Poisson Distribution Calculator
Model goal and score probabilities using Poisson distribution. Essential for soccer, hockey, and low-scoring sports.
How Poisson Distribution Works for Betting
The Poisson distribution models the probability of a given number of events (goals, runs) occurring in a fixed interval when events happen at a known average rate (λ, lambda).
The Poisson Formula
P(k goals) = (λ^k × e^-λ) / k!
Where:
λ = expected goals (from team strength, xG, etc.)
k = number of goals to calculate probability for
e = Euler's number (≈ 2.718)
Where:
λ = expected goals (from team strength, xG, etc.)
k = number of goals to calculate probability for
e = Euler's number (≈ 2.718)
Sports Where Poisson Works Best
- Soccer: Low scoring (2-3 goals avg), independent events — ideal for Poisson
- Hockey: Slightly higher scoring but still works well
- Baseball: Useful for run totals and exact score props
- Not ideal: Basketball, football (too high-scoring, correlated scoring)
Finding Expected Goals (λ)
The accuracy of Poisson modeling depends on your λ estimate. Sources include:
- xG (Expected Goals) from data providers
- Implied team totals from betting lines
- Historical scoring rates adjusted for opponent strength
Get model-projected goal totals
Join sharp bettors getting xG-based predictions and edge alerts.
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