{"id":4745,"date":"2023-11-13T16:55:06","date_gmt":"2023-11-13T15:55:06","guid":{"rendered":"https:\/\/ingenius.ecoledesponts.fr\/?p=4745"},"modified":"2023-11-17T08:36:47","modified_gmt":"2023-11-17T07:36:47","slug":"using-mathematics-for-a-fairer-fifa-world-cup","status":"publish","type":"post","link":"https:\/\/ingenius.ecoledesponts.fr\/en\/articles\/using-mathematics-for-a-fairer-fifa-world-cup\/","title":{"rendered":"Using mathematics for a fairer FIFA World Cup"},"content":{"rendered":"\n\n\n
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Unsplash<\/figcaption><\/figure>\n\n\n\n

Alongside the Olympic Games, the FIFA World Cup is the most popular sporting event on the planet. In the past, however, it has suffered from serious issues of fairness concerning the draw procedure and teams’ initial ranking. For the next event, scheduled to take place in 2026 in the USA, Canada and Mexico, a new problem has arisen: for the first time, the competition format will include 48 teams instead of the 32 teams that have been involved since the 1998 World Cup in France. The work of mathematicians like me at the Centre d’Enseignement et de Recherche en Math\u00e9matIques et Calcul Scientifique<\/em> (CERMICS<\/a>) has helped quantify the unfairness in the proposed procedure and convince the F\u00e9d\u00e9ration Internationale de Football Association<\/em> (FIFA) to change the draw procedure, the rule for calculating the FIFA ranking and the format of the future World Cup.<\/p>\n\n\n\n

The 2018 World Cup: a fairer draw<\/strong><\/h2>\n\n\n\n

As a mathematician with a passion for soccer, I began to take a close interest in fairness in sports in December 2013 while I was in Brazil for the draw for the 2014 World Cup, organized by the South American giant. Despite FIFA’s desire to create balanced groups, the draw produced three very strong groups and four very weak ones. In fact, FIFA divided the 32 teams into four pots according to their geographical zone, each group then being made up of a team drawn at random from each of the pots. This 60-year-old practice enabled FIFA to easily ensure its regulatory geographical constraints: apart from Europe, two teams from the same continent could not be in the same group.<\/p>\n\n\n\n

Statistical analysis has shown that this practice not only produces unbalanced groups but also – more annoyingly for sporting fairness – unfairly penalizes certain teams by increasing their chances of falling into a difficult group – as was the case with the USA and Chile in 2014. This study helped put forward two new draw procedures that are fairer and easier to implement in practice, excluding computerized draws, which lack transparency.<\/p>\n\n\n\n

The publication of these results in the New York Times<\/a>, Le Monde<\/a>, El Pa\u00eds<\/a>, and then in the Journal of Quantitative Analysis of Sports<\/a>, as well as letters addressed directly to the FIFA president, vice-presidents and confederation presidents, did much to encourage the adoption of a fairer draw procedure. In fact, since the 2018 World Cup, the pots are now organized by level, and the geographical constraint is guaranteed thanks to a backtracking algorithm as suggested in an article published in 2014 on the Social Science Research Network website<\/a>. The backtracking algorithm identifies the groups for which the team drawn is eligible, so that the geographical constraint can be satisfied for all the teams still to be drawn.<\/p>\n\n\n\n

The 2022 World Cup: a fairer FIFA ranking<\/strong><\/h2>\n\n\n\n

However, there is still a problem. Creating pots by level naturally uses a ranking system for teams, the “FIFA ranking”, based on past performance. However, until 2018, the way these rankings were calculated poorly reflected the true value of the teams. For example, not playing a friendly match for a year gave the team an artificial boost in the rankings. Some teams, including Poland and Wales, exploited this loophole, with Poland managing to be one of the eight seeds at the 2018 World Cup, even though its level of play failed to justify this, according to the specialists.<\/p>\n\n\n\n

Several scientists have proposed better methods of calculation, in particular adaptations of the Elo method<\/a>, a ranking of chess players proposed by Hungarian-born American physicist Arpad Elo in the 1950s and a process I suggested in this New York Times article<\/a>. The Elo method is a zero-sum game of self-correction: if a team’s match result is better than expected (based on the Elo ranking of the two teams before the match), that team wins points. The more unlikely the outcome, the higher the number of points obtained.  The other team loses the same number of points.<\/p>\n\n\n\n

FIFA adopted the Elo method for calculating rankings in summer 2018. However, some critics point to the omission of goal difference and home\/away play in calculating the points.<\/p>\n\n\n\n

In 2022, FIFA, finally having both a fair draw procedure and an accurate initial ranking, carried out the fairest and most balanced World Cup draw in history. This helped make the suspense-filled group phase of the 2022 World Cup one of the most exciting to follow in World Cup history.<\/p>\n\n\n\n

The 2026 World Cup: avoiding an unfair new format<\/strong><\/h2>\n\n\n\n

Thanks to the work of mathematicians, the fairness problems that plagued the World Cup finally seemed to have been resolved. However, in January 2017, the FIFA Council unanimously voted for a complete overhaul of the competition’s format: from 2026 onwards, 48 teams will take part in the World Cup, instead of 32; they will be divided into 16 groups of three; and in each group of three, two teams will qualify for the Round of 16.<\/p>\n\n\n\n

At the time, the media focused on the move from 32 to 48 teams, overlooking the serious threat posed by groups of three to the World Cup, and soccer in general, given the risk of collusion between teams.<\/p>\n\n\n\n

Indeed, if there is a result that qualifies the two teams playing each other in the final group match at the expense of the third team in the group, they can be satisfied with that result and refuse to engage with each other competitively.<\/p>\n\n\n\n

Such was the case with the famous “Disgrace of Gij\u00f3n<\/a>” a game between West Germany and Austria during the 1982 World Cup. Both teams knew that a 1-0 or 2-0 win for West Germany would see them through, at the expense of Algeria, who had already played their final group match against Chile the day before. As soon as the West Germans scored a quick goal, the two teams stopped attacking each other completely, offering a pitiful spectacle of passes between central defenders for 80 minutes. Since then, to limit the risk of collusion, FIFA has imposed that in a group of four, the last two matches must be played simultaneously.<\/p>\n\n\n\n

Of course, this is impossible with groups of three. A probabilistic model quantified the risk of collusion in this format and showed, in articles published in the New York Times<\/a> and Le Monde<\/a> as early as June 2018 and in the academic publication Journal of Sports Analytics<\/a>, that this risk was very high, raising serious concerns about its suitability for the World Cup, soccer, and indeed sport in general, since the uncertainty of the outcome is the very basis of the popularity of sporting events. This paper won second prize in the “Best Research Paper Award” at the 2021 MIT Sloan Sports Conference, the world’s biggest quantitative sports analysis conference, held each year by MIT.<\/p>\n\n\n\n

As part of a “Modeling, Programming, Simulation” project with Nathan Fredholm and Simon Guipaud, two students at \u00c9cole des Ponts ParisTech, we proposed two alternative formats and demonstrated that they would entail a lower risk of collusion: (a) 12 groups of four, (b) eight groups of six, each group of six being divided into two sub-groups of three in cross-competition (the classic format with groups of six is not feasible: the group phase would last too long). Following direct exchanges with FIFA, it finally decided in March 2023 to change the format it had initially adopted, precisely to limit the risk of collusion<\/a>. As suggested back in June 2018 in the New York Times article<\/a>, the 48 teams will ultimately be divided into 12 groups of four, with the eight best third-place finishers joining the 24 first- and second-place finishers to form the Round of 16. It is commendable that FIFA had the wisdom, based on these studies, to recognize its initial error and choose a fairer format, which encourages teams to play their best to win every match, minimizes the risk of repeating “Disgrace of Gij\u00f3n”, and will offer the finest spectacle to hundreds of millions of soccer fans around the world.<\/p>\n","protected":false},"excerpt":{"rendered":"

Alongside the Olympic Games, the FIFA World Cup is the most popular sporting event on the planet. In the past, […]<\/p>\n","protected":false},"author":6,"featured_media":4577,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_related_content_post":[],"_related_content_subject":[124,690],"_related_content_author":[4747],"_related_content_category":[1716],"_related_content_folder":[],"_excerpt":"The FIFA World Cup, one of the world\u2019s most watched sporting events, has long been marred by problems of fairness. However, mathematicians, including those at the Centre d'Enseignement et de Recherche en Math\u00e9matiques et Calcul Scientifique<\/em> (CERMICS), have successfully quantified these biases and offered fairer solutions, prompting the F\u00e9d\u00e9ration Internationale de Football Association<\/em> to review the rules governing the World Cup draw and the method of calculating the FIFA rankings as well as the format of the next tournament in 2026.","_duration":6,"_manual_duration":false,"footnotes":""},"article-types":[13,27],"class_list":["post-4745","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","article-types-article","article-types-folder"],"has_blocks":true,"block_data":[{"blockName":"enpc\/excerpt","attrs":{"lock":[],"metadata":[],"className":"","style":""},"innerBlocks":[],"innerHTML":"","innerContent":[],"rendered":""},{"blockName":"core\/image","attrs":{"align":"wide","id":4577,"sizeSlug":"large","linkDestination":"none","blob":"","url":"https:\/\/ingenius.ecoledesponts.fr\/wp-content\/uploads\/2023\/10\/fauzan-saari-AmhdN68wjPc-unsplash-1024x576.jpg","alt":"","caption":"Unsplash","lightbox":[],"title":"","href":"","rel":"","linkClass":"","width":"","height":"","aspectRatio":"","scale":"","linkTarget":"","lock":[],"metadata":[],"className":"wp-block-image alignwide size-large","style":"","borderColor":"","anchor":""},"innerBlocks":[],"innerHTML":"\n

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Unsplash<\/figcaption><\/figure>\n","innerContent":["\n
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Unsplash<\/figcaption><\/figure>\n"],"rendered":"\n
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Unsplash<\/figcaption><\/figure>\n"},{"blockName":"core\/paragraph","attrs":{"align":"","content":"Alongside the Olympic Games, the FIFA World Cup is the most popular sporting event on the planet. In the past, however, it has suffered from serious issues of fairness concerning the draw procedure and teams' initial ranking. For the next event, scheduled to take place in 2026 in the USA, Canada and Mexico, a new problem has arisen: for the first time, the competition format will include 48 teams instead of the 32 teams that have been involved since the 1998 World Cup in France. The work of mathematicians like me at the Centre d'Enseignement et de Recherche en Math\u00e9matIques et Calcul Scientifique (CERMICS) has helped quantify the unfairness in the proposed procedure and convince the F\u00e9d\u00e9ration Internationale de Football Association (FIFA) to change the draw procedure, the rule for calculating the FIFA ranking and the format of the future World Cup.","dropCap":false,"placeholder":"","direction":"","lock":[],"metadata":[],"className":"","style":"","backgroundColor":"","textColor":"","gradient":"","fontSize":"","fontFamily":"","borderColor":"","anchor":""},"innerBlocks":[],"innerHTML":"\n

Alongside the Olympic Games, the FIFA World Cup is the most popular sporting event on the planet. In the past, however, it has suffered from serious issues of fairness concerning the draw procedure and teams' initial ranking. For the next event, scheduled to take place in 2026 in the USA, Canada and Mexico, a new problem has arisen: for the first time, the competition format will include 48 teams instead of the 32 teams that have been involved since the 1998 World Cup in France. The work of mathematicians like me at the Centre d'Enseignement et de Recherche en Math\u00e9matIques et Calcul Scientifique<\/em> (CERMICS<\/a>) has helped quantify the unfairness in the proposed procedure and convince the F\u00e9d\u00e9ration Internationale de Football Association<\/em> (FIFA) to change the draw procedure, the rule for calculating the FIFA ranking and the format of the future World Cup.<\/p>\n","innerContent":["\n

Alongside the Olympic Games, the FIFA World Cup is the most popular sporting event on the planet. In the past, however, it has suffered from serious issues of fairness concerning the draw procedure and teams' initial ranking. For the next event, scheduled to take place in 2026 in the USA, Canada and Mexico, a new problem has arisen: for the first time, the competition format will include 48 teams instead of the 32 teams that have been involved since the 1998 World Cup in France. The work of mathematicians like me at the Centre d'Enseignement et de Recherche en Math\u00e9matIques et Calcul Scientifique<\/em> (CERMICS<\/a>) has helped quantify the unfairness in the proposed procedure and convince the F\u00e9d\u00e9ration Internationale de Football Association<\/em> (FIFA) to change the draw procedure, the rule for calculating the FIFA ranking and the format of the future World Cup.<\/p>\n"],"rendered":"\n

Alongside the Olympic Games, the FIFA World Cup is the most popular sporting event on the planet. In the past, however, it has suffered from serious issues of fairness concerning the draw procedure and teams' initial ranking. For the next event, scheduled to take place in 2026 in the USA, Canada and Mexico, a new problem has arisen: for the first time, the competition format will include 48 teams instead of the 32 teams that have been involved since the 1998 World Cup in France. The work of mathematicians like me at the Centre d'Enseignement et de Recherche en Math\u00e9matIques et Calcul Scientifique<\/em> (CERMICS<\/a>) has helped quantify the unfairness in the proposed procedure and convince the F\u00e9d\u00e9ration Internationale de Football Association<\/em> (FIFA) to change the draw procedure, the rule for calculating the FIFA ranking and the format of the future World Cup.<\/p>\n"},{"blockName":"core\/heading","attrs":{"textColor":"red","textAlign":"","content":"The 2018 World Cup: a fairer draw","level":2,"levelOptions":[],"placeholder":"","lock":[],"metadata":[],"align":"","className":"wp-block-heading has-red-color has-text-color","style":"","backgroundColor":"","gradient":"","fontSize":"","fontFamily":"","borderColor":"","anchor":""},"innerBlocks":[],"innerHTML":"\n

The 2018 World Cup: a fairer draw<\/strong><\/h2>\n","innerContent":["\n

The 2018 World Cup: a fairer draw<\/strong><\/h2>\n"],"rendered":"\n

The 2018 World Cup: a fairer draw<\/strong><\/h2>\n"},{"blockName":"core\/paragraph","attrs":{"align":"","content":"As a mathematician with a passion for soccer, I began to take a close interest in fairness in sports in December 2013 while I was in Brazil for the draw for the 2014 World Cup, organized by the South American giant. Despite FIFA's desire to create balanced groups, the draw produced three very strong groups and four very weak ones. In fact, FIFA divided the 32 teams into four pots according to their geographical zone, each group then being made up of a team drawn at random from each of the pots. This 60-year-old practice enabled FIFA to easily ensure its regulatory geographical constraints: apart from Europe, two teams from the same continent could not be in the same group.","dropCap":false,"placeholder":"","direction":"","lock":[],"metadata":[],"className":"","style":"","backgroundColor":"","textColor":"","gradient":"","fontSize":"","fontFamily":"","borderColor":"","anchor":""},"innerBlocks":[],"innerHTML":"\n

As a mathematician with a passion for soccer, I began to take a close interest in fairness in sports in December 2013 while I was in Brazil for the draw for the 2014 World Cup, organized by the South American giant. Despite FIFA's desire to create balanced groups, the draw produced three very strong groups and four very weak ones. In fact, FIFA divided the 32 teams into four pots according to their geographical zone, each group then being made up of a team drawn at random from each of the pots. This 60-year-old practice enabled FIFA to easily ensure its regulatory geographical constraints: apart from Europe, two teams from the same continent could not be in the same group.<\/p>\n","innerContent":["\n

As a mathematician with a passion for soccer, I began to take a close interest in fairness in sports in December 2013 while I was in Brazil for the draw for the 2014 World Cup, organized by the South American giant. Despite FIFA's desire to create balanced groups, the draw produced three very strong groups and four very weak ones. In fact, FIFA divided the 32 teams into four pots according to their geographical zone, each group then being made up of a team drawn at random from each of the pots. This 60-year-old practice enabled FIFA to easily ensure its regulatory geographical constraints: apart from Europe, two teams from the same continent could not be in the same group.<\/p>\n"],"rendered":"\n

As a mathematician with a passion for soccer, I began to take a close interest in fairness in sports in December 2013 while I was in Brazil for the draw for the 2014 World Cup, organized by the South American giant. Despite FIFA's desire to create balanced groups, the draw produced three very strong groups and four very weak ones. In fact, FIFA divided the 32 teams into four pots according to their geographical zone, each group then being made up of a team drawn at random from each of the pots. This 60-year-old practice enabled FIFA to easily ensure its regulatory geographical constraints: apart from Europe, two teams from the same continent could not be in the same group.<\/p>\n"},{"blockName":"core\/paragraph","attrs":{"align":"","content":"Statistical analysis has shown that this practice not only produces unbalanced groups but also - more annoyingly for sporting fairness - unfairly penalizes certain teams by increasing their chances of falling into a difficult group - as was the case with the USA and Chile in 2014. This study helped put forward two new draw procedures that are fairer and easier to implement in practice, excluding computerized draws, which lack transparency.","dropCap":false,"placeholder":"","direction":"","lock":[],"metadata":[],"className":"","style":"","backgroundColor":"","textColor":"","gradient":"","fontSize":"","fontFamily":"","borderColor":"","anchor":""},"innerBlocks":[],"innerHTML":"\n

Statistical analysis has shown that this practice not only produces unbalanced groups but also - more annoyingly for sporting fairness - unfairly penalizes certain teams by increasing their chances of falling into a difficult group - as was the case with the USA and Chile in 2014. This study helped put forward two new draw procedures that are fairer and easier to implement in practice, excluding computerized draws, which lack transparency.<\/p>\n","innerContent":["\n

Statistical analysis has shown that this practice not only produces unbalanced groups but also - more annoyingly for sporting fairness - unfairly penalizes certain teams by increasing their chances of falling into a difficult group - as was the case with the USA and Chile in 2014. This study helped put forward two new draw procedures that are fairer and easier to implement in practice, excluding computerized draws, which lack transparency.<\/p>\n"],"rendered":"\n

Statistical analysis has shown that this practice not only produces unbalanced groups but also - more annoyingly for sporting fairness - unfairly penalizes certain teams by increasing their chances of falling into a difficult group - as was the case with the USA and Chile in 2014. This study helped put forward two new draw procedures that are fairer and easier to implement in practice, excluding computerized draws, which lack transparency.<\/p>\n"},{"blockName":"core\/paragraph","attrs":{"align":"","content":"The publication of these results in the New York Times, Le Monde, El Pa\u00eds, and then in the Journal of Quantitative Analysis of Sports, as well as letters addressed directly to the FIFA president, vice-presidents and confederation presidents, did much to encourage the adoption of a fairer draw procedure. In fact, since the 2018 World Cup, the pots are now organized by level, and the geographical constraint is guaranteed thanks to a backtracking algorithm as suggested in an article published in 2014 on the Social Science Research Network website.\u00a0The backtracking algorithm identifies the groups for which the team drawn is eligible, so that the geographical constraint can be satisfied for all the teams still to be drawn.","dropCap":false,"placeholder":"","direction":"","lock":[],"metadata":[],"className":"","style":"","backgroundColor":"","textColor":"","gradient":"","fontSize":"","fontFamily":"","borderColor":"","anchor":""},"innerBlocks":[],"innerHTML":"\n

The publication of these results in the New York Times<\/a>, Le Monde<\/a>, El Pa\u00eds<\/a>, and then in the Journal of Quantitative Analysis of Sports<\/a>, as well as letters addressed directly to the FIFA president, vice-presidents and confederation presidents, did much to encourage the adoption of a fairer draw procedure. In fact, since the 2018 World Cup, the pots are now organized by level, and the geographical constraint is guaranteed thanks to a backtracking algorithm as suggested in an article published in 2014 on the Social Science Research Network website<\/a>. The backtracking algorithm identifies the groups for which the team drawn is eligible, so that the geographical constraint can be satisfied for all the teams still to be drawn.<\/p>\n","innerContent":["\n

The publication of these results in the New York Times<\/a>, Le Monde<\/a>, El Pa\u00eds<\/a>, and then in the Journal of Quantitative Analysis of Sports<\/a>, as well as letters addressed directly to the FIFA president, vice-presidents and confederation presidents, did much to encourage the adoption of a fairer draw procedure. In fact, since the 2018 World Cup, the pots are now organized by level, and the geographical constraint is guaranteed thanks to a backtracking algorithm as suggested in an article published in 2014 on the Social Science Research Network website<\/a>. The backtracking algorithm identifies the groups for which the team drawn is eligible, so that the geographical constraint can be satisfied for all the teams still to be drawn.<\/p>\n"],"rendered":"\n

The publication of these results in the New York Times<\/a>, Le Monde<\/a>, El Pa\u00eds<\/a>, and then in the Journal of Quantitative Analysis of Sports<\/a>, as well as letters addressed directly to the FIFA president, vice-presidents and confederation presidents, did much to encourage the adoption of a fairer draw procedure. In fact, since the 2018 World Cup, the pots are now organized by level, and the geographical constraint is guaranteed thanks to a backtracking algorithm as suggested in an article published in 2014 on the Social Science Research Network website<\/a>. The backtracking algorithm identifies the groups for which the team drawn is eligible, so that the geographical constraint can be satisfied for all the teams still to be drawn.<\/p>\n"},{"blockName":"core\/heading","attrs":{"textColor":"red","textAlign":"","content":"The 2022 World Cup: a fairer FIFA ranking","level":2,"levelOptions":[],"placeholder":"","lock":[],"metadata":[],"align":"","className":"wp-block-heading has-red-color has-text-color","style":"","backgroundColor":"","gradient":"","fontSize":"","fontFamily":"","borderColor":"","anchor":""},"innerBlocks":[],"innerHTML":"\n

The 2022 World Cup: a fairer FIFA ranking<\/strong><\/h2>\n","innerContent":["\n

The 2022 World Cup: a fairer FIFA ranking<\/strong><\/h2>\n"],"rendered":"\n

The 2022 World Cup: a fairer FIFA ranking<\/strong><\/h2>\n"},{"blockName":"core\/paragraph","attrs":{"align":"","content":"However, there is still a problem. Creating pots by level naturally uses a ranking system for teams, the \"FIFA ranking\", based on past performance. However, until 2018, the way these rankings were calculated poorly reflected the true value of the teams. For example, not playing a friendly match for a year gave the team an artificial boost in the rankings. Some teams, including Poland and Wales, exploited this loophole, with Poland managing to be one of the eight seeds at the 2018 World Cup, even though its level of play failed to justify this, according to the specialists.","dropCap":false,"placeholder":"","direction":"","lock":[],"metadata":[],"className":"","style":"","backgroundColor":"","textColor":"","gradient":"","fontSize":"","fontFamily":"","borderColor":"","anchor":""},"innerBlocks":[],"innerHTML":"\n

However, there is still a problem. Creating pots by level naturally uses a ranking system for teams, the \"FIFA ranking\", based on past performance. However, until 2018, the way these rankings were calculated poorly reflected the true value of the teams. For example, not playing a friendly match for a year gave the team an artificial boost in the rankings. Some teams, including Poland and Wales, exploited this loophole, with Poland managing to be one of the eight seeds at the 2018 World Cup, even though its level of play failed to justify this, according to the specialists.<\/p>\n","innerContent":["\n

However, there is still a problem. Creating pots by level naturally uses a ranking system for teams, the \"FIFA ranking\", based on past performance. However, until 2018, the way these rankings were calculated poorly reflected the true value of the teams. For example, not playing a friendly match for a year gave the team an artificial boost in the rankings. Some teams, including Poland and Wales, exploited this loophole, with Poland managing to be one of the eight seeds at the 2018 World Cup, even though its level of play failed to justify this, according to the specialists.<\/p>\n"],"rendered":"\n

However, there is still a problem. Creating pots by level naturally uses a ranking system for teams, the \"FIFA ranking\", based on past performance. However, until 2018, the way these rankings were calculated poorly reflected the true value of the teams. For example, not playing a friendly match for a year gave the team an artificial boost in the rankings. Some teams, including Poland and Wales, exploited this loophole, with Poland managing to be one of the eight seeds at the 2018 World Cup, even though its level of play failed to justify this, according to the specialists.<\/p>\n"},{"blockName":"core\/paragraph","attrs":{"align":"","content":"Several scientists have proposed better methods of calculation, in particular adaptations of the Elo method, a ranking of chess players proposed by Hungarian-born American physicist Arpad Elo in the 1950s and a process I suggested in this New York Times article. The Elo method is a zero-sum game of self-correction: if a team's match result is better than expected (based on the Elo ranking of the two teams before the match), that team wins points. The more unlikely the outcome, the higher the number of points obtained.\u00a0 The other team loses the same number of points.","dropCap":false,"placeholder":"","direction":"","lock":[],"metadata":[],"className":"","style":"","backgroundColor":"","textColor":"","gradient":"","fontSize":"","fontFamily":"","borderColor":"","anchor":""},"innerBlocks":[],"innerHTML":"\n

Several scientists have proposed better methods of calculation, in particular adaptations of the Elo method<\/a>, a ranking of chess players proposed by Hungarian-born American physicist Arpad Elo in the 1950s and a process I suggested in this New York Times article<\/a>. The Elo method is a zero-sum game of self-correction: if a team's match result is better than expected (based on the Elo ranking of the two teams before the match), that team wins points. The more unlikely the outcome, the higher the number of points obtained.  The other team loses the same number of points.<\/p>\n","innerContent":["\n

Several scientists have proposed better methods of calculation, in particular adaptations of the Elo method<\/a>, a ranking of chess players proposed by Hungarian-born American physicist Arpad Elo in the 1950s and a process I suggested in this New York Times article<\/a>. The Elo method is a zero-sum game of self-correction: if a team's match result is better than expected (based on the Elo ranking of the two teams before the match), that team wins points. The more unlikely the outcome, the higher the number of points obtained.  The other team loses the same number of points.<\/p>\n"],"rendered":"\n

Several scientists have proposed better methods of calculation, in particular adaptations of the Elo method<\/a>, a ranking of chess players proposed by Hungarian-born American physicist Arpad Elo in the 1950s and a process I suggested in this New York Times article<\/a>. The Elo method is a zero-sum game of self-correction: if a team's match result is better than expected (based on the Elo ranking of the two teams before the match), that team wins points. The more unlikely the outcome, the higher the number of points obtained.  The other team loses the same number of points.<\/p>\n"},{"blockName":"core\/paragraph","attrs":{"align":"","content":"FIFA adopted the Elo method for calculating rankings in summer 2018. However, some critics point to the omission of goal difference and home\/away play in calculating the points.","dropCap":false,"placeholder":"","direction":"","lock":[],"metadata":[],"className":"","style":"","backgroundColor":"","textColor":"","gradient":"","fontSize":"","fontFamily":"","borderColor":"","anchor":""},"innerBlocks":[],"innerHTML":"\n

FIFA adopted the Elo method for calculating rankings in summer 2018. However, some critics point to the omission of goal difference and home\/away play in calculating the points.<\/p>\n","innerContent":["\n

FIFA adopted the Elo method for calculating rankings in summer 2018. However, some critics point to the omission of goal difference and home\/away play in calculating the points.<\/p>\n"],"rendered":"\n

FIFA adopted the Elo method for calculating rankings in summer 2018. However, some critics point to the omission of goal difference and home\/away play in calculating the points.<\/p>\n"},{"blockName":"core\/paragraph","attrs":{"align":"","content":"In 2022, FIFA, finally having both a fair draw procedure and an accurate initial ranking, carried out the fairest and most balanced World Cup draw in history.\u00a0This helped make the suspense-filled group phase of the 2022 World Cup one of the most exciting to follow in World Cup history.","dropCap":false,"placeholder":"","direction":"","lock":[],"metadata":[],"className":"","style":"","backgroundColor":"","textColor":"","gradient":"","fontSize":"","fontFamily":"","borderColor":"","anchor":""},"innerBlocks":[],"innerHTML":"\n

In 2022, FIFA, finally having both a fair draw procedure and an accurate initial ranking, carried out the fairest and most balanced World Cup draw in history. This helped make the suspense-filled group phase of the 2022 World Cup one of the most exciting to follow in World Cup history.<\/p>\n","innerContent":["\n

In 2022, FIFA, finally having both a fair draw procedure and an accurate initial ranking, carried out the fairest and most balanced World Cup draw in history. This helped make the suspense-filled group phase of the 2022 World Cup one of the most exciting to follow in World Cup history.<\/p>\n"],"rendered":"\n

In 2022, FIFA, finally having both a fair draw procedure and an accurate initial ranking, carried out the fairest and most balanced World Cup draw in history. This helped make the suspense-filled group phase of the 2022 World Cup one of the most exciting to follow in World Cup history.<\/p>\n"},{"blockName":"core\/heading","attrs":{"textColor":"red","textAlign":"","content":"The 2026 World Cup: avoiding an unfair new format","level":2,"levelOptions":[],"placeholder":"","lock":[],"metadata":[],"align":"","className":"wp-block-heading has-red-color has-text-color","style":"","backgroundColor":"","gradient":"","fontSize":"","fontFamily":"","borderColor":"","anchor":""},"innerBlocks":[],"innerHTML":"\n

The 2026 World Cup: avoiding an unfair new format<\/strong><\/h2>\n","innerContent":["\n

The 2026 World Cup: avoiding an unfair new format<\/strong><\/h2>\n"],"rendered":"\n

The 2026 World Cup: avoiding an unfair new format<\/strong><\/h2>\n"},{"blockName":"core\/paragraph","attrs":{"align":"","content":"Thanks to the work of mathematicians, the fairness problems that plagued the World Cup finally seemed to have been resolved. However, in January 2017, the FIFA Council unanimously voted for a complete overhaul of the competition's format: from 2026 onwards, 48 teams will take part in the World Cup, instead of 32; they will be divided into 16 groups of three; and in each group of three, two teams will qualify for the Round of 16.","dropCap":false,"placeholder":"","direction":"","lock":[],"metadata":[],"className":"","style":"","backgroundColor":"","textColor":"","gradient":"","fontSize":"","fontFamily":"","borderColor":"","anchor":""},"innerBlocks":[],"innerHTML":"\n

Thanks to the work of mathematicians, the fairness problems that plagued the World Cup finally seemed to have been resolved. However, in January 2017, the FIFA Council unanimously voted for a complete overhaul of the competition's format: from 2026 onwards, 48 teams will take part in the World Cup, instead of 32; they will be divided into 16 groups of three; and in each group of three, two teams will qualify for the Round of 16.<\/p>\n","innerContent":["\n

Thanks to the work of mathematicians, the fairness problems that plagued the World Cup finally seemed to have been resolved. However, in January 2017, the FIFA Council unanimously voted for a complete overhaul of the competition's format: from 2026 onwards, 48 teams will take part in the World Cup, instead of 32; they will be divided into 16 groups of three; and in each group of three, two teams will qualify for the Round of 16.<\/p>\n"],"rendered":"\n

Thanks to the work of mathematicians, the fairness problems that plagued the World Cup finally seemed to have been resolved. However, in January 2017, the FIFA Council unanimously voted for a complete overhaul of the competition's format: from 2026 onwards, 48 teams will take part in the World Cup, instead of 32; they will be divided into 16 groups of three; and in each group of three, two teams will qualify for the Round of 16.<\/p>\n"},{"blockName":"core\/paragraph","attrs":{"align":"","content":"At the time, the media focused on the move from 32 to 48 teams, overlooking the serious threat posed by groups of three to the World Cup, and soccer in general, given the risk of collusion between teams.","dropCap":false,"placeholder":"","direction":"","lock":[],"metadata":[],"className":"","style":"","backgroundColor":"","textColor":"","gradient":"","fontSize":"","fontFamily":"","borderColor":"","anchor":""},"innerBlocks":[],"innerHTML":"\n

At the time, the media focused on the move from 32 to 48 teams, overlooking the serious threat posed by groups of three to the World Cup, and soccer in general, given the risk of collusion between teams.<\/p>\n","innerContent":["\n

At the time, the media focused on the move from 32 to 48 teams, overlooking the serious threat posed by groups of three to the World Cup, and soccer in general, given the risk of collusion between teams.<\/p>\n"],"rendered":"\n

At the time, the media focused on the move from 32 to 48 teams, overlooking the serious threat posed by groups of three to the World Cup, and soccer in general, given the risk of collusion between teams.<\/p>\n"},{"blockName":"core\/paragraph","attrs":{"align":"","content":"Indeed, if there is a result that qualifies the two teams playing each other in the final group match at the expense of the third team in the group, they can be satisfied with that result and refuse to engage with each other competitively.","dropCap":false,"placeholder":"","direction":"","lock":[],"metadata":[],"className":"","style":"","backgroundColor":"","textColor":"","gradient":"","fontSize":"","fontFamily":"","borderColor":"","anchor":""},"innerBlocks":[],"innerHTML":"\n

Indeed, if there is a result that qualifies the two teams playing each other in the final group match at the expense of the third team in the group, they can be satisfied with that result and refuse to engage with each other competitively.<\/p>\n","innerContent":["\n

Indeed, if there is a result that qualifies the two teams playing each other in the final group match at the expense of the third team in the group, they can be satisfied with that result and refuse to engage with each other competitively.<\/p>\n"],"rendered":"\n

Indeed, if there is a result that qualifies the two teams playing each other in the final group match at the expense of the third team in the group, they can be satisfied with that result and refuse to engage with each other competitively.<\/p>\n"},{"blockName":"core\/paragraph","attrs":{"align":"","content":"Such was the case with the famous \"Disgrace of Gij\u00f3n\" a game between West Germany and Austria during the 1982 World Cup. Both teams knew that a 1-0 or 2-0 win for West Germany would see them through, at the expense of Algeria, who had already played their final group match against Chile the day before. As soon as the West Germans scored a quick goal, the two teams stopped attacking each other completely, offering a pitiful spectacle of passes between central defenders for 80 minutes. Since then, to limit the risk of collusion, FIFA has imposed that in a group of four, the last two matches must be played simultaneously.","dropCap":false,"placeholder":"","direction":"","lock":[],"metadata":[],"className":"","style":"","backgroundColor":"","textColor":"","gradient":"","fontSize":"","fontFamily":"","borderColor":"","anchor":""},"innerBlocks":[],"innerHTML":"\n

Such was the case with the famous \"Disgrace of Gij\u00f3n<\/a>\" a game between West Germany and Austria during the 1982 World Cup. Both teams knew that a 1-0 or 2-0 win for West Germany would see them through, at the expense of Algeria, who had already played their final group match against Chile the day before. As soon as the West Germans scored a quick goal, the two teams stopped attacking each other completely, offering a pitiful spectacle of passes between central defenders for 80 minutes. Since then, to limit the risk of collusion, FIFA has imposed that in a group of four, the last two matches must be played simultaneously.<\/p>\n","innerContent":["\n

Such was the case with the famous \"Disgrace of Gij\u00f3n<\/a>\" a game between West Germany and Austria during the 1982 World Cup. Both teams knew that a 1-0 or 2-0 win for West Germany would see them through, at the expense of Algeria, who had already played their final group match against Chile the day before. As soon as the West Germans scored a quick goal, the two teams stopped attacking each other completely, offering a pitiful spectacle of passes between central defenders for 80 minutes. Since then, to limit the risk of collusion, FIFA has imposed that in a group of four, the last two matches must be played simultaneously.<\/p>\n"],"rendered":"\n

Such was the case with the famous \"Disgrace of Gij\u00f3n<\/a>\" a game between West Germany and Austria during the 1982 World Cup. Both teams knew that a 1-0 or 2-0 win for West Germany would see them through, at the expense of Algeria, who had already played their final group match against Chile the day before. As soon as the West Germans scored a quick goal, the two teams stopped attacking each other completely, offering a pitiful spectacle of passes between central defenders for 80 minutes. Since then, to limit the risk of collusion, FIFA has imposed that in a group of four, the last two matches must be played simultaneously.<\/p>\n"},{"blockName":"core\/paragraph","attrs":{"align":"","content":"Of course, this is impossible with groups of three. A probabilistic model quantified the risk of collusion in this format and showed, in articles published in the New York Times and Le Monde as early as June 2018 and in the academic publication Journal of Sports Analytics, that this risk was very high, raising serious concerns about its suitability for the World Cup, soccer, and indeed sport in general, since the uncertainty of the outcome is the very basis of the popularity of sporting events. This paper won second prize in the \"Best Research Paper Award\" at the 2021 MIT Sloan Sports Conference, the world's biggest quantitative sports analysis conference, held each year by MIT.","dropCap":false,"placeholder":"","direction":"","lock":[],"metadata":[],"className":"","style":"","backgroundColor":"","textColor":"","gradient":"","fontSize":"","fontFamily":"","borderColor":"","anchor":""},"innerBlocks":[],"innerHTML":"\n

Of course, this is impossible with groups of three. A probabilistic model quantified the risk of collusion in this format and showed, in articles published in the New York Times<\/a> and Le Monde<\/a> as early as June 2018 and in the academic publication Journal of Sports Analytics<\/a>, that this risk was very high, raising serious concerns about its suitability for the World Cup, soccer, and indeed sport in general, since the uncertainty of the outcome is the very basis of the popularity of sporting events. This paper won second prize in the \"Best Research Paper Award\" at the 2021 MIT Sloan Sports Conference, the world's biggest quantitative sports analysis conference, held each year by MIT.<\/p>\n","innerContent":["\n

Of course, this is impossible with groups of three. A probabilistic model quantified the risk of collusion in this format and showed, in articles published in the New York Times<\/a> and Le Monde<\/a> as early as June 2018 and in the academic publication Journal of Sports Analytics<\/a>, that this risk was very high, raising serious concerns about its suitability for the World Cup, soccer, and indeed sport in general, since the uncertainty of the outcome is the very basis of the popularity of sporting events. This paper won second prize in the \"Best Research Paper Award\" at the 2021 MIT Sloan Sports Conference, the world's biggest quantitative sports analysis conference, held each year by MIT.<\/p>\n"],"rendered":"\n

Of course, this is impossible with groups of three. A probabilistic model quantified the risk of collusion in this format and showed, in articles published in the New York Times<\/a> and Le Monde<\/a> as early as June 2018 and in the academic publication Journal of Sports Analytics<\/a>, that this risk was very high, raising serious concerns about its suitability for the World Cup, soccer, and indeed sport in general, since the uncertainty of the outcome is the very basis of the popularity of sporting events. This paper won second prize in the \"Best Research Paper Award\" at the 2021 MIT Sloan Sports Conference, the world's biggest quantitative sports analysis conference, held each year by MIT.<\/p>\n"},{"blockName":"core\/paragraph","attrs":{"align":"","content":"As part of a \"Modeling, Programming, Simulation\" project with Nathan Fredholm and Simon Guipaud, two students at \u00c9cole des Ponts ParisTech, we proposed two alternative formats and demonstrated that they would entail a lower risk of collusion: (a) 12 groups of four, (b) eight groups of six, each group of six being divided into two sub-groups of three in cross-competition (the classic format with groups of six is not feasible: the group phase would last too long). Following direct exchanges with FIFA, it finally decided in March 2023 to change the format it had initially adopted, precisely to limit the risk of collusion. As suggested back in June 2018 in the New York Times article, the 48 teams will ultimately be divided into 12 groups of four, with the eight best third-place finishers joining the 24 first- and second-place finishers to form the Round of 16. It is commendable that FIFA had the wisdom, based on these studies, to recognize its initial error and choose a fairer format, which encourages teams to play their best to win every match, minimizes the risk of repeating \"Disgrace of Gij\u00f3n\", and will offer the finest spectacle to hundreds of millions of soccer fans around the world.","dropCap":false,"placeholder":"","direction":"","lock":[],"metadata":[],"className":"","style":"","backgroundColor":"","textColor":"","gradient":"","fontSize":"","fontFamily":"","borderColor":"","anchor":""},"innerBlocks":[],"innerHTML":"\n

As part of a \"Modeling, Programming, Simulation\" project with Nathan Fredholm and Simon Guipaud, two students at \u00c9cole des Ponts ParisTech, we proposed two alternative formats and demonstrated that they would entail a lower risk of collusion: (a) 12 groups of four, (b) eight groups of six, each group of six being divided into two sub-groups of three in cross-competition (the classic format with groups of six is not feasible: the group phase would last too long). Following direct exchanges with FIFA, it finally decided in March 2023 to change the format it had initially adopted, precisely to limit the risk of collusion<\/a>. As suggested back in June 2018 in the New York Times article<\/a>, the 48 teams will ultimately be divided into 12 groups of four, with the eight best third-place finishers joining the 24 first- and second-place finishers to form the Round of 16. It is commendable that FIFA had the wisdom, based on these studies, to recognize its initial error and choose a fairer format, which encourages teams to play their best to win every match, minimizes the risk of repeating \"Disgrace of Gij\u00f3n\", and will offer the finest spectacle to hundreds of millions of soccer fans around the world.<\/p>\n","innerContent":["\n

As part of a \"Modeling, Programming, Simulation\" project with Nathan Fredholm and Simon Guipaud, two students at \u00c9cole des Ponts ParisTech, we proposed two alternative formats and demonstrated that they would entail a lower risk of collusion: (a) 12 groups of four, (b) eight groups of six, each group of six being divided into two sub-groups of three in cross-competition (the classic format with groups of six is not feasible: the group phase would last too long). Following direct exchanges with FIFA, it finally decided in March 2023 to change the format it had initially adopted, precisely to limit the risk of collusion<\/a>. As suggested back in June 2018 in the New York Times article<\/a>, the 48 teams will ultimately be divided into 12 groups of four, with the eight best third-place finishers joining the 24 first- and second-place finishers to form the Round of 16. It is commendable that FIFA had the wisdom, based on these studies, to recognize its initial error and choose a fairer format, which encourages teams to play their best to win every match, minimizes the risk of repeating \"Disgrace of Gij\u00f3n\", and will offer the finest spectacle to hundreds of millions of soccer fans around the world.<\/p>\n"],"rendered":"\n

As part of a \"Modeling, Programming, Simulation\" project with Nathan Fredholm and Simon Guipaud, two students at \u00c9cole des Ponts ParisTech, we proposed two alternative formats and demonstrated that they would entail a lower risk of collusion: (a) 12 groups of four, (b) eight groups of six, each group of six being divided into two sub-groups of three in cross-competition (the classic format with groups of six is not feasible: the group phase would last too long). Following direct exchanges with FIFA, it finally decided in March 2023 to change the format it had initially adopted, precisely to limit the risk of collusion<\/a>. As suggested back in June 2018 in the New York Times article<\/a>, the 48 teams will ultimately be divided into 12 groups of four, with the eight best third-place finishers joining the 24 first- and second-place finishers to form the Round of 16. It is commendable that FIFA had the wisdom, based on these studies, to recognize its initial error and choose a fairer format, which encourages teams to play their best to win every match, minimizes the risk of repeating \"Disgrace of Gij\u00f3n\", and will offer the finest spectacle to hundreds of millions of soccer fans around the world.<\/p>\n"}],"seo":{"title":"Using mathematics for a fairer FIFA World Cup"},"media":{"img":"\"\"","src":"https:\/\/ingenius.ecoledesponts.fr\/wp-content\/uploads\/2023\/10\/fauzan-saari-AmhdN68wjPc-unsplash-scaled.jpg"},"url":"\/en\/articles\/using-mathematics-for-a-fairer-fifa-world-cup\/","related":{"post":[],"author":[{"title":"Julien Guyon","url":"\/en\/authors\/julien-guyon\/","id":"4747","media":"\"\"","slug":"julien-guyon"}],"subject":[{"title":"Economics & Society","url":"\/en\/subjects\/economics-society\/","id":"124","media":"\"\"","slug":"economics-society"},{"title":"Digital Technology, Modeling & Artificial Intelligence","url":"\/en\/subjects\/digital-technology-modeling-artificial-intelligence\/","id":"690","media":"\"\"","slug":"digital-technology-modeling-artificial-intelligence"}],"category":[{"title":"Articles","url":"\/en\/articles\/category\/articles\/","id":"1716","media":"","slug":"articles","_related_post_type":""}],"folder":[]},"translated":"https:\/\/ingenius.ecoledesponts.fr\/articles\/coupe-du-monde-de-football-les-mathematiques-au-service-de-lequite-sportive\/","icon":"icon-article","duration":"6","custom_excerpt":"The FIFA World Cup, one of the world\u2019s most watched sporting events, has long been marred by problems of fairness. However, mathematicians, including those at the Centre d'Enseignement et de Recherche en Math\u00e9matiques et Calcul Scientifique<\/em> (CERMICS), have successfully quantified these biases and offered fairer solutions, prompting the F\u00e9d\u00e9ration Internationale de Football Association<\/em> to review the rules governing the World Cup draw and the method of calculating the FIFA rankings as well as the format of the next tournament in 2026.","duration_type":"","_links":{"self":[{"href":"https:\/\/ingenius.ecoledesponts.fr\/en\/wp-json\/wp\/v2\/posts\/4745","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ingenius.ecoledesponts.fr\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ingenius.ecoledesponts.fr\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ingenius.ecoledesponts.fr\/en\/wp-json\/wp\/v2\/users\/6"}],"replies":[{"embeddable":true,"href":"https:\/\/ingenius.ecoledesponts.fr\/en\/wp-json\/wp\/v2\/comments?post=4745"}],"version-history":[{"count":2,"href":"https:\/\/ingenius.ecoledesponts.fr\/en\/wp-json\/wp\/v2\/posts\/4745\/revisions"}],"predecessor-version":[{"id":4757,"href":"https:\/\/ingenius.ecoledesponts.fr\/en\/wp-json\/wp\/v2\/posts\/4745\/revisions\/4757"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/ingenius.ecoledesponts.fr\/en\/wp-json\/wp\/v2\/media\/4577"}],"wp:attachment":[{"href":"https:\/\/ingenius.ecoledesponts.fr\/en\/wp-json\/wp\/v2\/media?parent=4745"}],"wp:term":[{"taxonomy":"article-types","embeddable":true,"href":"https:\/\/ingenius.ecoledesponts.fr\/en\/wp-json\/wp\/v2\/article-types?post=4745"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}