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France: Worthy Winners. But Here's What The Statistics Say About Who's Best In World Cup History

France has been crowned football champions of the world, after beating Croatia 4-2 in a thrilling World Cup final. Les Bleus timed their run to perfection, having been unconvincing in the group stage, with narrow wins over Australia and Peru and a draw with Denmark, but stepping it up in the knockout stages, sweeping aside Argentina, Uruguay, Belgium and Croatia to lift the trophy.

France's success was all the more impressive given that they battled through what was widely considered to be the much tougher half of the draw. But how did their route to victory compare to previous World Cup winners?

We can compare France 2018 to every other World Cup winner using a "tournament performance rating" (TPR), based on the Elo rating system which is commonly used in a number of sports and games.

The Elo system was devised by Hungarian physicist Arpad Elo for ranking chess players. The system was adopted by the world chess federation FIDE in 1970 and has since been adopted by a number of other sports, including soccer.

The FIFA Women's World Rankings are based on an Elo system, and the men's rankings will also move to an Elo system in August.

This ranking system adds points for every victory and subtracts points for every defeat based on the relative strengths of the opponents. Teams gain more points for beating a higher-rated opponent than they do for beating a lower-ranked side.

TPR can be used to evaluate how well a player or team performed during a particular event. The rating is based on the following simple formula: TPR = average opponent rating + result adjustment.

The average opponent rating is as simple as it sounds - you add up the pre-tournament Elo ratings of all the opponents you faced during the tournament and divide by the number of games played.

The result adjustment is a value which is added or subtracted depending on the team's results during the competition. A team which wins every game will receive the maximum adjustment of 800 points while a team which loses every game would be deducted 800 points. A team which wins as many games as it loses has an adjustment of zero. The adjustments are based on the same mathematical formula which is used to calculate the Elo ratings. For more information, see Section 8 here.

We can therefore calculate France's 2018 World Cup TPR as follows. During the tournament the team faced Australia (rating 1742), Peru (1915), Denmark (1856), Argentina (1985), Uruguay (1893), Belgium (1939) and Croatia (1853), giving an average opponent rating of 1883. During the tournament, France won six matches and drew one (against Denmark in the group stage), which corresponds to a score of 6.5/7 - or 93%. Using the Elo formula, this corresponds to a result adjustment of 422 points. Therefore France's 2018 World Cup TPR was 1883 + 422 = 2305.

Best Team Ever

This calculation can then be repeated for every team at each of the 21 World Cup tournaments which have been held to date, allowing us to directly compare performances across different tournaments. Note that matches which went to a penalty shootout were counted as draws.

In order to reward teams who progressed through the tournament, each team's performance was based on the maximum number of matches which they could have played. For example, Germany was knocked out in the group stage in 2018, having picked up one win and two defeats. They were given a score of 1/7 rather than 1/3, since they could have played seven matches had they progressed to the final.

The table below shows the top 20 best performances in World Cup history. The list is unsurprisingly topped by the legendary Brazil 1970 side featuring Pele, Jairzinho and Carlos Alberto.

Brazil also occupy second place with their 2002 side featuring the three Rs: Ronaldo, Rivaldo and Ronaldinho.

This year's French team sits in sixth place, six positions better off than their 1998 side, due to facing more difficult opponents. England's 1966 side find themselves in the ninth spot, partly due to having drawn with Uruguay in their opening game of the tournament.

The highest-ranked non-winners are Poland's 1974 side, who were unfortunate to miss out on the final after finishing runners-up to Germany in the second group stage. The Poles actually obtained a higher performance rating than Germany, having faced higher-rated opponents in the first round, when they won a group containing Italy and Argentina. The worst ranked winners were Germany's 1990 side, who are 28th on the list with a TPR of 2134.



Top 20 tournament performance ratings in World Cup history. *Did not win tournament.

Similar to the video assistant referee (VAR) system introduced at this World Cup, the tournament performance rating is not without its flaws, and is unlikely to ever fully settle any pub debates. But it provides a fairly simple method of comparing teams across different World Cups based on their results and the difficulty of their matches. In the aftermath of the final, France are widely regarded as deserving winners who compared favorably to previous world champions - and the numbers seem to agree.

Craig Anderson is a lecturer in statistics at the University of Glasgow. This article was originally published on The Conversation.

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