Lead distance under a pickoff limit in Major League Baseball: A sequential game model

TL;DR

This paper models the strategic interaction between pitchers and runners in MLB under pickoff limits as a sequential game, providing optimal strategies and a practical rule of thumb for runners.

Contribution

It introduces a novel game-theoretic model of pickoff dynamics in baseball and derives optimal strategies and actionable rules for runners.

Findings

Optimal game equilibria for pitcher-runner interactions.

The Two-Foot Rule for runner lead adjustments.

Statistical models predicting pickoff and stolen base outcomes.

Abstract

Major League Baseball (MLB) recently limited pitchers to three pickoff attempts, creating a cat-and-mouse game between pitcher and runner. Each failed attempt adds pressure on the pitcher to avoid using another, and the runner can intensify this pressure by extending their leadoff toward the next base. We model this dynamic as a two-player zero-sum sequential game in which the runner first chooses a lead distance, and then the pitcher chooses whether to attempt a pickoff. We establish optimality characterizations for the game and present variants of value iteration and policy iteration to solve the game. Using lead distance data, we estimate generalized linear mixed-effects models for pickoff and stolen base outcome probabilities given lead distance, context, and player skill. We compute the game-theoretic equilibria under the two-player model, as well as the optimal runner policy under a simplified one-player Markov decision process (MDP) model. In the one-player setting, our results establish an actionable rule of thumb: the Two-Foot Rule, which recommends that a runner increase their lead by two feet after each pickoff attempt.