Poisson distribution for football goals

What problem Poisson solves

When you want to estimate the probability that a team scores 0/1/2… goals, the Poisson model is a simple baseline.

The formula

P(k; λ) = e^{-λ} * λ^k / k!

How to estimate λ

Use recent matches to get average goals; calibrate with league average & home advantage.

From single-team goals to scoreline

Assume independence; multiply two teams’ goal distributions to get P(i,j).

Next

Try the calculator: /tools/poisson