World Football Rating System

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

We 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
0 0.500 0.500
10 0.514 0.486
20 0.529 0.471
30 0.543 0.457
40 0.557 0.443
50 0.571 0.429
60 0.585 0.415
70 0.599 0.401
80 0.613 0.387
90 0.627 0.373
100 0.640 0.360
110 0.653 0.347
120 0.666 0.334
130 0.679 0.321
140 0.691 0.309
150 0.703 0.297
160 0.715 0.285
170 0.727 0.273
180 0.738 0.262
190 0.749 0.251
200 0.760 0.240
210 0.770 0.230
220 0.780 0.220
230 0.790 0.210
240 0.799 0.201
250 0.808 0.192
260 0.817 0.183
270 0.826 0.174
280 0.834 0.166
290 0.841 0.159
300 0.849 0.151
325 0.867 0.133
350 0.882 0.118
375 0.896 0.104
400 0.909 0.091
425 0.920 0.080
450 0.930 0.070
475 0.939 0.061
500 0.947 0.053
525 0.954 0.046
550 0.960 0.040
575 0.965 0.035
600 0.969 0.031
625 0.973 0.027
650 0.977 0.023
675 0.980 0.020
700 0.983 0.017
725 0.985 0.015
750 0.987 0.013
775 0.989 0.011
800 0.990 0.010