Football Poisson Calculator (Match Score & 1X2 Probabilities)

How it works

P(team scores k) = e^(−λ) λᵏ ÷ k! · P(score i-j) = P_home(i) × P_away(j) (independent) · home win = Σ P(i > j), draw = Σ P(i = j), away = Σ P(i < j) · both teams to score = (1 − e^(−λh))(1 − e^(−λa)) · fair odds = 1 ÷ probability

The Poisson model (Maher, 1982) treats each team's goals as independent random events with an average rate λ — its expected goals for this match. Multiplying the two Poisson distributions gives the probability of every scoreline, which adds up to home-win, draw, away-win, totals and both-teams-to-score probabilities. A common way to get λ is attack strength × opponent defence weakness × league average goals, or a match xG projection. The basic model slightly underestimates draws and low scores (the Dixon–Coles adjustment corrects this), so treat the fair odds as a starting point, not a certainty.

Worked example

With the home side expected to score 1.6 goals and the visitors 1.1, the model gives a home win 48.96%, a draw 24.89% and an away win 26.15% — fair odds of about 2.04 / 4.02 / 3.82. Over 2.5 goals is 50.64%, both teams score 53.24% of the time, and the most likely score is 1-1 (11.83%).

Sources: Maher (1982) — Modelling association football scores, Statistica Neerlandica · Dixon & Coles (1997) — Modelling association football scores and inefficiencies in the football betting market

Frequently asked questions