Model

The Elo rating system in football: strengths and blind spots

Published 2026-09-01

Borrowed from chess and adapted by football analysts decades ago, the Elo rating system in football is the most widely copied rating method in the sport — a single number per team, updated after every match, from which a win probability can be read directly. Its appeal is that you can implement it in twenty lines of code and understand every one of them. Its danger is the same thing: it is simple enough that people forget how much it leaves out.

This post walks through the arithmetic with hypothetical ratings, then does the part most explainers skip — the places where a one-number rating stops being enough, and how to check whether an Elo model is actually any good.

Where the number comes from

Every team carries a rating, conventionally starting near 1500. Only the difference between two ratings matters. That difference is converted into an expected score with a logistic curve:

E = 1 / (1 + 10^(-d / 400))

where d is the rating gap. The 400 is a scale constant: it defines a 400-point gap as ten-to-one odds. Run a few gaps through it:

Note the word score, not win probability. Elo’s expected score is a points-per-match figure on a 0–1 scale, where a draw counts 0.5. That distinction is the single most misread thing about Elo in football, and the rest of this post keeps coming back to it.

How the Elo rating system in football updates after a match

After the match, each team’s rating moves by the gap between what happened and what was expected:

R_new = R_old + K × (S − E)

S is the actual result — 1 for a win, 0.5 for a draw, 0 for a defeat. K sets how fast ratings react. Take a side rated 100 points above its opponent, so E = 0.64, with K = 20:

• Win: 20 × (1 − 0.64) = +7.2 points
• Draw: 20 × (0.5 − 0.64) = −2.8 points
• Defeat: 20 × (0 − 0.64) = −12.8 points

The system is self-correcting by construction. Beating a team you were expected to beat earns almost nothing; losing to them is expensive. Ratings can only rise by outperforming the model’s own expectations.

Football versions add two adjustments to that skeleton:

• Home advantage is applied before the expectation is computed, by adding a fixed number of rating points — typically 50 to 100 — to the home side. Add 65 points to an otherwise even fixture and the home team’s expected score becomes 0.592, which is roughly the share of points home teams collect across a season in most European leagues.
• Margin of victory scales K. A 4–0 win is stronger evidence than a 1–0 win, so implementations multiply the update by a goal-difference factor — commonly 1.5 for a two-goal margin, rising gently from there. The multiplier is kept modest on purpose: blowouts are noisy, and letting them dominate makes ratings jump around.

Choosing K is a genuine trade-off, not a detail. Too low and ratings lag real changes in team strength for months. Too high and they chase noise, treating one bad afternoon as new information about a squad. Values in the 20–30 range are typical for league football, and the right way to pick one is to test it out of sample, not to argue about it.

The draw problem

Here is where football breaks the chess inheritance. Chess has draws too, but Elo never needed to price them separately — the expected score was the whole answer. Football markets ask for three numbers, and an expected score does not contain three numbers.

Suppose Elo gives a home side an expected score of 0.59. Both of these are consistent with it:

• 59% win, 0% draw, 41% loss
• 40% win, 38% draw, 22% loss

Same expected score, wildly different 1X2 markets. Elo alone cannot tell you which one you are looking at, because that information was never in the rating gap. Every football Elo model that quotes 1X2 probabilities has bolted on a separate assumption to split the expected score — usually a draw function fitted empirically, where draw probability peaks when the teams are evenly matched and falls away as the gap widens.

That bolt-on is doing real work, and it is where the model’s accuracy on draws lives. Anyone publishing Elo-derived 1X2 numbers should be able to say what their draw function is. If they cannot, the probabilities are guesswork wearing a formula.

What a single rating cannot price

The deeper limitation is dimensionality. Elo compresses a team into one number, so it cannot distinguish two sides that are equally good in different ways: a team that wins 3–2 and a team that wins 1–0 can converge on the same rating despite being nothing alike.

That matters the moment you leave the match-result market. Goals markets need a distribution over scorelines, not a strength ranking:

• Over/under 2.5 goals needs the total-goals distribution, which depends on both teams’ attacking and defensive tendencies separately.
• Both teams to score needs the joint probability that each side scores at least once — again a scoreline question, not a strength question.
• Correct score needs the full grid.

None of those can be derived from a rating gap. This is why goals-based models — Poisson with a Dixon-Coles correction, and its descendants — estimate separate attack and defence ratings per team and produce a scoreline grid: from a grid you can price every market at once, consistently. Elo gives you one market and an expected score.

Two further blind spots are worth naming. Elo carries no measure of its own uncertainty: a newly promoted club with six matches on record and an established side with two hundred can hold identical ratings, and the system treats both with equal confidence. And ratings do not transfer across leagues unless the leagues are linked by matches between them, which in domestic football they mostly are not — a 1600 in one division and a 1600 in another are not comparable numbers.

How to judge an Elo model honestly

The test is the same one that applies to any prediction method, and it is not “how many results did it call correctly”. Accuracy on the favourite says almost nothing, because the favourite wins often regardless of who is doing the picking.

Score the probabilities instead. A Brier score measures squared error against outcomes and rewards being confident only when confidence is warranted. Then check calibration separately: bucket every fixture the model rated near 60%, and see whether the home side actually won close to 60% of them. A model can rank teams beautifully and still be badly calibrated — Elo systems with an aggressive K often are, producing probabilities that swing further than reality does.

Both checks require one thing to be meaningful: predictions recorded before kick-off and kept afterwards, wins and losses alike.

Where Elo sits in our model

Our published methodology is a Dixon-Coles goals model with time decay, with Elo-style ratings as a second signal rather than the primary engine — the reasoning and the inputs are set out on the how it works page. The goals model produces the scoreline grid every market is priced from; the rating signal contributes to team strength. That split follows directly from the limitation above: a rating system answers “who is better”, and a scoreline model answers “what is likely to happen”, and only the second question prices a football card.

Whether that combination earns its keep is not something we would ask you to take on trust. Every prediction is graded after full time and kept permanently, so the consequences show up in the public track record rather than in a description of the method. That is the standard any Elo model — ours, or the one behind a rating table you found online — should be held to.