The Poisson distribution in football, explained with real numbers
By FootInsights · Published · Updated 26 Sep 2026 · 4 min read
Strip almost any football prediction model down to its engine and you find the same thing: a formula published long before football had crossbars. The Poisson distribution describes how often a rare event happens in a fixed window, and a goal is exactly that kind of event.
The core idea
Football produces surprisingly few scoring events. Across the 17,495 finished matches in our dataset, the average game produced 2.75 goals — 1.53 from the home side and 1.22 from the away side. Poisson takes one input, the expected number of goals for a team, and returns the probability of every exact count.
Say a team’s expected goals against a given opponent is 1.4:
| Goals | Probability |
|---|---|
| 0 | 24.7% |
| 1 | 34.5% |
| 2 | 24.2% |
| 3 | 11.3% |
| 4+ | 5.3% |
Do the same for the opponent — say 1.1 expected — multiply the two tables together, and you have the probability of every scoreline. Sum the right cells and you have match odds, Over/Under and BTTS from one engine. That is the whole trick.
How well does it actually fit?
Most articles assert that Poisson “does not fit football” and move on. It is a checkable claim, so we checked it against our own record.
Using each league’s own average scoring rates — not per-team ratings, just the league means — an independent Poisson predicts the four most common scorelines like this:
| Scoreline | Actual | Poisson | Difference |
|---|---|---|---|
| 1-1 | 12.07% | 11.87% | +0.20pp |
| 1-0 | 10.08% | 9.91% | +0.17pp |
| 0-1 | 7.49% | 7.88% | −0.39pp |
| 0-0 | 6.53% | 6.62% | −0.09pp |
Every error is under half a percentage point. At the level of a whole league, the plain independent Poisson reproduces football’s most common results remarkably well — which is a more interesting result than the folklore, and worth saying plainly.
What that test does not prove
It would be easy to over-read the table above, so here is the limitation.
Those numbers use one pair of scoring rates for an entire league. A real forecast uses a pair estimated for this home side against that away side, and the dependence between the two teams’ scoring — the thing Dixon and Coles corrected in 1997 — operates at that per-match level. Aggregating thousands of fixtures with very different expected scores blends them together, and the blending can hide an effect that is present in every individual match.
So the honest summary is: the Poisson shape is a good description of league-level scoring, and that is not the same as saying an independent Poisson is a good match model. The Dixon-Coles correction adjusts exactly the low-scoring corner of the grid, and it is the standard first upgrade for anyone building a goal model.
Where do the expected goals come from?
The distribution is only as good as its input, and this is where models genuinely differ — the Poisson step afterwards is standard machinery anyone can implement.
Expected goals come from attack and defence ratings fitted over seasons of results, adjusted for a home-advantage term and weighted toward recent matches. Every meaningful modelling decision lives in that estimation: how far back to look, how fast to discount, how much to regularise a club with little history. Our guide to prediction algorithms walks the full chain, and every one of those choices is a chance to fit noise rather than signal.
Why the draw is the number to watch
25.4% of matches in our dataset end level. Almost nobody picks draws, which is exactly why draw probabilities are where naive models and gut feeling lose most of their edge — and why a model that cannot put a credible number on the draw cannot price the other two either, since all three must sum to 100.
Draw rates also vary more by competition than people expect, from 23.8% in the Premier League to 27.5% in Brazil’s Série A. A single global assumption gets both ends wrong, which is why any serious model has to let league context move the draw. The practical side of forecasting them is in how to predict draws in football.
Reading a match page with new eyes
On any match page you are looking at the output of this machinery: a scoreline grid collapsed into three bars for 1X2, with the goals markets read off the same grid. The probabilities will not always be right — we grade every one publicly — but they are always mutually consistent, which is more than a hunch can offer.