The Poisson distribution in football, explained with real numbers
Published
If you strip almost any football prediction model down to its engine, you find the same thing: a formula published long before football had crossbars. The Poisson distribution describes how many times a rare event happens in a fixed window — and a goal is exactly that kind of event.
The core idea
Football averages surprisingly few scoring events. Across the 14,772 finished matches in our dataset (eight leagues, 2021–2026), the average game produced 2.77 goals. Poisson takes just one input — the expected number of goals for a team in a match — and returns the probability of every exact count.
Say a team’s expected goals against a given opponent is 1.4. Poisson says:
| 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 get the probability of every scoreline: 1-0, 1-1, 2-1, and the rest. Sum the right cells and you have match odds — that’s the whole trick, and it’s how our own model prices 1X2, Over/Under 2.5 and BTTS from a single engine.
Where do the expected goals come from?
The distribution is only as good as its input. Models estimate each team’s expected goals from attack and defence ratings fitted over seasons of results, adjusted for home advantage and weighted towards recent form. That estimation step is where models genuinely differ; the Poisson step afterwards is standard machinery. Our guide to prediction algorithms walks through the full chain.
Where Poisson breaks — and the fix
Pure Poisson treats the two teams’ goal counts as independent. Reality disagrees in one specific corner: low-scoring games. Draws at 0-0 and 1-1 happen more often than independence predicts, and 1-0/0-1 slightly less — teams respond to the state of the game.
Mark Dixon and Stuart Coles quantified this in 1997 and proposed a targeted correction that adjusts only those four scorelines. The Dixon-Coles model — the one we run — is essentially Poisson with that patch plus time-decayed ratings. Thirty years on it remains the reference baseline that fancier machine-learning models are judged against.
Why draws matter more than you think
A quarter of football matches — 25.3% in our dataset — end level. Almost no casual bettor picks draws, which is precisely why draw probabilities are where naive models and gut feeling lose most of their accuracy. Any model that can’t put a credible number on the draw can’t price the other two outcomes either: the three probabilities must sum to 100%.
Try reading a match page with new eyes
On any FootInsights match page you’re looking at the output of exactly this machinery: a scoreline grid collapsed into three bars for 1X2, plus goals markets from the same grid. The probabilities won’t always be right — we grade every one publicly — but they are always consistent, which is more than a hunch can say.