CalculatorsUpdated 21 Jul 20263 min read
Poisson Calculator
Football's scoring is close enough to a Poisson process that two numbers — how many goals each side is expected to score — pin down the probability of every scoreline. Set the two rates and the grid below fills in, with every common market read off it.
Scoreline probability
home ↓ · away →| 0 | 1 | 2 | 3 | 4 | 5 | |
|---|---|---|---|---|---|---|
| 0 | 7.1 | 6.6 | 4.2 | 1.6 | 0.5 | 0.1 |
| 1 | 9.5 | 12.5 | 6.8 | 2.6 | 0.7 | 0.2 |
| 2 | 8.2 | 9.4 | 5.4 | 2.1 | 0.6 | 0.1 |
| 3 | 4.4 | 5.0 | 2.9 | 1.1 | 0.3 | 0.1 |
| 4 | 1.7 | 2.0 | 1.2 | 0.4 | 0.1 | 0.0 |
| 5 | 0.6 | 0.6 | 0.4 | 0.1 | 0.0 | 0.0 |
Percentages, shaded by likelihood. The grid runs to 8-8 behind the scenes; scorelines above 5 are too rare to be worth the ink.
Most likely scorelines
These are fair probabilities — no bookmaker margin. A real price for the same outcome will always be shorter than the fair odds shown, and the gap is the book's fee.
How to read the grid#
Rows are home goals, columns away goals, and each cell is the probability of that exact scoreline. The markets above it aren't separate estimates — they're sums of cells:
- Home win — every cell below the diagonal; draw — the diagonal itself; away win — every cell above it.
- Over 2.5 — every cell where the two numbers add to 3 or more.
- BTTS yes — every cell where both numbers are at least 1.
Because they all come from one grid, they can't contradict each other. That's the main practical argument for modelling scorelines rather than pricing each market separately: get the grid right and the whole book is consistent by construction.
Two fixtures can have identical 1X2 probabilities and completely different totals. A 2.2 v 0.8 game and a 1.5 v 1.5 game are both roughly 60/40 in the home side's favour, but one is far more likely to go over 2.5. Move the sliders and watch the match result barely shift while the totals swing.
The formula#
For a team expected to score λ goals, the chance of scoring exactly k is:
P(k) = e−λ × λk ÷ k!
Do that for both sides and multiply for each pair. A 1-0 with rates 1.6 and 1.1 is P(1 goal at 1.6) × P(0 goals at 1.1).
What the Dixon-Coles toggle does#
Plain Poisson assumes the two teams' goal counts are independent. They very nearly are — except at the bottom, where 0-0 and 1-1 happen more often than independence predicts. Dixon-Coles adjusts exactly those four cells, and because two of them are draws, the correction mostly shows up as more draws.
Turn the toggle off and watch the draw probability fall. That gap is the single most valuable line of code in a football goals model, and it's why the models behind Tofiko use the corrected version.
Where the model stops#
This calculator prices a fixture given the expected goals. It has no opinion on what those should be — that's the hard part, and it's where a real model earns its keep: form, opponent strength, home advantage, rest, personnel. Garbage in, confidently-formatted garbage out.
It also assumes both rates hold for the full 90 minutes, which red cards and early goals break. Treat the output as a pre-match baseline, not a live price.
For the maths itself, read the Poisson distribution; for where the goal rates come from, expected goals. To turn any fair probability here into a bookmaker-comparable price, use the odds converter.
Related
- The Poisson Distribution: Turning Expected Goals Into Scorelines
- How Our Models Work: Poisson, Dixon-Coles and Elo
- Expected Goals (xG), Explained Without the Hype
- Over/Under 2.5 Goals Explained: The Market That Ignores the Winner
- BTTS — Both Teams To Score, Explained
- Fair Odds Calculator — Remove the Bookmaker Margin from Any 1X2 Book
- Odds Converter — Decimal, Fractional, American & Implied Probability
Frequently asked questions
How do you calculate football match probabilities with Poisson?
Estimate each team's expected goals, use the Poisson distribution to get the chance of each team scoring 0, 1, 2, … goals, then multiply the two to fill a grid of scorelines. Summing the right cells gives home/draw/away, Over/Under and BTTS. That is exactly what this calculator does.
What expected goals numbers should I enter?
Anything from about 0.5 to 3.0 per side covers almost all football. An average team at home sits near 1.5 and an average away side near 1.1. If you have xG figures for a specific fixture, use those; otherwise start from each team's season scoring and conceding rates.
What is the Dixon-Coles correction and should I use it?
Plain Poisson treats the two teams' goals as independent, which underrates 0-0 and 1-1 — and draws live there. The Dixon-Coles correction nudges those four lowest scorelines. Leave it on: it makes the draw probability more realistic, which is where the naive model is most wrong.
Are these real betting odds?
No — they are fair odds, with no bookmaker margin. Any real price for the same outcome will be shorter, and the difference is the bookmaker's fee. Compare the fair odds here against a real price to see whether a bet has value.