Poisson Calculator

Over the line—

Give an expected rate and a line and this becomes the probability of going over it.

Expected rate (λ)Line

Distribution — P(X = k)

emerald = over the line · gold = push spot · grey = under

Poisson assumes independent events at a constant rate — a strong model for counts like strikeouts, shots, or corners, and a poor one for high-variance totals. It is a model, not the market.

Show the math

P(X = k) = e^{−λ} λ^k / k!λ = 2.5

P(over) = 1 − CDF(⌊line⌋)= 45.62%

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What this will not claimA model, not the market. Poisson assumes independent events at a constant rate — strong for strikeouts, shots and corners, poor for high-variance totals.

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How is the Poisson distribution used in betting?

The Poisson distribution turns one number — the expected rate λ — into a full probability curve for counting stats, giving P(X = k) = e^(−λ)·λ^k/k! for goals, strikeouts, shots, corners, or any low-count prop.

How it works & common questions

Poisson assumes independent events at a constant rate — strong for true counting processes, weak for high-variance totals — and the tool says so on its face.

How it works

Set the expected rate. A projection or a market-derived λ for the stat.
Set the line. Half-point lines split cleanly; integer lines get an explicit push probability.
Read fair odds. Over/under probabilities and the no-push fair prices to compare against any book.

Which props does the Poisson model fit best?

Low-count, roughly independent events: soccer goals, pitcher strikeouts, shots on goal, corners, and similar markets. It fits poorly where events cluster or the rate shifts in-game, so treat its output as a model estimate to compare against the market, not as truth.

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