Model │ Math · Free tool
Poisson Calculator
Two xG values in, every score and every market probability out. The classic Poisson model, used to read score-line markets the way sportsbooks do.
A number greater than 0, typically 0.4 to 3.0.
A number greater than 0, typically 0.4 to 3.0.
Expected goals, your model's read on how each side should score.
- Home win ,
- Draw ,
- Away win ,
- Both teams to score ,
- Over 1.5 goals ,
- Over 2.5 goals ,
- Over 3.5 goals ,
Score probability grid
Every cell is the modelled chance of that exact result. Darker gold means more likely; the most likely scoreline is outlined.
| Home goals | Away goals | |||||
|---|---|---|---|---|---|---|
| H \ A | 0 | 1 | 2 | 3 | 4 | 5+ |
| 0 | , | , | , | , | , | , |
| 1 | , | , | , | , | , | , |
| 2 | , | , | , | , | , | , |
| 3 | , | , | , | , | , | , |
| 4 | , | , | , | , | , | , |
| 5+ | , | , | , | , | , | , |
The 5+ row and column aggregate every result with five or more goals on that side, the long tail of the distribution.
What the Poisson model assumes
Each team's goals in a match are modelled as a Poisson random variable, one parameter per side, the expected goals (xG). Multiply the home and away marginals to get every joint scoreline, then sum the cells that make up each market. Fast, transparent, easy to argue with.
- xG is the input that matters
- The output is only as honest as the xG you feed it. Optimistic xG produces optimistic markets. Build your numbers from a model, not from a feeling.
- The independence assumption is a simplification
- The model treats home and away goals as independent. Real matches show a small negative correlation around 0–0 and 1–1 (the Dixon-Coles correction). Score lines like 0–0 and 1–1 are slightly more common in practice than a pure Poisson predicts.
- Tails are truncated at 5+
- The visible grid shows 0–4 explicitly and folds 5-or-more into a single column. Internally the markets sum well into the tail (0–7 each side); the truncation is purely a display choice.
Pair this with the Expected Value calculator to turn a score-line probability into a market edge.