" sizes=\"(max-width: 24px) 100vw, 24px\" \/><\/strong>= 26<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 25<\/li>\n<li><strong><img loading=\"lazy\" class=\"alignnone wp-image-2278\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/paraguayflag.png\" alt=\"\" width=\"27\" height=\"15\" \/><\/strong>= 25<\/li>\n<\/ol>\n<\/td>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 28<\/li>\n<li><strong><img loading=\"lazy\" class=\"alignnone wp-image-2278\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/paraguayflag.png\" alt=\"\" width=\"27\" height=\"15\" \/><\/strong>=27<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 26 (27)(29)<\/li>\n<li><strong><img loading=\"lazy\" class=\"alignnone wp-image-2277\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag.png\" alt=\"\" width=\"24\" height=\"16\" srcset=\"https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag.png 200w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag-100x70.png 100w\" sizes=\"(max-width: 24px) 100vw, 24px\" \/><\/strong>= 26<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 25<\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"142\">\n<ol>\n<li><strong><img loading=\"lazy\" class=\"alignnone wp-image-2277\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag.png\" alt=\"\" width=\"24\" height=\"16\" srcset=\"https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag.png 200w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag-100x70.png 100w\" sizes=\"(max-width: 24px) 100vw, 24px\" \/><\/strong>= 27<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 26 (27) (29)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 26<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 25<\/li>\n<li><strong><img loading=\"lazy\" class=\"alignnone wp-image-2278\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/paraguayflag.png\" alt=\"\" width=\"27\" height=\"15\" \/><\/strong>= 24<\/li>\n<\/ol>\n<\/td>\n<td width=\"142\">\n<ol>\n<li><strong><img loading=\"lazy\" class=\"alignnone wp-image-2277\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag.png\" alt=\"\" width=\"24\" height=\"16\" srcset=\"https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag.png 200w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag-100x70.png 100w\" sizes=\"(max-width: 24px) 100vw, 24px\" \/><\/strong>= 27<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 26 (27) (29)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 26<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 25<\/li>\n<li><strong><img loading=\"lazy\" class=\"alignnone wp-image-2278\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/paraguayflag.png\" alt=\"\" width=\"27\" height=\"15\" \/><\/strong>= 25<\/li>\n<\/ol>\n<\/td>\n<td width=\"142\">\n<ol>\n<li><strong><img loading=\"lazy\" class=\"alignnone wp-image-2277\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag.png\" alt=\"\" width=\"24\" height=\"16\" srcset=\"https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag.png 200w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag-100x70.png 100w\" sizes=\"(max-width: 24px) 100vw, 24px\" \/><\/strong>= 27<\/li>\n<li><strong><img loading=\"lazy\" class=\"alignnone wp-image-2278\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/paraguayflag.png\" alt=\"\" width=\"27\" height=\"15\" \/><\/strong>= 27<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 26 (27) (29)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 26<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 25<\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"142\">\n<ol>\n<li><strong><img loading=\"lazy\" class=\"alignnone wp-image-2277\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag.png\" alt=\"\" width=\"24\" height=\"16\" srcset=\"https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag.png 200w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag-100x70.png 100w\" sizes=\"(max-width: 24px) 100vw, 24px\" \/><\/strong>= 29<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 26 (27) (29)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 25<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 25<\/li>\n<li><strong><img loading=\"lazy\" class=\"alignnone wp-image-2278\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/paraguayflag.png\" alt=\"\" width=\"27\" height=\"15\" \/><\/strong>= 24<\/li>\n<\/ol>\n<\/td>\n<td width=\"142\">\n<ol>\n<li><strong><img loading=\"lazy\" class=\"alignnone wp-image-2277\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag.png\" alt=\"\" width=\"24\" height=\"16\" srcset=\"https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag.png 200w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag-100x70.png 100w\" sizes=\"(max-width: 24px) 100vw, 24px\" \/><\/strong>= 29<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 26 (27) (29)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 25<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 25<\/li>\n<li><strong><img loading=\"lazy\" class=\"alignnone wp-image-2278\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/paraguayflag.png\" alt=\"\" width=\"27\" height=\"15\" \/><\/strong>= 25<\/li>\n<\/ol>\n<\/td>\n<td width=\"142\">\n<ol>\n<li><strong><img loading=\"lazy\" class=\"alignnone wp-image-2277\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag.png\" alt=\"\" width=\"24\" height=\"16\" srcset=\"https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag.png 200w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag-100x70.png 100w\" sizes=\"(max-width: 24px) 100vw, 24px\" \/><\/strong>= 29<\/li>\n<li><strong><img loading=\"lazy\" class=\"alignnone wp-image-2278\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/paraguayflag.png\" alt=\"\" width=\"27\" height=\"15\" \/><\/strong>= 27<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 26 (27) (29)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 25<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 25<\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: center;\"><strong><span style=\"text-decoration: underline;\">2) Ecuador ties\u00a0Argentina<\/span><\/strong><\/p>\n<table>\n<caption>Table 2<\/caption>\n<tbody>\n<tr>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 28<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 26 (27) (29)<\/li>\n<li><strong><img loading=\"lazy\" class=\"alignnone wp-image-2277\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag.png\" alt=\"\" width=\"24\" height=\"16\" srcset=\"https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag.png 200w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag-100x70.png 100w\" sizes=\"(max-width: 24px) 100vw, 24px\" \/><\/strong>= 26<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 26<\/li>\n<li><strong><img loading=\"lazy\" class=\"alignnone wp-image-2278\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/paraguayflag.png\" alt=\"\" width=\"27\" height=\"15\" \/><\/strong>= 24<\/li>\n<\/ol>\n<\/td>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 28<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 26 (27) (29)<\/li>\n<li><strong><img loading=\"lazy\" class=\"alignnone wp-image-2277\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag.png\" alt=\"\" width=\"24\" height=\"16\" srcset=\"https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag.png 200w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag-100x70.png 100w\" sizes=\"(max-width: 24px) 100vw, 24px\" \/><\/strong>= 26<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 26<\/li>\n<li><strong><img loading=\"lazy\" class=\"alignnone wp-image-2278\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/paraguayflag.png\" alt=\"\" width=\"27\" height=\"15\" \/><\/strong>= 25<\/li>\n<\/ol>\n<\/td>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 28<\/li>\n<li><strong><img loading=\"lazy\" class=\"alignnone wp-image-2278\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/paraguayflag.png\" alt=\"\" width=\"27\" height=\"15\" \/><\/strong>=27<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 26 (27)(29)<\/li>\n<li><strong><img loading=\"lazy\" class=\"alignnone wp-image-2277\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag.png\" alt=\"\" width=\"24\" height=\"16\" srcset=\"https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag.png 200w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag-100x70.png 100w\" sizes=\"(max-width: 24px) 100vw, 24px\" \/><\/strong>= 26<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 26<\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"142\">\n<ol>\n<li><strong><img loading=\"lazy\" class=\"alignnone wp-image-2277\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag.png\" alt=\"\" width=\"24\" height=\"16\" srcset=\"https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag.png 200w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag-100x70.png 100w\" sizes=\"(max-width: 24px) 100vw, 24px\" \/><\/strong>= 27<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 26 (27) (29)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 26<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 26<\/li>\n<li><strong><img loading=\"lazy\" class=\"alignnone wp-image-2278\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/paraguayflag.png\" alt=\"\" width=\"27\" height=\"15\" \/><\/strong>= 24<\/li>\n<\/ol>\n<\/td>\n<td width=\"142\">\n<ol>\n<li><strong><img loading=\"lazy\" class=\"alignnone wp-image-2277\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag.png\" alt=\"\" width=\"24\" height=\"16\" srcset=\"https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag.png 200w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag-100x70.png 100w\" sizes=\"(max-width: 24px) 100vw, 24px\" \/><\/strong>= 27<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 26 (27) (29)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 26<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 26<\/li>\n<li><strong><img loading=\"lazy\" class=\"alignnone wp-image-2278\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/paraguayflag.png\" alt=\"\" width=\"27\" height=\"15\" \/><\/strong>= 25<\/li>\n<\/ol>\n<\/td>\n<td width=\"142\">\n<ol>\n<li><strong><img loading=\"lazy\" class=\"alignnone wp-image-2277\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag.png\" alt=\"\" width=\"24\" height=\"16\" srcset=\"https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag.png 200w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag-100x70.png 100w\" sizes=\"(max-width: 24px) 100vw, 24px\" \/><\/strong>= 27<\/li>\n<li><strong><img loading=\"lazy\" class=\"alignnone wp-image-2278\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/paraguayflag.png\" alt=\"\" width=\"27\" height=\"15\" \/><\/strong>= 27<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 26 (27) (29)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 26<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 26<\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"142\">\n<ol>\n<li><strong><img loading=\"lazy\" class=\"alignnone wp-image-2277\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag.png\" alt=\"\" width=\"24\" height=\"16\" srcset=\"https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag.png 200w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag-100x70.png 100w\" sizes=\"(max-width: 24px) 100vw, 24px\" \/><\/strong>= 29<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 26 (27) (29)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 26<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 25<\/li>\n<li><strong><img loading=\"lazy\" class=\"alignnone wp-image-2278\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/paraguayflag.png\" alt=\"\" width=\"27\" height=\"15\" \/><\/strong>= 24<\/li>\n<\/ol>\n<\/td>\n<td width=\"142\">\n<ol>\n<li style=\"list-style-type: none;\">\n<ol>\n<li><strong><img loading=\"lazy\" class=\"alignnone wp-image-2277\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag.png\" alt=\"\" width=\"24\" height=\"16\" srcset=\"https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag.png 200w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag-100x70.png 100w\" sizes=\"(max-width: 24px) 100vw, 24px\" \/><\/strong>= 29<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 26 (27) (29)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 26<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 25<\/li>\n<li><strong><img loading=\"lazy\" class=\"alignnone wp-image-2278\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/paraguayflag.png\" alt=\"\" width=\"27\" height=\"15\" \/><\/strong>= 25<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<\/td>\n<td width=\"142\">\n<ol>\n<li><strong><img loading=\"lazy\" class=\"alignnone wp-image-2277\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag.png\" alt=\"\" width=\"24\" height=\"16\" srcset=\"https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag.png 200w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag-100x70.png 100w\" sizes=\"(max-width: 24px) 100vw, 24px\" \/><\/strong>= 29<\/li>\n<li><strong><img loading=\"lazy\" class=\"alignnone wp-image-2278\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/paraguayflag.png\" alt=\"\" width=\"27\" height=\"15\" \/><\/strong>= 27<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 26 (27) (29)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 26<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 25<\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: center;\"><strong><span style=\"text-decoration: underline;\">3) Argentina beats\u00a0Ecuador<\/span><\/strong><\/p>\n<table>\n<caption>Table 3<\/caption>\n<tbody>\n<tr>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 28<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 28<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 26 (27) (29)<\/li>\n<li><strong><img loading=\"lazy\" class=\"alignnone wp-image-2277\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag.png\" alt=\"\" width=\"24\" height=\"16\" srcset=\"https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag.png 200w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag-100x70.png 100w\" sizes=\"(max-width: 24px) 100vw, 24px\" \/><\/strong>= 26<\/li>\n<li><strong><img loading=\"lazy\" class=\"alignnone wp-image-2278\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/paraguayflag.png\" alt=\"\" width=\"27\" height=\"15\" \/><\/strong>= 24<\/li>\n<\/ol>\n<\/td>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 28<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 28<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 26 (27) (29)<\/li>\n<li><strong><img loading=\"lazy\" class=\"alignnone wp-image-2277\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag.png\" alt=\"\" width=\"24\" height=\"16\" srcset=\"https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag.png 200w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag-100x70.png 100w\" sizes=\"(max-width: 24px) 100vw, 24px\" \/><\/strong>= 26<\/li>\n<li><strong><img loading=\"lazy\" class=\"alignnone wp-image-2278\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/paraguayflag.png\" alt=\"\" width=\"27\" height=\"15\" \/><\/strong>= 25<\/li>\n<\/ol>\n<\/td>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 28<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 28<\/li>\n<li><strong><img loading=\"lazy\" class=\"alignnone wp-image-2278\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/paraguayflag.png\" alt=\"\" width=\"27\" height=\"15\" \/><\/strong>=27<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 26 (27)(29)<\/li>\n<li><strong><img loading=\"lazy\" class=\"alignnone wp-image-2277\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag.png\" alt=\"\" width=\"24\" height=\"16\" srcset=\"https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag.png 200w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag-100x70.png 100w\" sizes=\"(max-width: 24px) 100vw, 24px\" \/><\/strong>= 26<\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 28<\/li>\n<li><strong><img loading=\"lazy\" class=\"alignnone wp-image-2277\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag.png\" alt=\"\" width=\"24\" height=\"16\" srcset=\"https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag.png 200w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag-100x70.png 100w\" sizes=\"(max-width: 24px) 100vw, 24px\" \/><\/strong>= 27<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 26 (27) (29)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 26<\/li>\n<li><strong><img loading=\"lazy\" class=\"alignnone wp-image-2278\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/paraguayflag.png\" alt=\"\" width=\"27\" height=\"15\" \/><\/strong>= 24<\/li>\n<\/ol>\n<\/td>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 28<\/li>\n<li><strong><img loading=\"lazy\" class=\"alignnone wp-image-2277\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag.png\" alt=\"\" width=\"24\" height=\"16\" srcset=\"https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag.png 200w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag-100x70.png 100w\" sizes=\"(max-width: 24px) 100vw, 24px\" \/><\/strong>= 27<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 26 (27) (29)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 26<\/li>\n<li><strong><img loading=\"lazy\" class=\"alignnone wp-image-2278\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/paraguayflag.png\" alt=\"\" width=\"27\" height=\"15\" \/><\/strong>= 25<\/li>\n<\/ol>\n<\/td>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 28<\/li>\n<li><strong><img loading=\"lazy\" class=\"alignnone wp-image-2277\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag.png\" alt=\"\" width=\"24\" height=\"16\" srcset=\"https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag.png 200w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag-100x70.png 100w\" sizes=\"(max-width: 24px) 100vw, 24px\" \/><\/strong>= 27<\/li>\n<li><strong><img loading=\"lazy\" class=\"alignnone wp-image-2278\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/paraguayflag.png\" alt=\"\" width=\"27\" height=\"15\" \/><\/strong>= 27<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 26 (27) (29)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 26<\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"142\">\n<ol>\n<li><strong><img loading=\"lazy\" class=\"alignnone wp-image-2277\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag.png\" alt=\"\" width=\"24\" height=\"16\" srcset=\"https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag.png 200w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag-100x70.png 100w\" sizes=\"(max-width: 24px) 100vw, 24px\" \/><\/strong>= 29<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 28<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 26 (27) (29)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 25<\/li>\n<li><strong><img loading=\"lazy\" class=\"alignnone wp-image-2278\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/paraguayflag.png\" alt=\"\" width=\"27\" height=\"15\" \/><\/strong>= 24<\/li>\n<\/ol>\n<\/td>\n<td width=\"142\">\n<ol>\n<li><strong><img loading=\"lazy\" class=\"alignnone wp-image-2277\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag.png\" alt=\"\" width=\"24\" height=\"16\" srcset=\"https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag.png 200w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag-100x70.png 100w\" sizes=\"(max-width: 24px) 100vw, 24px\" \/><\/strong>= 29<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 28<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 26 (27) (29)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 25<\/li>\n<li><strong><img loading=\"lazy\" class=\"alignnone wp-image-2278\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/paraguayflag.png\" alt=\"\" width=\"27\" height=\"15\" \/><\/strong>= 25<\/li>\n<\/ol>\n<\/td>\n<td width=\"142\">\n<ol>\n<li><strong><img loading=\"lazy\" class=\"alignnone wp-image-2277\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag.png\" alt=\"\" width=\"24\" height=\"16\" srcset=\"https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag.png 200w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/colombiaflag-100x70.png 100w\" sizes=\"(max-width: 24px) 100vw, 24px\" \/><\/strong>= 29<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 28<\/li>\n<li><strong><img loading=\"lazy\" class=\"alignnone wp-image-2278\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/paraguayflag.png\" alt=\"\" width=\"27\" height=\"15\" \/><\/strong>= 27<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 26 (27) (29)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 25<\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\"><!--nextpage--><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 12pt;\"><strong>September\u00a011<sup>th<\/sup>,\u00a02017<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\">The Conmebol Qualifiers are reaching the final stretch and fans everywhere cannot stop\u00a0checking the standings. There are 10 teams and two games left for each one. How many results can arise? They seem not to be a lot, will they? Each team can win, draw or lose. Three states! What is better, come in pairs, if one team wins the other is meant\u00a0to lose, if one ties the other is meant\u00a0to tie. Sounds interesting: <strong>The state of one team automatically conditions the state of the other<\/strong>. No! This is not <strong><span style=\"color: #3366ff;\"><em>quantum entanglement.<\/em><\/span><\/strong>\u00a0Don&#8217;t be\u00a0confused, we are in the classical world, we will leave quantum mechanics aside. Here, we will only give basic notions of the theory of probability.<\/p>\n<p style=\"text-align: justify;\">In one matchday there are five games\u00a0and the results of each one can be 3 (win, draw or lose), how many combinations will be there? The answer is 3 x 3 x 3 x 3 x 3 = 243. This means that\u00a0in matchday 17\u00a0there are 243 ways in which the standings\u00a0can be left. Wow! That&#8217;s not all, in matchday 18\u00a0will be the same. So how many combinations are there in total? The answer is 243 x 243 = 59049. Yes, I know, the number is gigantic and we have not considered the number of goals.<br \/>\nThe objective is to reduce this number, study all the options available, and determine the teams that will qualify (in this article, a &#8220;qualified team&#8221; includes the team that\u00a0advances to the inter-confederation play-offs). Let&#8217;s check the games,<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" class=\"aligncenter wp-image-2047\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/tablafinal-300x160.png\" alt=\"\" width=\"500\" height=\"267\" srcset=\"https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/tablafinal-300x160.png 300w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/tablafinal-768x410.png 768w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/tablafinal-696x372.png 696w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/tablafinal-786x420.png 786w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/tablafinal.png 923w\" sizes=\"(max-width: 500px) 100vw, 500px\" \/><\/p>\n<p style=\"text-align: justify;\">Pay attention to the match Bolivia vs Brazil. Do you think this match will change the standings?<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" class=\"aligncenter wp-image-2160\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/tablefinal2-300x207.png\" alt=\"\" width=\"500\" height=\"345\" srcset=\"https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/tablefinal2-300x207.png 300w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/tablefinal2-100x70.png 100w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/tablefinal2-218x150.png 218w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/tablefinal2-608x420.png 608w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/tablefinal2.png 679w\" sizes=\"(max-width: 500px) 100vw, 500px\" \/><\/p>\n<p style=\"text-align: justify;\">Of course not! Brazil is 1<sup>st<\/sup>\u00a0and Bolivia 9<sup>th<\/sup><sup>.<\/sup> We can say that the standings won&#8217;t change even if Bolivia wins. Consequently, matchday 17 has only 4 important games. Following the calculations made previously,<\/p>\n<ul>\n<li>Possible combinations in matchday 17: 3 x 3 x 3 x 3 = 81<\/li>\n<li>Possible combinations in matchday 18:\u00a03 x 3 x 3 x 3 x 3 = 243<\/li>\n<li>Total possible combinations: 81 x 243 = <strong>19683<\/strong><\/li>\n<\/ul>\n<p style=\"text-align: justify;\">Wow! Instead of\u00a059049 cases we have\u00a019683. We are on the right track. What else can we do? Let&#8217;s check\u00a0the matches of Uruguay. She\u00a0plays against Venezuela in Caracas and against Bolivia in Montevideo. In addition, her\u00a0goal difference is much higher than any other team (excluding Brazil). Uruguay needs to win one game to be in the World Cup, and needs to tie one to qualify.\u00a0It is possible, very easy indeed. Therefore, we are going to assume, without fearing of making\u00a0any mistake, that Uruguay is already qualified\u00a0and that Bolivia and Venezuela won&#8217;t change the standings even if they win. Therefore, in matchday 17 there are only 3 important games\u00a0and in matchday 18 only 4. We have,<\/p>\n<ul>\n<li>Possible combinations in matchday 17: 3 x 3 x 3 = 27<\/li>\n<li>Possible combinations in matchday 18: 3 x 3 x 3 x 3 = 81<\/li>\n<li>Total possible combinations: 27 x 81 = <strong>2187<\/strong><\/li>\n<\/ul>\n<p style=\"text-align: justify;\">Wow! Instead of 19683 cases we have 2187. Among the remaining games\u00a0there is one that marks a before and after in the outcome of the Qualifiers. It is the game of Colombia vs Paraguay. If Paraguay wins we would have to analyze 2187 cases because Colombia, being third, could be eliminated. For obvious reasons, this case will be excluded from the analysis. Later we will study the case in which they tie. For now we will consider that Colombia wins in Barranquilla, then Paraguay is eliminated and Colombia qualifies\u00a0(we will check this premise later). How many cases remain to be analyzed? With Colombia winning, Paraguay&#8217;s game against Venezuela becomes irrelevant, so we only have two crucial games in matchday 17\u00a0and three in matchday 18. This gives us,<\/p>\n<ul>\n<li>Possible combinations in matchday 17: 3 x 3 = 9<\/li>\n<li>Possible combinations in matchday 18: 3 x 3 x 3 = 27<\/li>\n<li>Total possible combinations: 9 x 27 = <strong>243<\/strong><\/li>\n<\/ul>\n<p style=\"text-align: justify;\">That&#8217;s right! If Colombia wins we have 243 combinations left. Using all of them we will determine the remaining two teams to qualify. Candidates are, Ecuador, Chile, Argentina, and Peru. The missing games are as follow,<\/p>\n<p style=\"text-align: center;\"><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>Chile\u00a0vs\u00a0Ecuador<img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>Argentina vs Peru<img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/><\/p>\n<p style=\"text-align: center;\"><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>Ecuador vs Argentina<img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>Peru vs &#8212;&#8212;&#8212;<br \/>\n&#8212;&#8212;&#8212; vs Chile<img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/><\/p>\n<p style=\"text-align: justify;\">You can see that it doesn&#8217;t matter against which teams play Peru and Chile in matchday 18\u00a0because their rivals won&#8217;t alter the standings. We will now use the theory of probability\u00a0to know which teams are favorites &#8220;mathematically.&#8221; Here we are not taking into account historic events, or the fact that one team is in a better position in the FIFA ranking, or the advantage of playing at home. No! Here the result is purely mathematical and the conclusions may go beyond what intuition or belief can dictaminate. Precisely, that&#8217;s how the theory of probability was born. Initially, it was believed that chance was determined by a superior being, that if you threw the dice and a six came out, it was meant to be. Over the years, mathematics overcame beliefs, men such as Cardano, Galileo, Pascal, and Fermat laid the first foundations of the theory of probability, which simply indicates that the chances of an event to happen out of a total of N possible probable cases are equal to the ratio between the number of occurrences n of this\u00a0event (favorable cases) and the total number of possible cases, that is, n \/ N. Let&#8217;s look at some simple examples with the Conmebol Qualifiers.<\/p>\n<p style=\"text-align: center;\">What is the probability that a team wins its match?<br \/>\n<strong>P = 1\/3 = 33.3%.<\/strong><\/p>\n<p style=\"text-align: center;\">What is the probability that Argentina wins against\u00a0Peru and Chile wins against\u00a0Ecuador in matchday 17?<br \/>\n<strong>P (<img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>) \u2229 P (<img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>) = 1\/3 x 1\/3 =<\/strong> <strong>1\/9 = 11.1%<\/strong>.<\/p>\n<p style=\"text-align: justify;\">Since each team\u00a0can only win (W), draw (D) or lose (L), then the probability of winning is 1 out of 3. And since Argentina and Chile have independent games in matchday 17, the total probability is given by the product, 1 out of 9. This number also indicates that there are nine ways in which Argentina vs Peru and Chile vs Ecuador can be grouped, which are,<\/p>\n<p style=\"text-align: center;\">A) Chile vs Ecuador (WL) &#8211; Argentina vs Peru (WL)<br \/>\nB) Chile vs Ecuador (DD) &#8211; Argentina vs Peru (WL)<br \/>\nC) Chile vs Ecuador (LW) &#8211; Argentina vs Peru (WL)<br \/>\nD) Chile vs Ecuador (WL) &#8211; Argentina vs Peru (DD)<br \/>\nE) Chile vs Ecuador (DD) &#8211; Argentina vs Peru (DD)<br \/>\nF) Chile vs Ecuador (LW) &#8211; Argentina vs Peru (DD)<br \/>\nG) Chile vs Ecuador (WL) &#8211; Argentina vs Peru (LW)<br \/>\nH) Chile vs Ecuador (DD) &#8211; Argentina vs Peru (LW)<br \/>\nI) Chile vs Ecuador (LW) &#8211; Argentina vs Peru (LW)<\/p>\n<p style=\"text-align: justify;\">Each sub-group is labeled with letters from A to I. WL\u00a0indicates that the local team wins, DD indicates a\u00a0tie, and LW\u00a0indicates that the visitor team wins.<\/p>\n<p style=\"text-align: center;\">What is the probability of obtaining H?<br \/>\n<strong>P (H) = 1\/9 = 11.1%<\/strong><\/p>\n<p style=\"text-align: justify;\">On matchday 18 what could happen? There are 27 possible consequences for each sub-group. The results are detailed in the supplementary file. <a href=\"http:\/\/www.cientificos.pe\/index.php\/2017\/10\/07\/qualifiers-to-the-world-cup-russia-2018-an-introduction-to-the-theory-of-probability\/4\/\">Click here<\/a> to see the 243 possible combinations.<\/p>\n<p style=\"text-align: center;\">What is the probability of obtaining A and then Peru beats Colombia?<\/p>\n<p style=\"text-align: center;\"><strong>P (A)\u00a0\u2229 P (<img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>)\u00a0= 1\/9 x 9\/27 = 9\/243 = 3.7%<\/strong><\/p>\n<p style=\"text-align: justify;\">Having studied the data shown in the supplementary file, the most interesting conclusions from the theory of probability are,<\/p>\n<p style=\"text-align: justify;\"><em>I.<\/em> <span style=\"text-decoration: underline;\"><em>Results strongly depend on goal difference<\/em><\/span><\/p>\n<p style=\"text-align: justify;\">We just need to look at Tables A.2, B.2, C.2, D.2, E.2, F.2, G.2, H.2, and I.2 in the <a href=\"http:\/\/www.cientificos.pe\/index.php\/2017\/10\/07\/qualifiers-to-the-world-cup-russia-2018-an-introduction-to-the-theory-of-probability\/4\/\">supplementary information<\/a>. One can appreciate that the qualifying probability increases considerably by having a better goal difference. This is expected since Argentina,\u00a0Chile, and Peru have almost the same amount of points, and what is worse, they have the same goal difference. Therefore, teams that manage to score\u00a0two goals or more in their matches may considerably increase\u00a0their options to reach the World Cup.<\/p>\n<p><em>II. <span style=\"text-decoration: underline;\">Peru is almost qualified if she wins her match\u00a0against Argentina<\/span><\/em><\/p>\n<p style=\"text-align: justify;\">Let&#8217;s see the results of sub-group G where Peru beats Argentina and Chile beats Ecuador,<\/p>\n<table>\n<caption>Table G.2<\/caption>\n<tbody>\n<tr>\n<td style=\"text-align: center;\">Qualifying probability<\/td>\n<td style=\"text-align: center;\">If Brazil beats Chile<\/td>\n<td style=\"text-align: center;\">If Brazil ties Chile<\/td>\n<td style=\"text-align: center;\">If Chile beats Brazil<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/><\/td>\n<td style=\"text-align: center;\">\u00a03\/9<\/td>\n<td style=\"text-align: center;\">\u00a00 (3\/9)<\/td>\n<td style=\"text-align: center;\">\u00a00 (1\/9)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/><\/td>\n<td style=\"text-align: center;\">\u00a09\/9<\/td>\n<td style=\"text-align: center;\">\u00a08\/9 (9\/9)<\/td>\n<td style=\"text-align: center;\">\u00a0\u00a08\/9 (9\/9)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/><\/td>\n<td style=\"text-align: center;\">\u00a00<\/td>\n<td style=\"text-align: center;\">\u00a00<\/td>\n<td style=\"text-align: center;\">0<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/><\/td>\n<td style=\"text-align: center;\">\u00a06\/9<\/td>\n<td style=\"text-align: center;\">\u00a06\/9 (9\/9)<\/td>\n<td style=\"text-align: center;\">\u00a09\/9<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">As shown in Table G.2, the qualifying probability of Peru ranges from 89% to 100%, and this is considering that she may lose\u00a0against Colombia.\u00a0The values in parentheses show the probability in case the team has the best goal difference. Therefore, Peru qualifies, even if Chile beats Brazil, as long as she\u00a0beats Argentina with a goal difference of 2 (assuming that the others win by 1).<\/p>\n<p style=\"text-align: justify;\">What happens if Peru ties Argentina? The results of sub-group D, where Peru ties Argentina and Chile beats Ecuador, show:<\/p>\n<table>\n<caption>Tabla D.2<\/caption>\n<tbody>\n<tr style=\"height: 26px;\">\n<td style=\"height: 26px; text-align: center;\">Qualifying probability<\/td>\n<td style=\"height: 26px; text-align: center;\">If Brazil beats Chile<\/td>\n<td style=\"height: 26px; text-align: center;\">If Brazil ties Chile<\/td>\n<td style=\"height: 26px; text-align: center;\">If\u00a0Chile beats Brazil<\/td>\n<\/tr>\n<tr style=\"height: 26px;\">\n<td style=\"height: 26px; text-align: center;\"><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/><\/td>\n<td style=\"height: 26px; text-align: center;\">4\/9 (7\/9)<\/td>\n<td style=\"height: 26px; text-align: center;\">4\/9 (6\/9)<\/td>\n<td style=\"height: 26px; text-align: center;\">3\/9 (6\/9)<\/td>\n<\/tr>\n<tr style=\"height: 26px;\">\n<td style=\"height: 26px; text-align: center;\"><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/><\/td>\n<td style=\"height: 26px; text-align: center;\">4\/9 (7\/9)<\/td>\n<td style=\"height: 26px; text-align: center;\">4\/9 (6\/9)<\/td>\n<td style=\"height: 26px; text-align: center;\">3\/9 (6\/9)<\/td>\n<\/tr>\n<tr style=\"height: 26px;\">\n<td style=\"height: 26px; text-align: center;\"><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/><\/td>\n<td style=\"height: 26px; text-align: center;\">0<\/td>\n<td style=\"height: 26px; text-align: center;\">0<\/td>\n<td style=\"height: 26px; text-align: center;\">0<\/td>\n<\/tr>\n<tr style=\"height: 26px;\">\n<td style=\"height: 26px; text-align: center;\"><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/><\/td>\n<td style=\"height: 26px; text-align: center;\">\u00a03\/9 (8\/9)<\/td>\n<td style=\"height: 26px; text-align: center;\">8\/9<\/td>\n<td style=\"height: 26px; text-align: center;\">\u00a09\/9<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">The qualifying probability ranges from 3\/9 to 4\/9. However, Peru&#8217;s chances increase up to 7\/9 if she has the\u00a0best goal difference, meaning, if she beats Colombia with a goal difference of 2 or more. Therefore, to avoid complex scenarios, Peru must beat Argentina and consequently\u00a0forget about Colombia.<\/p>\n<p><em>III. <span style=\"text-decoration: underline;\">Argentina needs to beat Peru to be (almost)\u00a0qualified<\/span><\/em><\/p>\n<p style=\"text-align: justify;\">Like Peru, Argentina&#8217;s odds range from 89% to 100%. Consider the results of sub-group A where Argentina beats\u00a0Peru and Chile beats\u00a0Ecuador,<\/p>\n<table>\n<caption>Tabla A.2<\/caption>\n<tbody>\n<tr style=\"height: 26px;\">\n<td style=\"height: 26px; text-align: center;\">Qualifying probability<\/td>\n<td style=\"height: 26px; text-align: center;\">If Brazil beats Chile<\/td>\n<td style=\"height: 26px; text-align: center;\">If Brazil ties Chile<\/td>\n<td style=\"height: 26px; text-align: center;\">If\u00a0Chile beats Brazil<\/td>\n<\/tr>\n<tr style=\"height: 26px;\">\n<td style=\"height: 26px; text-align: center;\"><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/><\/td>\n<td style=\"text-align: center; height: 26px;\">9\/9<\/td>\n<td style=\"text-align: center; height: 26px;\">8\/9 (9\/9)<\/td>\n<td style=\"text-align: center; height: 26px;\">8\/9 (9\/9)<\/td>\n<\/tr>\n<tr style=\"height: 26px;\">\n<td style=\"height: 26px; text-align: center;\"><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/><\/td>\n<td style=\"text-align: center; height: 26px;\">3\/9<\/td>\n<td style=\"text-align: center; height: 26px;\">3\/9 (6\/9)<\/td>\n<td style=\"text-align: center; height: 26px;\">0<\/td>\n<\/tr>\n<tr style=\"height: 26px;\">\n<td style=\"height: 26px; text-align: center;\"><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/><\/td>\n<td style=\"text-align: center; height: 26px;\">0<\/td>\n<td style=\"text-align: center; height: 26px;\">0<\/td>\n<td style=\"text-align: center; height: 26px;\">0<\/td>\n<\/tr>\n<tr style=\"height: 26px;\">\n<td style=\"height: 26px; text-align: center;\"><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/><\/td>\n<td style=\"height: 26px; text-align: center;\">6\/9<\/td>\n<td style=\"height: 26px; text-align: center;\">6\/9 (9\/9)<\/td>\n<td style=\"height: 26px; text-align: center;\">\u00a09\/9<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">As seen from the Table, even if\u00a0Chile beats Brazil, the qualifying probability of Argentina oscillates between 8\/9 and 9\/9. Therefore, we can conclude that the match Argentina vs Peru is an important game where the winner, no matter what happens in the other games, regardless that she loses her last game, is practically\u00a0qualified. And\u00a0the loser (as seen from Tables A.2 and G.2), reaching as much 3\/9,\u00a0is left with Chile for the last qualifying spot (in case Chile beats Ecuador).<\/p>\n<p style=\"text-align: justify;\"><em>IV.\u00a0<span style=\"text-decoration: underline;\">Chile depends\u00a0on her goals<\/span><\/em><\/p>\n<p style=\"text-align: justify;\">As seen from the Tables above (A.2, D.2, and G.2), if Chile\u00a0thrash Ecuador her qualifying probability increases considerably\u00a0and it doesn&#8217;t matter what happens with the match Argentina vs Peru, because regardless of this, her qualifying probability remains above of one or both teams.<\/p>\n<p><em>V. <span style=\"text-decoration: underline;\">Ecuador is on the edge of the abyss<\/span><\/em><\/p>\n<p style=\"text-align: justify;\">Ecuador can survive beating Chile. By doing so, her qualifying probability can reach values of 3\/9 = 33.3%. The curious thing is that if Ecuador ties, there is still a chance for her to qualify, but she must wait for Peru to beat\u00a0Argentina and on her last match\u00a0she must thrash her rival\u00a0(see Table H.1 in the <a href=\"http:\/\/www.cientificos.pe\/index.php\/2017\/10\/07\/qualifiers-to-the-world-cup-russia-2018-an-introduction-to-the-theory-of-probability\/4\/\">supplementary information<\/a>). If Ecuador\u00a0loses in Santiago, her options are\u00a0over.<\/p>\n<p>Let us now answer the following questions:<\/p>\n<ol>\n<li><span style=\"text-decoration: underline;\"><strong>What happens if Colombia ties Paraguay?<\/strong><\/span><\/li>\n<\/ol>\n<p style=\"text-align: justify;\">The points of the &#8220;last qualified team&#8221; ranges from\u00a024 to\u00a029 (in the following question we detail these numbers), which shows that Colombia qualifies beating Paraguay. In case of a tie, Colombia would make 27 points (losing against Peru) and Paraguay would reach 25 (beating Venezuela in her\u00a0last match). Within all the combinations shown in the supplementary file, the upper bound\u00a0of the &#8220;best eliminated team&#8221; is 28 points, but only occurs once among all the 243 possibilities. It happens when Argentina and Peru tie in matchday 17\u00a0and everybody wins (except Ecuador) on matchday 18. If this is not the case, Colombia would be almost qualified, and I say almost because there are 20 combinations out of 243 in which the &#8220;best eliminated team&#8221; gets 27 points, the same points as Colombia. Therefore, the qualification\u00a0will depend on the goal difference and, luckily for the <em>parceros, <\/em>they\u00a0arrive well in this aspect as they have a superior number compared to their rivals. Consequently, the chances of Colombia are very high even if she loses\u00a0against Peru and ties Paraguay.<\/p>\n<p style=\"text-align: justify;\">Paraguay, on the other hand, would reach 25 points as much (tying Colombia and winning against Venezuela), with this number Paraguay could qualify. However, remember that Paraguay has a goal difference of -6; therefore, to qualify she\u00a0requires to beat Venezuela \u00a07-0. The easiest option is to think about the probability of Paraguay to qualify without thinking of goal differences, this means, we need to check in how many cases the &#8220;last qualified team&#8221; has 24 points, in order for Paraguay to surpass this team with her points. This leads us to answer the following question first.<\/p>\n<p>2.<em><span style=\"text-decoration: underline;\"><strong>\u00a0How many points is likely to have the last qualified team?<\/strong><\/span><\/em><\/p>\n<p style=\"text-align: justify;\">For this we will use the tree diagram. There are 9 sub-groups (labeled from A to I). In each sub-group we calculate the probability, P(X), of\u00a0reaching the last qualifying\u00a0position with\u00a0X\u00a0points (see Tables A.3, B.3, C.3, D.3, E.3, F .3, G.3, H.3, I.3 in the <a href=\"http:\/\/www.cientificos.pe\/index.php\/2017\/10\/07\/qualifiers-to-the-world-cup-russia-2018-an-introduction-to-the-theory-of-probability\/4\/\">supplementary information<\/a>). We have:<\/p>\n<p><img loading=\"lazy\" class=\"wp-image-2068 aligncenter\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/tree1-194x300.png\" alt=\"\" width=\"340\" height=\"525\" srcset=\"https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/tree1-194x300.png 194w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/tree1-768x1187.png 768w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/tree1-663x1024.png 663w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/tree1-696x1075.png 696w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/tree1-1068x1650.png 1068w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/tree1-272x420.png 272w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/tree1.png 1559w\" sizes=\"(max-width: 340px) 100vw, 340px\" \/><\/p>\n<p>For example, P(29) indicates the probability of obtaining 29 points in the\u00a0last qualifying spot (fifth position).<\/p>\n<p style=\"text-align: center;\">What is the probability of obtaining 29 points through A in the last qualifying position?<br \/>\n<strong>P (A \u2229 29) = P (A) x P (29 \/ A) = 1\/9 x 3\/27 = 3\/243 = 1.2%.<\/strong><\/p>\n<p style=\"text-align: justify;\">This is known as a conditional probability because we want to find a value by conditioning it to appear from one of the branches of the tree. Its result is given by the probability of obtaining A multiplied by the probability of obtaining 29 points in A. It is usually denoted P (A \u2229 29). Then, the total probability of obtaining 29 across all branches would be the sum of each of them, i.e., P (29) = P (A \u2229 29) + P (B \u2229 29) + P (C \u2229 29) + P (D \u2229 29) + P (E \u2229 29) + P (F \u2229 29) + P (G \u2229 29) + P (H \u2229 29) + P (I \u2229 29). Doing this for all values \u200b\u200bwe get:<\/p>\n<p style=\"text-align: center;\">P (29) = 6\/243<br \/>\nP (28) = 19\/243<br \/>\nP (27) = 85\/243<br \/>\nP (26) = 75\/243<br \/>\nP (25) = 48\/243<br \/>\nP (24) = 10\/243<\/p>\n<p style=\"text-align: justify;\">Therefore, it is likely that the 5<sup>th<\/sup> place in the Conmebol Qualifiers will have\u00a027 points, P (27) = 85\/243 = 35%. From here we can culminate the previous analysis. We said that for Paraguay to qualify she needs to reach the qualifying position without paying attention to her goal difference. That is, the chances of Paraguay are reduced to P (24) = 10\/243 = 4%. A probability so low that it is better to accept the reality of saying goodbye to the World Cup. Therefore, <strong>a tie between Colombia and Paraguay does not greatly affect the results shown in this article<\/strong>. We initially\u00a0said that Uruguay would be qualified by making just one point in her last two matches. If this happens Uruguay would reach 28 points with a goal difference that is far superior than the others. Consequently, the probability of being eliminated\u00a0is P (29) = 6\/243 = 2.5%. The funny thing is that for this to happen Chile must beat Brazil. Therefore, getting\u00a0one point in two games should not cause any concern\u00a0to Uruguay.<\/p>\n<p><em><span style=\"text-decoration: underline;\"><strong>3. Which teams will qualify?<\/strong><\/span><\/em><\/p>\n<p style=\"text-align: justify;\">Mathematics indicates that Argentina, Chile and Peru are the ones fighting for the last qualifying spots (Ecuador is left behind for having a very low\u00a0probability). Two out of three wil take their songs to the World Cup. Will Chile sing, &#8220;<em>prep\u00e1rate Rusia que aqu\u00ed vamos por m\u00e1s<\/em>&#8220;? Or Peru will shout, &#8220;<em>porque yo creo en ti, \u00a1vamos vamos Per\u00fa!<\/em>&#8221; Or it will be Argentina who will say, &#8220;<em>esta barra quilombera no te deja de alentar.<\/em>&#8221; The total qualifying probability of each team is,<\/p>\n<table>\n<caption>Total qualifying probability\u00a0<\/caption>\n<tbody>\n<tr>\n<td style=\"text-align: center;\">with the best goal difference<\/td>\n<td style=\"text-align: center;\">with the worst goal difference<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">\n<h4>P(<img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>) =\u00a0190\/243 = \u00a078.2%<\/h4>\n<h4>P(<img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>) =\u00a0184\/243 = \u00a075.7%<\/h4>\n<h5>P(<img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>) =\u00a0144\/243 = 59.3%<\/h5>\n<h6>P(<img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>) = 29\/243 = 11.9%<\/h6>\n<\/td>\n<td style=\"text-align: center;\">\n<h4>P(<img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>) =\u00a0153\/243 = 62.9%<\/h4>\n<h4>P(<img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>) =\u00a0151\/243 = 62.1%<\/h4>\n<h5>P(<img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>) =\u00a0100\/243 = 41.2%<\/h5>\n<h6>P(<img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>) = 17\/243 = 6.9%<\/h6>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">The analysis is similar to the tree diagram developed previously, here we only show the results for simplicity (based on the data in Tables A.2, B.2, C.2, D.2, E.2, F.2, G.2, H.2, and I.2 in the <a href=\"http:\/\/www.cientificos.pe\/index.php\/2017\/10\/07\/qualifiers-to-the-world-cup-russia-2018-an-introduction-to-the-theory-of-probability\/4\/\">supplementary information<\/a>). The interesting thing is that although Argentina and Peru have the same amount of points\u00a0before playing their matches, once\u00a0they finish them, the qualifying probability of Peru is higher. The reason is because Argentina plays against direct rivals whereas Peru, in the last match, does it with a &#8220;qualified team.&#8221; Another interesting detail is to see how it affects to have the best goal difference. Chile proves to be the most benefited with this, increasing 18.1% its qualifying probability just by scoring more goals, in contrast, Peru and Argentina increase their qualifying probability by 15.3% and 13.6%, respectively; therefore, to use this advantage, the Chileans should focus on thrashing Ecuador at home. By doing so, they will have the best goal difference and therefore they will be 2.8% below Argentina or 3.6% below Peru (since one of them shall have the worst goal difference). Nonetheless, Chile still has the lowest qualifying probability (excluding Ecuador), although we have included the possibility of them beating Brazil in Sao Paulo. <em>If we assume\u00a0that these results are decisive, we can conclude that the 5 qualified teams will be: Brazil, Uruguay, Colombia, Peru and Argentina.<\/em> The pending question would be, which team qualifies directly? Peru or Argentina? Carrying out a similar analysis to the previous one we have:<\/p>\n<table>\n<caption>Total probability of qualifying directly to the World Cup<\/caption>\n<tbody>\n<tr>\n<td style=\"text-align: center;\">with the best goal difference<\/td>\n<td style=\"text-align: center;\">with the worst goal difference<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">P(<img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>) =\u00a0121\/243 = \u00a049.8%<br \/>\nP(<img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>) =\u00a0121\/243 = \u00a049.8%<\/td>\n<td style=\"text-align: center;\">P(<img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>) = 83\/243 = 34.2%<br \/>\nP(<img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>) = 81\/243 = 33.3%<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">Argentina gets a slightly higher probability of occupying the 4<sup>th<\/sup> place in the Qualifiers. The reason is the same as the previous case and takes relevance in\u00a0sub-group F (see <a href=\"http:\/\/www.cientificos.pe\/index.php\/2017\/10\/07\/qualifiers-to-the-world-cup-russia-2018-an-introduction-to-the-theory-of-probability\/4\/\">supplementary information<\/a>). If this slight advantage is meant to be a determining factor, Peru would end up facing New Zealand on November 11<sup>th<\/sup>. The<em>\u00a0<\/em>Inca team led by Gareca<em>\u00a0<\/em>would get in the plane and make the most bizarre trip of their lives. They would cross the Pacific with the\u00a0clock from Santiago telling them that it takes 12 but instead it will last more than one day, and their way back will happen with their watches moving counterclockwise, but that would not matter&#8230; because Spain 82&#8242; could finally be left behind.<\/p>\n<p style=\"text-align: justify;\">Christian Ortiz, PhD.<\/p>\n<p style=\"text-align: justify;\"><!--nextpage--><\/p>\n<h3><span style=\"font-family: verdana, geneva, sans-serif; font-size: 12pt;\"><strong>September\u00a011<sup>th<\/sup>,\u00a02017<\/strong><\/span><\/h3>\n<h3><span style=\"text-decoration: underline;\"><strong>Supplementary Information\u00a0<\/strong><\/span>(1<span style=\"font-size: 18.3333px;\"><sup>st<\/sup><\/span>\u00a0part of the article)<\/h3>\n<p style=\"text-align: justify;\">There are 243 configurations in which the standings can be arranged at the end of the competition. In matchday 17 there are 9 possible configurations:<\/p>\n<p style=\"text-align: center;\">A) Chile vs Ecuador (WL) &#8211; Argentina vs Peru (WL)<br \/>\nB) Chile vs Ecuador (DD) &#8211; Argentina vs Peru (WL)<br \/>\nC) Chile vs Ecuador (LW) &#8211; Argentina vs Peru (WL)<br \/>\nD) Chile vs Ecuador (WL) &#8211; Argentina vs Peru (DD)<br \/>\nE) Chile vs Ecuador (DD) &#8211; Argentina vs Peru (DD)<br \/>\nF) Chile vs Ecuador (LW) &#8211; Argentina vs Peru (DD)<br \/>\nG) Chile vs Ecuador (WL) &#8211; Argentina vs Peru (LW)<br \/>\nH) Chile vs Ecuador (DD) &#8211; Argentina vs Peru (LW)<br \/>\nI) Chile vs Ecuador (LW) &#8211; Argentina vs Peru (LW)<\/p>\n<p style=\"text-align: justify;\"><strong>(DD)<\/strong> means a draw. <strong>(WL)<\/strong> means that the home team wins and the visitor loses. <strong>(LW)<\/strong> means that the home team loses and the visitor wins. Each of these 9 sub-groups is labeled with letters from A to I. In each sub-group matchday 18 provides 27 possible configurations. Below we show all of them.<\/p>\n<ul>\n<li style=\"text-align: justify;\">In Tables A.1, B.1, C.1, D.1, E.1, F.1, G.1, H.1, and I.1, we show the standings. We have grouped 9 standing tables for each sub-group. For each one, Chile has 3 values depending on the match against Brazil (giving a total of 27 possible configurations for each sub-group). The first place qualifies directly to the World Cup, the second place advances to the inter-confederation play-offs.<\/li>\n<li style=\"text-align: justify;\">In Tables A.2, B.2, C.2, D.2, E.2, F.2, G.2, H.2, and I.2, we show the qualifying probability of each team\u00a0after knowing the result of the match Brazil vs Chile. Note that by &#8220;qualifying team&#8221; we also imply the team who advances to the inter-confederation play-offs. In parentheses we show the qualifying probability when the team has the best goal difference.<\/li>\n<li style=\"text-align: justify;\">In Tables A.3, B.3, C.3, D.3, E.3, F.3, G.3, H.3, and I.3, we show the probability, P(X), of\u00a0reaching the last qualifying\u00a0position with\u00a0X\u00a0points. e.g., P (27) indicates the probability of reaching the \u00a0inter-confederations play-offs (2nd place here) with 27 points.<\/li>\n<\/ul>\n<p style=\"text-align: center;\"><strong><span style=\"text-decoration: underline;\">A) Chile vs Ecuador (WL) &#8211; Argentina vs Peru (WL)<\/span><\/strong><\/p>\n<table>\n<caption>Table A.1<\/caption>\n<tbody>\n<tr>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 30<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 29 (27) (26)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 24<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 20<\/li>\n<\/ol>\n<\/td>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 29 (27) (26)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 28<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 24<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 21<\/li>\n<\/ol>\n<\/td>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 29 (27) (26)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 27<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 24<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 24<\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 30<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 27 (26) (29)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 25<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 20<\/li>\n<\/ol>\n<\/td>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 28<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 27 (26) (29)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 25<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 21<\/li>\n<\/ol>\n<\/td>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 27 (26) (29)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 27<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 25<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 24<\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0=30<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 27<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 26 (27) (29)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 20<\/li>\n<\/ol>\n<\/td>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 28<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 27<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 26 (27) (29)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 21<\/li>\n<\/ol>\n<\/td>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 27<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 27<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 26 (27) (29)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 24<\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table>\n<caption>Table A.2<\/caption>\n<tbody>\n<tr style=\"height: 26px;\">\n<td style=\"height: 26px; text-align: center;\">Qualifying probability<\/td>\n<td style=\"height: 26px; text-align: center;\">If Brazil beats Chile<\/td>\n<td style=\"height: 26px; text-align: center;\">If Brazil ties Chile<\/td>\n<td style=\"height: 26px; text-align: center;\">If Chile beats Brazil<\/td>\n<\/tr>\n<tr style=\"height: 26px;\">\n<td style=\"height: 26px; text-align: center;\"><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/><\/td>\n<td style=\"text-align: center; height: 26px;\">9\/9<\/td>\n<td style=\"text-align: center; height: 26px;\">8\/9 (9\/9)<\/td>\n<td style=\"text-align: center; height: 26px;\">8\/9 (9\/9)<\/td>\n<\/tr>\n<tr style=\"height: 26px;\">\n<td style=\"height: 26px; text-align: center;\"><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/><\/td>\n<td style=\"text-align: center; height: 26px;\">3\/9<\/td>\n<td style=\"text-align: center; height: 26px;\">3\/9 (6\/9)<\/td>\n<td style=\"text-align: center; height: 26px;\">0<\/td>\n<\/tr>\n<tr style=\"height: 26px;\">\n<td style=\"height: 26px; text-align: center;\"><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/><\/td>\n<td style=\"text-align: center; height: 26px;\">0<\/td>\n<td style=\"text-align: center; height: 26px;\">0<\/td>\n<td style=\"text-align: center; height: 26px;\">0<\/td>\n<\/tr>\n<tr style=\"height: 26px;\">\n<td style=\"height: 26px; text-align: center;\"><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/><\/td>\n<td style=\"height: 26px; text-align: center;\">6\/9<\/td>\n<td style=\"height: 26px; text-align: center;\">6\/9 (9\/9)<\/td>\n<td style=\"height: 26px; text-align: center;\">\u00a09\/9<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table>\n<caption>Table A.3<\/caption>\n<tbody>\n<tr style=\"height: 26px;\">\n<td style=\"text-align: center; height: 26px;\">Probability, P(X), of\u00a0reaching the last qualifying\u00a0position with\u00a0X\u00a0points<\/td>\n<\/tr>\n<tr style=\"height: 26px;\">\n<td style=\"text-align: center; height: 26px;\">P(29) = 3\/27<\/td>\n<\/tr>\n<tr style=\"height: 26px;\">\n<td style=\"text-align: center; height: 26px;\">P(28) = 3\/27<\/td>\n<\/tr>\n<tr style=\"height: 26px;\">\n<td style=\"text-align: center; height: 26px;\">P(27) = 15\/27<\/td>\n<\/tr>\n<tr style=\"height: 26px;\">\n<td style=\"text-align: center; height: 26px;\">P(26) = 6\/27<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<hr \/>\n<p style=\"text-align: center;\"><strong><span style=\"text-decoration: underline;\">B) Chile vs Ecuador (DD) &#8211; Argentina vs Peru (WL)<\/span><\/strong><\/p>\n<table>\n<caption>Table B.1<\/caption>\n<tbody>\n<tr>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 30<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 27 (25) (24)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 24<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 21<\/li>\n<\/ol>\n<\/td>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 28<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 27 (25) (24)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 24<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 22<\/li>\n<\/ol>\n<\/td>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 27 (25) (24)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 27<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 24<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 24<\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 30<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 25 (27) (24)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 25<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 21<\/li>\n<\/ol>\n<\/td>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 28<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 25 (27) (24)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 25<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 22<\/li>\n<\/ol>\n<\/td>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 27<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 25 (27) (24)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 25<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 24<\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 30<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 27<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 24 (25) (27)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 21<\/li>\n<\/ol>\n<\/td>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 28<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 27<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 24 (25) (27)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 22<\/li>\n<\/ol>\n<\/td>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 27<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 27<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 24 (25) (27)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 24<\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table>\n<caption>Table B.2<\/caption>\n<tbody>\n<tr>\n<td style=\"text-align: center;\">Qualifying probability<\/td>\n<td style=\"text-align: center;\">If Brazil beats Chile<\/td>\n<td style=\"text-align: center;\">If Brazil ties Chile<\/td>\n<td style=\"text-align: center;\">If Chile beats Brazil<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/><\/td>\n<td style=\"text-align: center;\">9\/9<\/td>\n<td style=\"text-align: center;\">9\/9<\/td>\n<td style=\"text-align: center;\">8\/9 (9\/9)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/><\/td>\n<td style=\"text-align: center;\">6\/9 (9\/9)<\/td>\n<td style=\"text-align: center;\">3\/9 (6\/9)<\/td>\n<td style=\"text-align: center;\">0 (3\/9)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/><\/td>\n<td style=\"text-align: center;\">0<\/td>\n<td style=\"text-align: center;\">0<\/td>\n<td style=\"text-align: center;\">0<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/><\/td>\n<td style=\"text-align: center;\">0 (3\/9)<\/td>\n<td style=\"text-align: center;\">3\/9 (6\/9)<\/td>\n<td style=\"text-align: center;\">\u00a06\/9 (9\/9)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table>\n<caption>Table B.3<\/caption>\n<tbody>\n<tr>\n<td style=\"text-align: center;\">Probability, P(X), of\u00a0reaching the last qualifying\u00a0position with\u00a0X\u00a0points<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">P(27) = 15\/27<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">P(25) = 9\/27<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">P(24) = 3\/27<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<hr \/>\n<p style=\"text-align: center;\"><strong><span style=\"text-decoration: underline;\">C) Chile vs Ecuador (LW) &#8211; Argentina vs Peru (WL)<\/span><\/strong><\/p>\n<table>\n<caption>Table C.1<\/caption>\n<tbody>\n<tr>\n<td>\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052 aligncenter\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 30<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 26 (23)(24)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 24<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 23<\/li>\n<\/ol>\n<\/td>\n<td>\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 28<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 26(23)(24)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 24<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 24<\/li>\n<\/ol>\n<\/td>\n<td>\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 27<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 26<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 26(23)(24)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 24<\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<tr>\n<td>\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 30<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 25<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 24 (23)(26)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 23<\/li>\n<\/ol>\n<\/td>\n<td>\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 28<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 25<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 24(23)(26)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 24<\/li>\n<\/ol>\n<\/td>\n<td>\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 27<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 26<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 25<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 24(23)(26)<\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<tr>\n<td>\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 30<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 27<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 23<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 23 (24)(26)<\/li>\n<\/ol>\n<\/td>\n<td>\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 28<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 27<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 24<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 23(24)(26)<\/li>\n<\/ol>\n<\/td>\n<td>\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 27<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 27<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 26<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 23(24)(26)<\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table>\n<caption>Table C.2<\/caption>\n<tbody>\n<tr style=\"height: 52px;\">\n<td style=\"text-align: center; height: 52px;\">Qualifying probability<\/td>\n<td style=\"text-align: center; height: 52px;\">If Brazil beats Chile<\/td>\n<td style=\"text-align: center; height: 52px;\">If Brazil ties Chile<\/td>\n<td style=\"text-align: center; height: 52px;\">If Chile beats Brazil<\/td>\n<\/tr>\n<tr style=\"height: 26px;\">\n<td style=\"text-align: center; height: 26px;\"><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/><\/td>\n<td style=\"text-align: center; height: 26px;\">9\/9<\/td>\n<td style=\"text-align: center; height: 26px;\">9\/9<\/td>\n<td style=\"text-align: center; height: 26px;\">9\/9<\/td>\n<\/tr>\n<tr style=\"height: 26px;\">\n<td style=\"text-align: center; height: 26px;\"><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/><\/td>\n<td style=\"text-align: center; height: 26px;\">6\/9 (7\/9)<\/td>\n<td style=\"text-align: center; height: 26px;\">5\/9 (7\/9)<\/td>\n<td style=\"text-align: center; height: 26px;\">3\/9<\/td>\n<\/tr>\n<tr style=\"height: 26px;\">\n<td style=\"text-align: center; height: 26px;\"><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/><\/td>\n<td style=\"text-align: center; height: 26px;\">2\/9 (3\/9)<\/td>\n<td style=\"text-align: center; height: 26px;\">2\/9 (3\/9)<\/td>\n<td style=\"text-align: center; height: 26px;\">0 (2\/9)<\/td>\n<\/tr>\n<tr style=\"height: 26px;\">\n<td style=\"text-align: center; height: 26px;\"><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/><\/td>\n<td style=\"text-align: center; height: 26px;\">0<\/td>\n<td style=\"text-align: center; height: 26px;\">0 (2\/9)<\/td>\n<td style=\"text-align: center; height: 26px;\">\u00a04\/9 (6\/9)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table>\n<caption>Table C.3<\/caption>\n<tbody>\n<tr>\n<td style=\"text-align: center;\">Probability, P(X), of\u00a0reaching the last qualifying\u00a0position with\u00a0X\u00a0points<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">P(27) = 9\/27<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">P(26) = 10\/27<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">P(25) = 4\/27<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">P(24) = 4\/27<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<hr \/>\n<p style=\"text-align: center;\"><strong><span style=\"text-decoration: underline;\">D) Chile vs Ecuador (WL) &#8211; Argentina vs Peru (DD)<\/span><\/strong><\/p>\n<table>\n<caption>Table D.1<\/caption>\n<tbody>\n<tr>\n<td>\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>=29 (27)(26)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 28<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 25<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 20<\/li>\n<\/ol>\n<\/td>\n<td>\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>=29 (27)(26)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 26<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 25<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 21<\/li>\n<\/ol>\n<\/td>\n<td>\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 29 (27)(26)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>=25<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>=25<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 23<\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<tr>\n<td>\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>=28<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 27 (29)(26)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 26<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>= 20<\/li>\n<\/ol>\n<\/td>\n<td>\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>=27(29)(26)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>=26<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>=26<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>=21<\/li>\n<\/ol>\n<\/td>\n<td>\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>=27(29)(26)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>=26<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>=25<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>=23<\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<tr>\n<td>\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>=28<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>=28<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>=26 (27)(29)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>=20<\/li>\n<\/ol>\n<\/td>\n<td>\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>=28<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>=26(27)(29)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>=26<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>=21<\/li>\n<\/ol>\n<\/td>\n<td>\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>=28<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>=26(27)(29)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>=25<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>=23<\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table>\n<caption>Table D.2<\/caption>\n<tbody>\n<tr style=\"height: 26px;\">\n<td style=\"height: 26px; text-align: center;\">Qualifying probability<\/td>\n<td style=\"height: 26px; text-align: center;\">If Brazil beats Chile<\/td>\n<td style=\"height: 26px; text-align: center;\">If Brazil ties Chile<\/td>\n<td style=\"height: 26px; text-align: center;\">If Chile beats Brazil<\/td>\n<\/tr>\n<tr style=\"height: 26px;\">\n<td style=\"height: 26px; text-align: center;\"><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/><\/td>\n<td style=\"height: 26px; text-align: center;\">4\/9 (7\/9)<\/td>\n<td style=\"height: 26px; text-align: center;\">4\/9 (6\/9)<\/td>\n<td style=\"height: 26px; text-align: center;\">3\/9 (6\/9)<\/td>\n<\/tr>\n<tr style=\"height: 26px;\">\n<td style=\"height: 26px; text-align: center;\"><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/><\/td>\n<td style=\"height: 26px; text-align: center;\">4\/9 (7\/9)<\/td>\n<td style=\"height: 26px; text-align: center;\">4\/9 (6\/9)<\/td>\n<td style=\"height: 26px; text-align: center;\">3\/9 (6\/9)<\/td>\n<\/tr>\n<tr style=\"height: 26px;\">\n<td style=\"height: 26px; text-align: center;\"><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/><\/td>\n<td style=\"height: 26px; text-align: center;\">0<\/td>\n<td style=\"height: 26px; text-align: center;\">0<\/td>\n<td style=\"height: 26px; text-align: center;\">0<\/td>\n<\/tr>\n<tr style=\"height: 26px;\">\n<td style=\"height: 26px; text-align: center;\"><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/><\/td>\n<td style=\"height: 26px; text-align: center;\">\u00a05\/9 (8\/9)<\/td>\n<td style=\"height: 26px; text-align: center;\">8\/9<\/td>\n<td style=\"height: 26px; text-align: center;\">\u00a09\/9<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table>\n<caption>Table D.3<\/caption>\n<tbody>\n<tr style=\"height: 26px;\">\n<td style=\"text-align: center; height: 26px;\">Probability, P(X), of\u00a0reaching the last qualifying\u00a0position with\u00a0X\u00a0points<\/td>\n<\/tr>\n<tr style=\"height: 26px;\">\n<td style=\"text-align: center; height: 26px;\">P(28) = 7\/27<\/td>\n<\/tr>\n<tr style=\"height: 26px;\">\n<td style=\"text-align: center; height: 26px;\">P(27) = 4\/27<\/td>\n<\/tr>\n<tr style=\"height: 26px;\">\n<td style=\"text-align: center; height: 26px;\">P(26) = 13\/27<\/td>\n<\/tr>\n<tr style=\"height: 26px;\">\n<td style=\"text-align: center; height: 26px;\">P(25) = 3\/27<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<hr \/>\n<p style=\"text-align: center;\"><strong><span style=\"text-decoration: underline;\">E<\/span><\/strong><strong><span style=\"text-decoration: underline;\">) Chile vs Ecuador (DD) &#8211; Argentina vs Peru (DD)<\/span><\/strong><\/p>\n<table>\n<caption>Table E.1<\/caption>\n<tbody>\n<tr>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>=28<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>=27 (25)(24)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>=25<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>=21<\/li>\n<\/ol>\n<\/td>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>=27(25)(24)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>=26<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>=25<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>=22<\/li>\n<\/ol>\n<\/td>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>=27(25)(24)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>=25<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>=25<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>=24<\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>=28<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>=26<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>=25 (24)(27)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>=21<\/li>\n<\/ol>\n<\/td>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>=26<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>=26<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>=25(24)(27)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>=22<\/li>\n<\/ol>\n<\/td>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>=26<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>=25(24)(27)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>=25<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>=24<\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>=28<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>=28<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>=24(25)(27)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>=21<\/li>\n<\/ol>\n<\/td>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>=28<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>=26<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>=24(25)(27)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>=22<\/li>\n<\/ol>\n<\/td>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>=28<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>=25<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>=24<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>=24(25)(27)<\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table>\n<caption>Table E.2<\/caption>\n<tbody>\n<tr>\n<td style=\"text-align: center;\">Qualifying probability<\/td>\n<td style=\"text-align: center;\">If Brazil beats Chile<\/td>\n<td style=\"text-align: center;\">If Brazil ties Chile<\/td>\n<td style=\"text-align: center;\">If Chile beats Brazil<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/><\/td>\n<td style=\"text-align: center;\">9\/9<\/td>\n<td style=\"text-align: center;\">6\/9 (9\/9)<\/td>\n<td style=\"text-align: center;\">4\/9 (6\/9)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/><\/td>\n<td style=\"text-align: center;\">9\/9<\/td>\n<td style=\"text-align: center;\">6\/9 (9\/9)<\/td>\n<td style=\"text-align: center;\">4\/9 (6\/9)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/><\/td>\n<td style=\"text-align: center;\">0<\/td>\n<td style=\"text-align: center;\">0<\/td>\n<td style=\"text-align: center;\">0<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/><\/td>\n<td style=\"text-align: center;\">0<\/td>\n<td style=\"text-align: center;\">0 (5\/9)<\/td>\n<td style=\"text-align: center;\">\u00a08\/9<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table>\n<caption>Table E.3<\/caption>\n<tbody>\n<tr style=\"height: 26px;\">\n<td style=\"text-align: center; height: 26px;\">Probability, P(X), of\u00a0reaching the last qualifying\u00a0position with\u00a0X\u00a0points<\/td>\n<\/tr>\n<tr style=\"height: 26px;\">\n<td style=\"text-align: center; height: 26px;\">P(28) = 3\/27<\/td>\n<\/tr>\n<tr style=\"height: 26px;\">\n<td style=\"text-align: center; height: 26px;\">P(27) = 4\/27<\/td>\n<\/tr>\n<tr style=\"height: 26px;\">\n<td style=\"text-align: center; height: 26px;\">P(26) = 9\/27<\/td>\n<\/tr>\n<tr style=\"height: 26px;\">\n<td style=\"text-align: center; height: 26px;\">P(25) = 11\/27<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<hr \/>\n<p style=\"text-align: center;\"><strong><span style=\"text-decoration: underline;\">F) Chile vs Ecuador (LW) &#8211; Argentina vs Peru (DD)<\/span><\/strong><\/p>\n<table>\n<caption>Table F.1<\/caption>\n<tbody>\n<tr>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>=28<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>=26(24)(23)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>=25<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>=23<\/li>\n<\/ol>\n<\/td>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>=26(24)(23)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>=26<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>=25<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>=24<\/li>\n<\/ol>\n<\/td>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>=26<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>=26(24)(23)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>=25<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>=25<\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>=28<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>=26<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>=24 (23)(26)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>=23<\/li>\n<\/ol>\n<\/td>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>=26<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>=26<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>=24<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>=24(23)(26)<\/li>\n<\/ol>\n<\/td>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>=26<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>=26<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>=25<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>=24(23)(26)<\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>=28<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>=28<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>=23<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>=23(24)(26)<\/li>\n<\/ol>\n<\/td>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>=28<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>=26<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>=24<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>=23(24)(26)<\/li>\n<\/ol>\n<\/td>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>=28<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>=26<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>=25<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>=23(24)(26)<\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table>\n<caption>Table F.2<\/caption>\n<tbody>\n<tr>\n<td style=\"text-align: center;\">Qualifying probability<\/td>\n<td style=\"text-align: center;\">If Brazil beats Chile<\/td>\n<td style=\"text-align: center;\">If Brazil ties Chile<\/td>\n<td style=\"text-align: center;\">If Chile beats Brazil<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/><\/td>\n<td style=\"text-align: center;\">\u00a06\/9 (7\/9)<\/td>\n<td style=\"text-align: center;\">\u00a06\/9 (7\/9)<\/td>\n<td style=\"text-align: center;\">\u00a04\/9 (6\/9)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/><\/td>\n<td style=\"text-align: center;\">\u00a08\/9 (9\/9)<\/td>\n<td style=\"text-align: center;\">\u00a08\/9 (9\/9)<\/td>\n<td style=\"text-align: center;\">\u00a03\/9 (6\/9)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/><\/td>\n<td style=\"text-align: center;\">\u00a03\/9<\/td>\n<td style=\"text-align: center;\">\u00a03\/9<\/td>\n<td style=\"text-align: center;\">\u00a01\/9 (3\/9)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/><\/td>\n<td style=\"text-align: center;\">\u00a00<\/td>\n<td style=\"text-align: center;\">\u00a00<\/td>\n<td style=\"text-align: center;\">\u00a03\/9 (8\/9)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table>\n<caption>Table F.3<\/caption>\n<tbody>\n<tr style=\"height: 26px;\">\n<td style=\"text-align: center; height: 26px;\">Probability, P(X), of\u00a0reaching the last qualifying\u00a0position with\u00a0X\u00a0points<\/td>\n<\/tr>\n<tr style=\"height: 26px;\">\n<td style=\"text-align: center; height: 26px;\">P(28) = 3\/27<\/td>\n<\/tr>\n<tr style=\"height: 26px;\">\n<td style=\"text-align: center; height: 26px;\">P(26) = 18\/27<\/td>\n<\/tr>\n<tr style=\"height: 26px;\">\n<td style=\"text-align: center; height: 26px;\">P(25) = 6\/27<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<hr \/>\n<p style=\"text-align: center;\"><strong><span style=\"text-decoration: underline;\">G) Chile vs Ecuador (WL) &#8211; Argentina vs Peru (LW)<\/span><\/strong><\/p>\n<table>\n<caption>Table G.1<\/caption>\n<tbody>\n<tr>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 29 (26)(27)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>=27<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>=27<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>=20<\/li>\n<\/ol>\n<\/td>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>\u00a0= 29(26)(27)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>=27<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>=25<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>=21<\/li>\n<\/ol>\n<\/td>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>=29(26)(27)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>=27<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>=24<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>=23<\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>=28<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>=27(26)(29)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>=27<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>=20<\/li>\n<\/ol>\n<\/td>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>=28<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>=27(26)(29)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>=25<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>=21<\/li>\n<\/ol>\n<\/td>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>=28<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>=27(26)(29)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>=24<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>=23<\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>=30<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>=27<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>=26(27)(29)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>=20<\/li>\n<\/ol>\n<\/td>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>=30<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>=26(27)(29)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>=25<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>=21<\/li>\n<\/ol>\n<\/td>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>=30<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>=26(27)(29)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>=23<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>=24<\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table>\n<caption>Table G.2<\/caption>\n<tbody>\n<tr>\n<td style=\"text-align: center;\">Qualifying probability<\/td>\n<td style=\"text-align: center;\">If Brazil beats Chile<\/td>\n<td style=\"text-align: center;\">If Brazil ties Chile<\/td>\n<td style=\"text-align: center;\">If Chile beats Brazil<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/><\/td>\n<td style=\"text-align: center;\">\u00a03\/9<\/td>\n<td style=\"text-align: center;\">\u00a00 (3\/9)<\/td>\n<td style=\"text-align: center;\">\u00a00 (1\/9)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/><\/td>\n<td style=\"text-align: center;\">\u00a09\/9<\/td>\n<td style=\"text-align: center;\">\u00a08\/9 (9\/9)<\/td>\n<td style=\"text-align: center;\">\u00a0\u00a08\/9 (9\/9)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/><\/td>\n<td style=\"text-align: center;\">\u00a00<\/td>\n<td style=\"text-align: center;\">\u00a00<\/td>\n<td style=\"text-align: center;\">0<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/><\/td>\n<td style=\"text-align: center;\">\u00a06\/9<\/td>\n<td style=\"text-align: center;\">\u00a06\/9 (9\/9)<\/td>\n<td style=\"text-align: center;\">\u00a09\/9<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table>\n<caption>Table G.3<\/caption>\n<tbody>\n<tr style=\"height: 26px;\">\n<td style=\"text-align: center; height: 26px;\">Probability, P(X), of\u00a0reaching the last qualifying\u00a0position with\u00a0X\u00a0points<\/td>\n<\/tr>\n<tr style=\"height: 26px;\">\n<td style=\"text-align: center; height: 26px;\">P(29) = 3\/27<\/td>\n<\/tr>\n<tr style=\"height: 26px;\">\n<td style=\"text-align: center; height: 26px;\">P(28) = 3\/27<\/td>\n<\/tr>\n<tr style=\"height: 26px;\">\n<td style=\"text-align: center; height: 26px;\">P(27) =14\/27<\/td>\n<\/tr>\n<tr style=\"height: 26px;\">\n<td style=\"text-align: center; height: 26px;\">P(26) = 7\/27<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<hr \/>\n<p style=\"text-align: center;\"><strong><span style=\"text-decoration: underline;\">H) Chile vs Ecuador (DD) &#8211; Argentina vs Peru (LW)<\/span><\/strong><\/p>\n<table>\n<caption>Table H.1<\/caption>\n<tbody>\n<tr>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>=27 (24)(25)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>=27<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>=27<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>=21<\/li>\n<\/ol>\n<\/td>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>=27(24)(25)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>=27<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>=25<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>=22<\/li>\n<\/ol>\n<\/td>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>=27(24)(25)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>=27<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>=24<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>=24<\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>=28<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>=27<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>=25(24)(27)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>=21<\/li>\n<\/ol>\n<\/td>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>=28<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>=25(24)(27)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>=25<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>=22<\/li>\n<\/ol>\n<\/td>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>=28<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>=25(24)(27)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>=24<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>=24<\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>=30<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>=27<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>=24(25)(27)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>=21<\/li>\n<\/ol>\n<\/td>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>=30<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>=25<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>=24(25)(27)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>=22<\/li>\n<\/ol>\n<\/td>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>=30<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>=24<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>=24(25)(27)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>=24<\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table>\n<caption>Table H.2<\/caption>\n<tbody>\n<tr>\n<td style=\"text-align: center;\">Qualifying probability<\/td>\n<td style=\"text-align: center;\">If Brazil beats Chile<\/td>\n<td style=\"text-align: center;\">If Brazil ties Chile<\/td>\n<td style=\"text-align: center;\">If Chile beats Brazil<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/><\/td>\n<td style=\"text-align: center;\">\u00a06\/9 (9\/9)<\/td>\n<td style=\"text-align: center;\">\u00a03\/9 (6\/9)<\/td>\n<td style=\"text-align: center;\">\u00a00 (3\/9)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/><\/td>\n<td style=\"text-align: center;\">\u00a09\/9<\/td>\n<td style=\"text-align: center;\">\u00a09\/9<\/td>\n<td style=\"text-align: center;\">\u00a08\/9 (9\/9)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/><\/td>\n<td style=\"text-align: center;\">\u00a00 (3\/9)<\/td>\n<td style=\"text-align: center;\">\u00a00<\/td>\n<td style=\"text-align: center;\">\u00a00<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/><\/td>\n<td style=\"text-align: center;\">\u00a00 (3\/9)<\/td>\n<td style=\"text-align: center;\">\u00a03\/9 (6\/9)<\/td>\n<td style=\"text-align: center;\">\u00a06\/9 (9\/9)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table>\n<caption>Table H.3<\/caption>\n<tbody>\n<tr style=\"height: 26px;\">\n<td style=\"text-align: center; height: 26px;\">Probability, P(X), of\u00a0reaching the last qualifying\u00a0position with\u00a0X\u00a0points<\/td>\n<\/tr>\n<tr style=\"height: 26px;\">\n<td style=\"text-align: center; height: 26px;\">P(27) = 15\/27<\/td>\n<\/tr>\n<tr style=\"height: 26px;\">\n<td style=\"text-align: center; height: 26px;\">P(25) = 9\/27<\/td>\n<\/tr>\n<tr style=\"height: 26px;\">\n<td style=\"text-align: center; height: 26px;\">P(24) = 3\/27<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<hr \/>\n<p style=\"text-align: center;\"><strong><span style=\"text-decoration: underline;\">I) Chile vs Ecuador (LW) &#8211; Argentina vs Peru (LW)<\/span><\/strong><\/p>\n<table>\n<caption>Table I.1<\/caption>\n<tbody>\n<tr>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>=27<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>=27<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>=26 (23)(24)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>=23<\/li>\n<\/ol>\n<\/td>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>=27<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>=26(23)(24)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>=25<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>=24<\/li>\n<\/ol>\n<\/td>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>=27<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>=26<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>=26(23)(24)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>=24<\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>=28<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>=27<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>=24(23)(26)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>=23<\/li>\n<\/ol>\n<\/td>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>=28<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>=25<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>=24<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>=24(23)(26)<\/li>\n<\/ol>\n<\/td>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>=28<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>=26<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>=24(23)(26)<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>=24<\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>=30<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>=27<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>=23<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>=23(26)(24)<\/li>\n<\/ol>\n<\/td>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>=30<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>=25<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>=24<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>=23(26)(24)<\/li>\n<\/ol>\n<\/td>\n<td width=\"142\">\n<ol>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/>=30<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/>=26<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/>=24<\/li>\n<li><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/>=23(26)(24)<\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table>\n<caption>Table I.2<\/caption>\n<tbody>\n<tr>\n<td style=\"text-align: center;\">\u00a0Qualifying probability<\/td>\n<td style=\"text-align: center;\">If Brazil beats Chile<\/td>\n<td style=\"text-align: center;\">If Brazil ties Chile<\/td>\n<td style=\"text-align: center;\">If Chile beats Brazil<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><img loading=\"lazy\" class=\"alignnone wp-image-2052\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Argentina.png\" alt=\"\" width=\"25\" height=\"15\" \/><\/td>\n<td style=\"text-align: center;\">\u00a06\/9<\/td>\n<td style=\"text-align: center;\">\u00a06\/9<\/td>\n<td style=\"text-align: center;\">\u00a03\/9<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><img loading=\"lazy\" class=\"alignnone wp-image-2053\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Peru.png\" alt=\"\" width=\"25\" height=\"15\" \/><\/td>\n<td style=\"text-align: center;\">\u00a09\/9<\/td>\n<td style=\"text-align: center;\">\u00a09\/9<\/td>\n<td style=\"text-align: center;\">\u00a09\/9<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><img loading=\"lazy\" class=\"alignnone wp-image-2051\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Ecuador.png\" alt=\"\" width=\"25\" height=\"15\" \/><\/td>\n<td style=\"text-align: center;\">\u00a03\/9<\/td>\n<td style=\"text-align: center;\">\u00a03\/9<\/td>\n<td style=\"text-align: center;\">\u00a00 (3\/9)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><img loading=\"lazy\" class=\"alignnone wp-image-2050\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/09\/flag-of-Chile.png\" alt=\"\" width=\"25\" height=\"15\" \/><\/td>\n<td style=\"text-align: center;\">\u00a00<\/td>\n<td style=\"text-align: center;\">\u00a00<\/td>\n<td style=\"text-align: center;\">\u00a03\/9 (6\/9)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table>\n<caption>Table I.3<\/caption>\n<tbody>\n<tr style=\"height: 26px;\">\n<td style=\"text-align: center; height: 26px;\">Probability, P(X), of\u00a0reaching the last qualifying\u00a0position with\u00a0X\u00a0points<\/td>\n<\/tr>\n<tr style=\"height: 26px;\">\n<td style=\"text-align: center; height: 26px;\">P(27) = 9\/27<\/td>\n<\/tr>\n<tr style=\"height: 26px;\">\n<td style=\"text-align: center; height: 26px;\">P(25) = 6\/27<\/td>\n<\/tr>\n<tr style=\"height: 26px;\">\n<td style=\"text-align: center; height: 26px;\">P(26) = 12\/27<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"<p>November\u00a015th,\u00a02017 Argentina, Colombia, and Peru qualified to the World Cup Russia 2018. The latter qualified beating New Zealanad 2-0 in the interconfederation play-off. October 7th,\u00a02017 In the first part of this article, published on September 11th, we elaborated a mathematical analysis to predict the Conmebol teams that will qualify to the World Cup Russia 2018. [&hellip;]<\/p>\n","protected":false},"author":9,"featured_media":2170,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[142,149,143],"tags":[],"_links":{"self":[{"href":"https:\/\/www.cientificos.pe\/index.php?rest_route=\/wp\/v2\/posts\/2159"}],"collection":[{"href":"https:\/\/www.cientificos.pe\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.cientificos.pe\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.cientificos.pe\/index.php?rest_route=\/wp\/v2\/users\/9"}],"replies":[{"embeddable":true,"href":"https:\/\/www.cientificos.pe\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2159"}],"version-history":[{"count":44,"href":"https:\/\/www.cientificos.pe\/index.php?rest_route=\/wp\/v2\/posts\/2159\/revisions"}],"predecessor-version":[{"id":2861,"href":"https:\/\/www.cientificos.pe\/index.php?rest_route=\/wp\/v2\/posts\/2159\/revisions\/2861"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.cientificos.pe\/index.php?rest_route=\/wp\/v2\/media\/2170"}],"wp:attachment":[{"href":"https:\/\/www.cientificos.pe\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2159"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.cientificos.pe\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2159"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.cientificos.pe\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2159"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}