This talk presents three applications of statistical methodology to research questions in baseball. First, we consider a modification of supervised learning techniques applied to pitch-tracking data. Specifically, we examine how the modeling framework changes when the objective is to evaluate the pitcher rather than the pitch. Second, we analyze the strategic interaction between pitcher and baserunner under Major League Baseball’s recently implemented pickoff limits. We model this cat-and-mouse dynamic as a stochastic game and investigate how a runner may optimally adjust leadoff distance in response to successive pickoff attempts. Third, we explore the newly available swing-level bat-tracking data released by MLB, which provide measurements of bat speed and swing length at the point of contact. We address the methodological challenge that the outcome itself determines the point of measurement and discuss potential approaches for inference in this setting.