Goals are rare events in a long match. Each side creates chances at some rate, and a chance becomes a goal with some probability, so the number of goals a side scores in ninety minutes is close to a Poisson count with a rate we call λ for the home side and μ for the away side.
The two sides' goal distributions at the rates a mid-table home fixture usually carries. The home side's extra third of a goal moves mass from 0 and 1 onto 2 and 3.
P(X = x) = e^{-λ} λ^x / x!
The rates come from the two sides. Every team has an attack strength and a defence strength, and the home side gets a home-advantage multiplier:
Fit on thousands of results, these strengths are what the Predict page shows as expected goals for and against an average side.
Where Poisson is wrong
Two independent Poissons put too little mass on 0–0 and 1–1 and too much on 1–0 and 0–1. Dixon and Coles (1997) fixed this with a single correction factor τ that moves probability between the four low scorelines, controlled by one parameter ρ. Fitted on our store, ρ is about −0.05: a small but real tilt toward the draws.
What ρ = −0.05 actually does: a little mass leaves 1-0 and 0-1 and lands on 0-0 and 1-1. It is a small correction, and it is the difference between a book that prices the draw properly and one that does not.
With λ, μ and ρ you have a probability for every scoreline, which is the whole game: every market on the board is a sum over cells of that grid. Try it below: pick two sides and read the rates, then look at the grid.
The whole model in one picture: every scoreline and its probability. Sum below the diagonal for the home win, along it for the draw, above it for the away win.