Elo Ratings Simulator
Elo gives every team one number. The gap between two numbers says what each side should expect from the match, and every result nudges both numbers towards the truth. Chess invented it; football's world rankings use it.
Ratings from 1000 to 2200. An average side is about 1500.
Try an example
- Home win expectancy
- Away win expectancy
Rating gap after home advantage: points. Expectancy counts a draw as half a win.
| If the result is | Home | Away |
|---|---|---|
| Home win | ||
| Draw | ||
| Away win |
What one side gains, the other loses. Beating a stronger side earns more than beating a weaker one.
How it works
The home side's win expectancy comes from the rating gap, after adding home advantage:
$$E = \frac{1}{1 + 10^{-(R_{\text{home}} + H - R_{\text{away}})/400}}$$After the match, each rating moves by K times the difference between what happened and what was expected:
$$R_{\text{new}} = R_{\text{old}} + K\,(W - E)$$In plain football
- \(R\) is a team's rating and \(H\) is the home advantage, counted as extra rating points.
- \(E\) is the share of the points the home side should take, counting a draw as half.
- \(W\) is what actually happened: 1 for a win, ½ for a draw, 0 for a defeat.
- \(K\) sets how fast ratings react. Big K chases every result; small K is slow to believe a change.
What a rating gap means
| Gap, points | Stronger side's expectancy |
|---|---|
| 0 | 50.0% |
| 60 (a typical home advantage) | 58.5% |
| 100 | 64.0% |
| 200 | 76.0% |
| 400 | 90.9% |
A 400-point gap is ten to one: the stronger side expects ten times the share of points its opponent does.
Expectancy is not a win probability
A 60% expectancy might be 50% wins and 20% draws, or 60% wins and no draws at all. Elo alone can't tell you which. Models that need separate win, draw and loss chances, like the Elo model on the SPFL Prediction Board, add a second step that turns the rating gap into those three numbers. The research on evaluating prediction models shows how that version of Elo compares with the others.
Where it goes wrong
- It ignores the score. A 1–0 and a 6–0 move the ratings by the same amount here, though some football versions of Elo scale by goal difference.
- New or promoted teams start with a guessed rating and need several matches before it means much.
- One home advantage for every ground and every team is a simplification.
These figures come from a statistical model and are for analysis and education. Football remains uncertain and model predictions will frequently be wrong.