FIFA introduces an Elo system

From chess to football

The usual chess rating system for evaluating the playing strength of chess players conceived by Prof. Arpad Elo is now increasingly used in other sports, sometimes in a slightly modified version adapted to the particular sport. For example, the Elo system also forms the basis for calculating the rankings in some table tennis associations.

Even in football, the formula developed by Elo is used as the basis for rankings. The ranking of women's national teams was determined by FIFA from the beginning, which was in 2003, officially based on the Elo formula. For this list, all women's matches since April 17th 1971 were considered. On this day, the first women's international match recognized by FIFA was played between France and the Netherlands. When calculating the Elo numbers for the women's national football teams, the importance of the game is taken into account, which is not a concept known in chess. The scored underlying the result is also included in the calculation.

Current FIFA Women's ranking (Top 20)

So far, FIFA has used a different basis for calculating its world ranking in men's football. On the one hand, the formula was quite complex, on the other hand, it was not well thought-out in some aspects and sometimes led to strange effects. As a result, the FIFA ranking has often been heavily criticized over the years.

Current FIFA Rankings (left) vs Unofficial football Elo list

In addition to the official FIFA ranking, unofficial leaderboards have also been run according to Elo, for national teams and also for club teams. As you can see (above right), the calculation according to Elo differs in part from the FIFA list, although the placement seems more "intuitively" plausible after the Elo calculation. More than a few football experts, for example, consider the Spanish national team stronger than the Swiss — with all due respect to the ever-improving skills of the Swiss football players.

The "Elo" numbers on this list seem a bit strange to the chess player because the values move in a different, lower range than chess. For chess fans, the numbers that Roman Korba produced in his calculation for the Bundesliga clubs last season are a little more familiar.

Ratings for the German League Teams

Last Sunday, FIFA announced that it will introduce a new ranking system based on the Elo formula following the 2018 World Cup, which started today in Russia, in line with the women's football system.

A group of experts has developed the new system with the aim of "... simplifying and refining the formula, eliminating opportunities to manipulate the rankings and giving all teams the same opportunity to improve their ranking".

New Formula

The rankings should now be calculated according to the following formula:

After a game P, the score of a team is calculated as follows:

Where P old stands for the score before the game. Initially, the score is used according to the old calculation method.

The following applies:

I - stands for the weighting of the game. These range from 5 for friendly matches played outside international windows to 60 for World Cup final rounds starting from the quarter-finals. 
W - is the score with: 
1 = win 
0.5 = draw 
0 = defeat

W e is the expected result, based on the scores P old of both teams A and B before the game: 

Since 1992, there have been no rankings. Recently, however, it has become increasingly important, not least because FIFA has used the rankings for the determination of the playing groups at World Cup.

Incidentally, the opening match is being played as we write, between host Russia and Saudi Arabia.

Translation from German: Macauley Peterson

Links

• Arpad Elo
• FIFA Wordcup