Elo rating system
The Elo rating system is a ranking method created by Arpad Elo for chess: each team has a number of points, the gap between two teams gives the expected result of their match, and after every game the points are updated according to the difference between the actual and the expected result.
Devised by the physicist and chess player Arpad Elo, and adopted by the International Chess Federation in 1970, the system rests on two formulas. A’s expected result against B is E = 1 / (1 + 10^(−Δ/400)), where Δ is the rating gap. After the match, R' = R + K × (S − E), with S = 1 for a win, 0.5 for a draw and 0 for a defeat. Beating a higher-rated opponent earns a lot; beating a weaker one earns little.
In football, the reference for national teams is the World Football Elo Ratings. There, the K factor depends on what is at stake: 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 friendlies. K is increased by half for a win by 2 goals, by 3/4 for 3 goals and by 3/4 + (N − 3)/8 beyond that; the home team gets a 100-point bonus in the calculation.
Since 2018, the men’s FIFA ranking has also used a formula derived from Elo. The system’s strengths: simplicity, automatic updates and allowance for the opponent’s strength. Its limits: it only looks at results and goal difference, not chance quality (xG), absences or squad changes, and it is slow to react when a team improves or declines quickly.
Example
Team A (1,600 points) plays B (1,500 points): Δ = 100, so E = 1 / (1 + 10^(−0.25)) ≈ 0.64. A is « worth » 64% of the points at stake, a draw counting as half: this is not its probability of winning. With K = 20 (a friendly), a win earns A 20 × (1 − 0.64) ≈ 7.2 points (1,607.2) and B loses the same; a draw costs A 2.8 points; a win for B earns it 12.8 points.
How Elofoot uses it
Despite its name, Elofoot doesn't compute an Elo rating. The starting idea is the same — measuring the relative strength of two teams — but the method differs: the model combines actual xG, recent form, points per game in the table and division strength, then goes through a Poisson distribution to get the probability of every score. It therefore accounts for the quality of chances, not just results.
Frequently asked questions
- How is an Elo rating calculated?
- Before the match, the expected result E = 1 / (1 + 10^(−Δ/400)) is worked out from the rating gap Δ. Afterwards, each team gains or loses K × (actual result − E) points, the actual result being 1, 0.5 or 0.
- Does the FIFA ranking use the Elo method?
- Yes for the men since 2018: FIFA adopted a formula derived from Elo, with weightings according to the importance of the match. The World Football Elo Ratings, independent of FIFA, has applied the Elo method to national teams for much longer.
- Does an expected result of 64% mean a 64% chance of winning?
- No. E is the expected share of the points at stake, with a draw counting as half. The win probability is lower, since part of that 64% comes from draws.
- Does Elofoot use an Elo rating?
- No, despite its name. Elofoot estimates the relative strength of teams from xG, form, league position and division strength, then calculates its probabilities with a Poisson distribution.
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