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:

Rn = Ro + K × (W - We)

Rn is the new rating, Ro 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).

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

We = 1 / (10(-dr/400) + 1)

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

Sample Winning Expectancies
Difference
in Ratings
Higher
Rated
Lower
Rated
00.5000.500
100.5140.486
200.5290.471
300.5430.457
400.5570.443
500.5710.429
600.5850.415
700.5990.401
800.6130.387
900.6270.373
1000.6400.360
1100.6530.347
1200.6660.334
1300.6790.321
1400.6910.309
1500.7030.297
1600.7150.285
1700.7270.273
1800.7380.262
1900.7490.251
2000.7600.240
2100.7700.230
2200.7800.220
2300.7900.210
2400.7990.201
2500.8080.192
2600.8170.183
2700.8260.174
2800.8340.166
2900.8410.159
3000.8490.151
3250.8670.133
3500.8820.118
3750.8960.104
4000.9090.091
4250.9200.080
4500.9300.070
4750.9390.061
5000.9470.053
5250.9540.046
5500.9600.040
5750.9650.035
6000.9690.031
6250.9730.027
6500.9770.023
6750.9800.020
7000.9830.017
7250.9850.015
7500.9870.013
7750.9890.011
8000.9900.010