The World Football Elo Ratings is a ranking system for men's national teams in association football. The method used to rank teams is based upon the Elo rating system method but modified to take various football-specific variables into account. Elo should not be confused with the FIFA World Rankings, which is more prevalent because it is the official rating system used by the international governing body of football to rank national teams.
This system, developed by Hungarian-American mathematician Dr. Árpád Élő, is used by FIDE, the international chess federation, to rate chess players, and by the European Go Federation, to rate Go players. In 1997 Bob Runyan adapted the Elo rating system to international football and posted the results on the Internet.
FootballDatabase uses the adapted Elo Rating formula and applies it to a number of important football club competitions around the globe, with the aim to provide fans a mathematical ranking of World Football Clubs.
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 factors taken into consideration when calculating a team's new rating are:
The different weights of international competitions in descending order are:
The different weights of national competitions (only top-tier league in each country is analyzed) in descending order are:
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 should be considered provisional. Match data are primarily from matches after January 01, 2009.
The basic principle behind the Elo ratings is only in its simplest form similar to that of a league, unlike the FIFA tables who effectively run their table as a normal league table, but with weightings to take into account the other factors, the Elo system has its one formula which takes into account the factors mentioned above. There is no first step as in the FIFA system where a team immediately receives points for the result, there is just one calculation in the Elo system.
The ratings are based on the following formulae:
R_n = R_o + K*G (W - W_e)
Where;
R_n = The new team rating
R_o = The old team rating
K = Weight index regarding the tournament of the match
G = A number from the index of goal differences
W = The result of the match
W_e = The expected result
The status of the match is incorporated by the use of a weight constant. The weight is a constant regarding the "weight" or importance of a match, defined by which tournament the match is in, they are as follows;
The FIFA Club World Cup, UEFA Champions League and Copa Libertadores weight the same:
AFC Champions League, CAF Champions League, CONCACAF Champions League, Europa League, the Copa Sudamericana and the OFC Champions League*:
For national leagues as follows:
The number of goals is taken into account by use of a goal difference index. G is increased by half if a game is won by two goals, and if the game is won by three or more goals by a number decided through the appropriate calculation shown below;
If the game is a draw or is won by one goal
G = 1
If the game is won by two goals
G = 1,5
If the game is won by three or more goals
G = (11+N)/8
Where N is the goal difference
Result of match - Obtaining the W valueW is the result of the game (1 for a win, 0.5 for a draw, and 0 for a loss).
Expected result of match - Obtaining the W_e valueW_e is the expected result (win expectancy with a draw counting as 0.5) from the following formula:
W_e = 1 / (10^(-dr/400) + 1)
Where dr equals the difference in ratings plus 100 points for a team playing at home. 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.
Initial ranking - Obtaining the W_o value for new teamsWhen a new team is promoted to the top division, its initial ranking W_o will be given depending on the strength of the league that this team belongs to. For example if a new team is promoted in England, its ranking will be 1500, in France 1450, in Netherlands 1400, in Greece 1350 and so on until 1250 for leagues with K = 5.
With information from: