The Poisson Model: How to Predict Football Scores and Odds

If you want to price a football match yourself — correct scores, 1X2, over/under — the Poisson distribution is the classic starting point. It's the model behind a huge share of the odds you see, and once you understand it you can turn two numbers into a full set of probabilities.

Why Poisson fits football

Goals are rare, roughly independent events that happen at a fairly steady rate — exactly the conditions the Poisson distribution describes. If a team is expected to score λ goals (its expected goals, or xG), Poisson gives the probability of them scoring 0, 1, 2, 3… goals.

From xG to a score matrix

Estimate each team's expected goals — from an xG data source, or by averaging goals scored and the opponent's goals conceded, adjusted for home advantage. Then the probability of a scoreline h–a is simply:

P(home = h) × P(away = a)

Do that for every plausible scoreline and you have the full score matrix. Sum the relevant cells and you get every derived market:

• 1X2: home win = all cells where home > away; draw = the diagonal; away win = the rest.
• Over/Under 2.5: add up every cell where the goals total is 3 or more.
• Correct score: read the individual cells directly.

Our free correct score & Poisson calculator builds the whole matrix from two xG figures and returns the most likely scores, 1X2 and over/under with fair odds.

Turning probabilities into fair odds

Fair odds are just 1 / probability. If the model says a 1–1 draw is 11.8% likely, the fair price is 1 / 0.118 = 8.47. Compare that to the bookmaker's price (after you remove the vig) and you've found value whenever the market is longer than your fair number.

Where basic Poisson falls short

Vanilla Poisson assumes goals are independent and ignores game state, so it slightly under-predicts draws and 0–0s. Pros add adjustments (Dixon–Coles, correlation terms) to fix this. But as a baseline — and a way to sanity-check a price — the Poisson model is hard to beat for the effort.