Approximating strike zone size and shape for baseball umpires under different conditions

A nonswung pitch is called either a strike or a ball depending on its location over the home plate. According to the baseball regulation, strike zone is rectangular in shape; however, the shape of strike zone is actually decided by umpires. In this paper, based on the locations of 5,297 nonswung pitches collected by Trackman radar in 2018, we verified the shape and size of the strike zone of individual umpires under various conditions such as different ball counts and batter handedness, etc. Two approaches were adopted to approximate the strike zone for the individual umpires. First, local polynomial regression was used to estimate the probability of pitches being called strikes at different locations under various circumstances. The contours of 0.5 and 0.75 probabilities were drawn to illustrate the strike zone. The area of the contour regions was then calculated for comparison. Second, we used decision tree algorithm to analyse strike judgement criteria among the umpires. With the approximated strike zone, the quality of each umpire's strike judgement can be evaluated. Our results demonstrate that the changing shape of the strike zone is common in baseball games and pitchers, catchers, and batters, etc., may leverage this knowledge to their advantage.