Poisson probability calculator
Web onlyEstimate exact, at-least, and at-most outcomes from an expected event average.
47.5%
With an average of 1.6, 2 or more happens 47.5% of the time: a fair +110.
- Exactly 2
- 25.84%
- 2 or fewer
- 78.34%
- 2 or more
- 47.51%
- Fair, at least
- +110
For counts that happen independently at a steady rate: goals, strikeouts, touchdowns.
How to use the Poisson probability calculator
The Poisson distribution estimates how often a count occurs when events happen independently at a stable average rate. It is commonly used as a starting model for sports totals.
- 1Enter the expected average number of events.
- 2Choose the exact, at-least, or at-most count you want to evaluate.
- 3Compare the model probability with the market price and your assumptions.
Formula and assumptions
P(X = k) = e^-λ × λ^k / k!, where λ is the expected average and k is the event count.
The model assumes independent events and a constant average rate. Real games can include changing pace, dependence, and overdispersion.
Questions
Answers about this free Poisson probability calculator, sports betting odds, payouts, and the math behind each result.
- Lambda is the expected average number of events during the period being modeled.
- It can struggle when events are dependent, rates change during play, or outcomes vary more than the Poisson distribution allows.