World Football Elo Ratings
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The World Football Elo Ratings are a ranking system for men's national
association football Association football, more commonly known as football or soccer, is a team sport played between two teams of 11 players who primarily use their feet to propel the ball around a rectangular field called a pitch. The objective of the game is ...
teams that is published by the website eloratings.net. It is based on the
Elo rating system The Elo rating system is a method for calculating the relative skill levels of players in zero-sum games such as chess. It is named after its creator Arpad Elo, a Hungarian-American physics professor. The Elo system was invented as an improved ch ...
but includes modifications to take various football-specific variables into account, like the margin of victory, importance of a match, and home field advantage. Other implementations of the Elo rating system are possible and there is no single nor any official Elo ranking for football teams. Since being developed, the Elo rankings have been found to have the highest predictive capability for football matches. FIFA's official rankings, both the
FIFA World Rankings The FIFA Men's World Ranking is a ranking system for men's national teams in association football, led by Brazil . The teams of the men's member nations of FIFA, football's world governing body, are ranked based on their game results with the ...
for men and the
FIFA Women's World Rankings The FIFA Women's World Rankings for Association football, football were introduced in 2003, with the first rankings published on 16 July of that year, as a follow-on to the existing FIFA World Rankings, Men's FIFA World Rankings. They attempt ...
are based on a modified version of the Elo formula, the men's rankings having switched away from FIFA's own system for matches played since June 2018.


History and overview

The Elo system, developed by Hungarian-American mathematician Árpád Élő, is used by
FIDE The International Chess Federation or World Chess Federation, commonly referred to by its French acronym FIDE ( Fédération Internationale des Échecs), is an international organization based in Switzerland that connects the various national c ...
, the international chess federation, to rate
chess Chess is a board game for two players, called White and Black, each controlling an army of chess pieces in their color, with the objective to checkmate the opponent's king. It is sometimes called international chess or Western chess to disti ...
players, and by the
European Go Federation The European Go Federation (EGF) is a non-profit organization with the purpose of encouraging, regulating, co-ordinating, and disseminating the playing of the board game Go in Europe. The EGF was founded in 1957, the same year that the inaugural ...
, to rate Go players. In 1997, Bob Runyan adapted the Elo rating system to international
football Football is a family of team sports that involve, to varying degrees, kicking a ball to score a goal. Unqualified, the word ''football'' normally means the form of football that is the most popular where the word is used. Sports commonly c ...
and posted the results on the Internet. He was also the first maintainer of the World Football Elo Ratings web site, currently maintained by Kirill Bulygin. Other implementations of the Elo rating system are possible.J. Lasek, Z. Szlávik and S. Bhulai (2013)
The predictive power of ranking systems in association football
, Int. J. Applied Pattern Recognition1: 27–46.
The Elo system was adapted for football by adding a weighting for the kind of match, an adjustment for the home team advantage, and an adjustment for goal difference in the match result. The ratings consider all official international matches for which results are available. Ratings tend to converge on a team's true strength relative to its competitors after about 30 matches. Ratings for teams with fewer than 30 matches are considered provisional.


Comparison with other systems

A 2009 comparative study of eight methods found that the implementation of the Elo rating system described below had the highest predictive capability for football matches, while the men's FIFA ranking method (2006–2018 system) performed poorly. The
FIFA World Rankings The FIFA Men's World Ranking is a ranking system for men's national teams in association football, led by Brazil . The teams of the men's member nations of FIFA, football's world governing body, are ranked based on their game results with the ...
is the official national teams rating system used by the international governing body of football. The FIFA Women's World Rankings system has used a modified version of the Elo formula since 2003. In June 2018, the FIFA ranking switched to an Elo-based ranking as well, starting from the current FIFA rating points.FIFA Council
2026 FIFA World Cup™: FIFA Council designates bids for final voting by the FIFA Congress
10 June 2018
The major difference between the World Football Elo Rating and the new men's FIFA rating system is that the latter does not consider goal differential and counts a
penalty shoot-out The penalty shootout is a method of determining a winner in sports matches that would have otherwise been drawn or tied. The rules for penalty shootouts vary between sports and even different competitions; however, the usual form is similar to pe ...
as a win/loss rather than a draw (neither method distinguishes a win in
extra time Overtime or extra time is an additional period of play specified under the rules of a sport to bring a game to a decision and avoid declaring the match a tie or draw where the scores are the same. In some sports, this extra period is played onl ...
from a win in regular time).FIFA council
Revision of the FIFA / Coca-Cola World Ranking
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Calculation principles

The ratings are based on the following formulae: :R_n = R_o + P where :P = K G (W - W_e) Where; "Points Change" is rounded to the nearest integer before updating the team rating.


Status of match

The status of the match is incorporated by the use of a weight constant. The constant reflects the importance of a match, which, in turn, is determined entirely by which tournament the match is in; the weight constant for each major tournament is: The FIFA adaptation of the Elo rating features 8 weights, with the knockout stages in the World Cup weighing 12 times more than some friendly matches.


Number of goals

The number of goals is taken into account by use of a goal difference index. If the game is a draw or is won by one goal :G = 1 If the game is won by two goals :G = \frac If the game is won by three or more goals: *Where N is the goal difference ( \forall N ≥ 3) :G = \frac Table of examples:


Result of match

W is the result of the game (1 for a win, 0.5 for a draw, and 0 for a loss). This also holds when a game is won or lost in extra time. If the match is decided on penalties, however, the result of the game is considered a draw (W = 0.5).


Expected result of match

We is the expected result (win expectancy with a draw counting as 0.5) from the following formula: :W_e = \frac where ''dr'' equals the difference in ratings (add 100 points for the home team). So ''dr'' of 0 gives 0.5, of 120 gives 0.666 to the higher-ranked team and 0.334 to the lower, and of 800 gives 0.99 to the higher-ranked team and 0.01 to the lower. The FIFA adaptation of the Elo rating does not incorporate a home team advantage and has a larger divisor in the formula (600 vs 400), making the points exchange less sensitive to the rating difference of two teams.


Examples for clarification

The same example of a three-team friendly tournament on neutral territory is used as on the
FIFA World Rankings The FIFA Men's World Ranking is a ranking system for men's national teams in association football, led by Brazil . The teams of the men's member nations of FIFA, football's world governing body, are ranked based on their game results with the ...
page. Beforehand team A had a rating of 630 points, team B 500 points, and teams C 480 points.
The first table shows the points allocations based on three possible outcomes of the match between the strongest team A, and the somewhat weaker team B: When the difference in strength between the two teams is less, so also will be the difference in points allocation. The next table illustrates how the points would be divided following the same results as above, but with two roughly equally ranked teams, B and C, being involved:


See also

* Statistical association football predictions


References


External links


Website
{{Sport world rankings Association football rankings Rating systems