Poisson calculator for betting
The chance of each count from an expected average: goals, shots on goal, strikeouts or any prop that counts events. Get the over / under chance and fair odds at any line.
Inputs
Result
updates as you typeRun this math on every line, automatically
Our prop tools fit a full fair ladder across every book's lines (Poisson and negative binomial for counts) instead of one guess at the average.
How it works
A Poisson distribution describes counts of independent events around an average λ (lambda), such as goals in a soccer match or shots on goal by one player:
P(X = k) = e−λ λk ÷ k!
P(over a half line L) = 1 − P(X ≤ L − ½) · P(under) = P(X ≤ L − ½)
whole-number line L: over wins on X > L, pushes on X = L; fair decimal for the over = 1 + P(under) ÷ P(over)
Enter the expected count, the line, and optionally the prices on each side to see how they compare with the Poisson chance. The fair odds are what the price would be with no vig if the average is right.
Worked example
A soccer match expected to produce 2.7 goals, priced on the 2.5 total:
P(0) = e−2.7 = 6.72% · P(1) = 18.15% · P(2) = 24.50%
P(under 2.5) = P(0) + P(1) + P(2) = 49.36% · P(over 2.5) = 50.64%
Fair odds: over −102.6, under +102.6
| Goals | Chance | Or fewer |
|---|---|---|
| 0 | 6.72% | 6.72% |
| 1 | 18.15% | 24.87% |
| 2 | 24.50% | 49.36% |
| 3 | 22.05% | 71.41% |
| 4 | 14.88% | 86.29% |
| 5 | 8.04% | 94.33% |
| 6 | 3.62% | 97.94% |
| 7 | 1.39% | 99.34% |
If a book offers the over at +100, the price beats the Poisson fair only if 2.7 is the right average; check it against the market's own lines first.
Things to watch
- The average is the whole model. A wrong λ gives a confident wrong answer; the market's own lines are usually a better guide than one number.
- Real counts are lumpier. Shots, strikeouts and assists often vary more than Poisson allows (overdispersion), which makes tails likelier than shown.
- Not for correlated events. Goals in a blowout or a game state change are not independent.