Calculator
Poisson Calculator — Model Game Totals and Goals
The Poisson distribution models discrete, randomly occurring events — like goals in soccer or runs in baseball. Enter the expected rate (λ) and an over/under line to see the probability of each exact outcome and whether the over or under is more likely.
P(Over) and P(Under) are the true probabilities implied by your model. Compare them to the book's implied probability to find an edge.
Compare book totals to find value →Average expected events per game — e.g. total expected goals, runs, or points
The total line from the sportsbook (e.g. 2.5 goals, 7.5 runs)
How this works
Formula
P(X=k) = (λ^k × e^-λ) / k!
Worked example
Soccer total goals 2.6 expected: P(0)=7.4%, P(1)=19.3%, P(2)=25.1%, Over 2.5 ≈ 48.2%.
FAQ
When does Poisson work?
Discrete, independent, low-rate events: soccer goals, hockey goals, MLB runs, NBA threes. Less good for highly correlated events.
Why is soccer the classic Poisson sport?
Goals are rare, discrete, and roughly independent — fits Poisson assumptions cleaner than any other major sport.
How do I derive λ?
Use team expected-goals (xG), implied totals (book total ÷ 2), or your own model. Better λ = better predictions.
What about overdispersion?
Real games show slightly more variance than Poisson predicts. Use negative-binomial for high-leverage models.
Can I price exact scores?
Yes — multiply each team's Poisson distribution to get the joint probability of any score.