UnjuicedPoisson Probability Calculator
Estimate exact, at-least, and at-most outcomes from an expected event average.
Event model
Poisson estimate
Exactly
14.88%
At least
28.59%
At most
86.29%
Fair odds for at least
+250
Poisson works best for independent events occurring at a stable average rate. It is less reliable when playing time or game state changes sharply.
How to use the Poisson Probability
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.
Poisson calculator FAQ
Answers about this free poisson probability calculator, sports betting odds, payouts, and the math behind each result.
What does lambda mean in a Poisson model?
Lambda is the expected average number of events during the period being modeled.
When is Poisson a poor sports model?
It can struggle when events are dependent, rates change during play, or outcomes vary more than the Poisson distribution allows.