# World Football Elo Ratings System

Due to the critisim of the official FIFA world rankings system, alternative rankings systems have surfaced over the years. The most prominent of these awards is the World Football ELO rankings. As the name suggests the system is based of the ELO ranking system designed by Hungarian mathematician Dr. Árpád Élő to rank chess players. The system was adopted for Football by Bob Runyan in 1997.

The ratings take into account all international “A” matches for which results could be found. Per the Elo website:

“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.”

This indeed looks like a tedious rating system, and to some, it remains an absolute head-scratcher. Regardless, if you want to debate the world rankings, Dr. Élő gives you that option with his difficult-to-follow rating system. Here’s the formula:

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:

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).

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: 0, 10, 20

Higher Rated: 0.500, 0.514, 0.529

Lower Rated: 0.500, 0.486, 0.471

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