국가대표 축구 ELO 레이팅 시스템

국가대표 축구 ELO 레이팅 시스템

http://www.eloratings.net/system.html

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 - Presentweb 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:

• 60 for World Cup finals;
• 50 for continental championship finals and major intercontinental tournaments;
• 40 for World Cup and continental qualifiers and major tournaments;
• 30 for all other tournaments;
• 20 for friendly matches.

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.

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