Guide
Poisson models for football
The Poisson distribution models how often a rare, roughly independent event happens in a fixed interval. Football goals fit the shape well enough that Poisson remains the backbone of most public prediction models.
Published 2026-08-25 · Last reviewed 2026-08-25 · BetBuddy editorial
From expected goals to scorelines
Give each side an expected goals value derived from attack strength, opponent defence and home advantage. The Poisson formula then returns the probability of each exact number of goals, and multiplying the two sides gives every scoreline.
P(k goals) = (λ^k × e^−λ) / k!
Worked example
With λ_home = 1.6 and λ_away = 1.1: P(home scores 1) = 0.323, P(away scores 1) = 0.366, so a 1-1 draw is 0.323 × 0.366 ≈ 11.8%. Summing all scorelines where the home side scores more gives the 1X2 home probability.
Known limitations
Basic Poisson treats the two teams as independent and under-predicts draws and 0-0s. Real matches are correlated: a red card or an early goal changes both sides at once. A model used on its own, without calibration against market prices, will be confidently wrong on exactly the fixtures that matter.