Poisson Distribution
The Poisson distribution is a probability model that predicts the number of times an event occurs in a fixed period — a perfect fit for football, where goals are rare, near-independent events scattered across 90 minutes.
How Poisson powers football predictions
Given an expected goal rate (lambda, λ) for each team, Poisson outputs the probability of every possible scoreline: 0-0, 1-0, 1-1, 2-1, and so on. Sum the right cells of that scoreline matrix and you instantly get probabilities for every market — 1X2, BTTS, Over/Under, correct score, and Asian handicap.
Final3rd's Poisson + ML stack
Final3rd's core engine is a Poisson model where each team's λ is computed from xG, opposition xGA, home advantage, fatigue, weather, and recent form. A machine-learning layer adjusts the raw Poisson output for context the base model cannot see — like managerial changes, rotation, or motivation.
Frequently asked questions
Is Poisson accurate for football predictions?
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Pure Poisson assumes events are independent — but football goals are slightly correlated (a team leading is more likely to score again, etc). Modified Poisson models like Dixon-Coles correct for this and are the industry standard for serious modelling.