Poisson Football Calculator

Enter each team’s expected goals to model the match — 1X2 probabilities, fair odds, the most likely scorelines, over/under 2.5 and both-teams-to-score.

How it works

P(team scores k) = e^(−xG) × xG^k / k!
P(scoreline i–j) = P(home = i) × P(away = j)
home win = Σ P(i–j) for i > j   ·   draw = Σ i = j   ·   away = Σ i < j
fair odds = 1 / probability

Probabilities are computed over scorelines up to 6–6 and normalized to sum to 100%. This is a pure Poisson model — a strong baseline that ignores correlation and game state.

FAQ

What is the Poisson distribution used for in football?

It models how many goals a team is likely to score given its average (expected goals). Feeding both teams’ expected goals into a Poisson model gives the probability of every scoreline, which you can combine into 1X2, over/under and both-teams-to-score probabilities.

What should I enter for expected goals?

Each team’s expected goals (xG) for the match — your estimate of how many they’ll average. You can base it on season xG-for/against, recent form, or a rating model. Home teams usually get a small boost.

How do you get match odds from Poisson?

Compute the probability of each scoreline (home goals × away goals probabilities), then sum: home win = all scorelines where home > away, draw = equal, away win = away > home. Fair odds are 1 ÷ probability.

Is Poisson accurate for betting?

It’s a solid baseline and great for spotting value, but it assumes goals are independent and ignores context (red cards, game state, correlation). Sharp models refine it (e.g. Dixon-Coles adjusts low scores).

Does this include the vig?

No — these are fair, vig-free probabilities and odds straight from the model. Compare them to a book’s price to find value; add the margin back with our Hold calculator if you want to see a “with-vig” line.

What’s a good expected-goals gap?

The bigger the xG difference, the more one-sided the match. Two evenly-matched teams (e.g. 1.4 vs 1.3) produce a high draw probability; a 2.2 vs 0.8 gap makes a home win far more likely.

Educational tool only. Not betting advice or a guarantee of profit. A Poisson model is a simplification of a real match.