Poisson score matrix
This is the engine room of most football models, as a toy you can drive: two expected-goals numbers in, a probability for every scoreline out — and every market price is just a region of this grid added up.
the average goals you expect the home side to score
and the away side
- Home win
- 44.1%
- Draw
- 25.5%
- Away win
- 30.4%
- Over 2.5
- 50.6%
- BTTS
- 54.3%
| Home goals by away goals | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|---|
| 0 | 6.7% | 8.1% | 4.8% | 1.9% | 0.6% | 0.1% | 0.0% |
| 1 | 10.1% | 12.1% | 7.3% | 2.9% | 0.9% | 0.2% | 0.0% |
| 2 | 7.6% | 9.1% | 5.4% | 2.2% | 0.7% | 0.2% | 0.0% |
| 3 | 3.8% | 4.5% | 2.7% | 1.1% | 0.3% | 0.1% | 0.0% |
| 4 | 1.4% | 1.7% | 1.0% | 0.4% | 0.1% | 0.0% | 0.0% |
| 5 | 0.4% | 0.5% | 0.3% | 0.1% | 0.0% | 0.0% | 0.0% |
| 6 | 0.1% | 0.1% | 0.1% | 0.0% | 0.0% | 0.0% | 0.0% |
Scores above 6 goals a side are folded into the derived numbers but not shown; the shading tracks each cell's probability, brightest at the most likely score.
What this grid actually is
Assume each side's goals arrive at a steady average rate and independently of the other side's. Then the probability of an exact score is one Poisson term for the home goals multiplied by one for the away goals, and the whole match collapses into this matrix. A match-result price is the triangle above or below the diagonal summed up; the draw is the diagonal itself; over 2.5 is everything past the anti-diagonal; both-teams-to-score is the grid minus its first row and column. The full derivation, with the formula written out, is in our guide to the Poisson distribution in football betting.
Where the toy ends and a real model begins
Two honest limits. First, the independence assumption is mildly wrong: real matches produce slightly more low-scoring draws than this grid predicts — the classic fix in the literature is the low-score correction of Dixon and Coles. The size of the error is quantified in why Poisson underrates draws. Second, the output is only as good as the two numbers you type: estimating those expected-goals inputs well, match after match, is most of the work and all of the difficulty. A textbook grid is a way to understand the markets, not a substitute for a tested model — our own calls, and how every one of them settled, are on the track record.
Things worth trying
Type 1.3 against 1.1 — a normal, evenly-matched fixture — and notice the most likely single score is 1-1 at about 13%, even though the home side is favourite to win the match. That gap between "most likely score" and "likely winner" confuses a lot of correct-score betting, and it's visible here at a glance: the win is spread across many cells, the draw concentrates in few. It is also why 1-1 keeps topping the real-world score charts while rarely paying much at the prices — and our match predictions state the likeliest score with exactly these single-digit probabilities attached, honestly stated.