From goals to probabilities
The Poisson engine
5 min
Two expected-goals numbers aren't a prediction yet — "1.6 vs 1.1" doesn't directly tell you the chance of a home win. Turning expected goals into probabilities is the job of the Poisson model.
Why Poisson
Goals arrive at a roughly steady but random rate through a match, and the Poisson distribution is the standard maths for exactly that: how many rare, independent events land in a fixed window. Feed it a team's expected goals and it returns the probability of that team scoring 0, 1, 2, 3… goals.
Building the scoreline grid
The model runs Poisson for both sides and combines them into a grid of every plausible scoreline and how likely each is. From that single grid, the headline markets fall out by adding up the right cells:
- Home win — the cells where home goals exceed away goals.
- Draw — the cells where they're equal.
- Away win — the cells where away goals exceed home goals.
Those three sum to the 1X2 probabilities. The same grid gives Over/Under — add up every cell whose total goals clear (or miss) the 2.5 line. One expected-goals estimate quietly prices the whole board.
What comes out
The model stores a win, draw and away probability, the predicted goals per side and the predicted total, and an Over/Under read — all from this one engine.
Poisson assumes goals are independent and the rate is stable. Neither is perfectly true, so treat it as a strong approximation of a noisy sport, never as certainty.