We introduce a three-step framework to determine, on a per-pitch basis, whether batters in Major League Baseball should swing at a pitch. Unlike traditional plate discipline metrics, which implicitly assume that all batters should always swing (resp. take) pitches inside (resp. outside) the strike zone, our approach explicitly accounts not only for the players and umpires involved but also in-game contextual information like the number of outs, the count, baserunners, and score. Specifically, we first fit flexible Bayesian nonparametric models to estimate (i) the probability that the pitch is called a strike if the batter takes the pitch; (ii) the probability that the batter makes contact if he swings; and (iii) the number of runs the batting team is expected to score following each pitch outcome (e.g. swing and miss, take a called strike, etc.). We then combine these intermediate estimates to determine whether swinging increases the batting team's run expectancy. Our approach enables natural uncertainty propagation so that we can not only determine the optimal swing/take decision but also quantify our confidence in that decision. We illustrate our framework using a case study of pitches faced by Mike Trout in 2019.

翻译：我们提出一个三步框架，用于逐球判定美国职业棒球大联盟击球员是否应对投球挥棒。与传统击球纪律指标不同（传统指标隐含假设所有击球员应始终对好球带内的球挥棒、对好球带外的球放弃挥棒），我们的方法不仅明确考虑了球员和裁判的个体差异，还整合了比赛情境信息（如出局数、好球坏球数、垒上跑垒员及比分）。具体而言，我们首先拟合灵活的贝叶斯非参数模型，以估计：(i) 若击球员放弃挥棒时投球被判为好球的概率；(ii) 击球员挥棒时击中球的概率；(iii) 每次投球结果（如挥棒落空、放弃挥棒被判好球等）后击球队的预期得分。随后结合这些中间估计值，判断挥棒是否能提升击球队的得分预期。本方法可实现自然的不确定性传播，不仅能确定最优的挥棒/放弃决策，还能量化对该决策的置信度。我们以2019年迈克·特劳特面对的投球案例研究来展示该框架。