Hurdle Model Calculator

The Hurdle model is a two-stage approach: first, did the event happen at all? Second, given it happened, how many times? This makes it ideal for props like RBIs, home runs, and goals where the probability of getting at least one is a separate question from the count distribution.

P(X=0) = 1 − p
P(X=k) = p × Poisson(k, λ) / (1 − e^(−λ))  for k ≥ 1

Hurdle Prob (p) is the probability the player crosses the hurdle (gets at least 1). Poisson Rate (λ) is the underlying Poisson parameter. The positive counts use a zero-truncated Poisson derived from this rate, so the conditional mean given at least 1 is λ/(1−e^(−λ)), which is higher than λ itself.

Hurdle vs ZIP: ZIP mixes extra zeros into the Poisson. Both structural and sampling zeros coexist. The Hurdle model cleanly separates the zero/nonzero decision from the count process. Use Hurdle when the "did it happen?" question has a distinct mechanism (lineup position, matchup, game script) from "how many?"

Example: A batter has a 62% chance of recording at least 1 RBI in a given game. When he does get RBIs, his count follows a truncated Poisson with λ = 1.8. Enter 62 for Hurdle Prob and 1.8 for Count Rate.