Zero-Inflated Poisson Calculator
Model props with excess zeros: scratched players, backup roles, and boom-or-bust events
Average when active
Extra zero probability
The over/under line
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Understanding Zero-Inflated Poisson
The Zero-Inflated Poisson (ZIP) model extends the standard Poisson by adding a separate zero-inflation parameter (π). It handles situations where zeros occur more often than a Poisson distribution predicts, common in props where a player may not participate at all.
P(X=0) = π + (1−π) × e^(−λ)
P(X=k) = (1−π) × (λ^k × e^(−λ)) / k! for k > 0
Lambda (λ) is the expected count when the player is active. Zero Inflation (π) is the extra probability of getting exactly zero beyond what Poisson predicts.
When to use ZIP over Poisson: Backup players who may get zero touches, weather-dependent props, platoon situations, or any market where "did not participate" is a meaningful outcome separate from just having a low average.
ZIP Mean = (1−π) × λ | ZIP Variance = (1−π) × λ × (1 + π × λ)
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