The World Football Elo Rating System

The World Football Elo Ratings are based on the Elo rating system, developed by Dr. Arpad Elo. This system is used by FIDE, the international chess federation, to rate chess players. In 1997 Bob Runyan adapted the Elo rating system to international football and posted the results on the Internet. He was also the first maintainer of the World Football Elo Ratings web site. The system was adapted to 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.

These ratings take into account all international "A" matches for which results could be found. 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 International Football 1872 - Present web site maintained by Raoul S. da Silva Curiel. Other sources are listed on the football links page. If you wish to be notified by e-mail every time the ratings are updated, use the sign-up form.

The ratings are based on the following formulas:

R_n = R_o + K × (W - W_e)

R_n is the new rating, R_o is the old (pre-match) rating.

K is the weight constant for the tournament played:

K is then adjusted for the goal difference in the game. It is increased by half if a game is won by two goals, by 3/4 if a game is won by three goals, and by 3/4 + (N-3)/8 if the game is won by four or more goals, where N is the goal difference.

W is the result of the game (1 for a win, 0.5 for a draw, and 0 for a loss).

W_e is the expected result (win expectancy), either from the chart or the following formula:

W_e = 1 / (10^(-dr/400) + 1)

dr equals the difference in ratings plus 100 points for a team playing at home.