Deriving Spin Signatures and the Components of Movement from Trackman Data for Pitcher Evaluation Glenn Healey Electrical Engineering and Computer Science University of California, Irvine, CA 92617 Email:
[email protected] Research Paper for 2019 SABR Analytics Conference 1 Introduction The 3-D pitch trajectories and total spin measurements acquired by the Trackman radar enable the recovery of the spin axis for individual pitches. We leverage a computational process proposed by Alan Nathan [6] in combination with fine-grained weather data to compute this recovery for every MLB pitch over a full season. This analysis allows the creation of a new spin signature representation for characterizing and comparing pitchers. As shown in Figure 1, three forces act on a baseball traveling through the air with a velocity vector v. Gravity pulls the ball down, drag acts opposite the velocity direction, and the Magnus force causes the ball to change direction due to spin. Figure 1: Forces on a spinning baseball in flight The Magnus force depends on the spin vector ω and causes movement [5] [7] on a pitch. The spin vector ω has a magnitude defined by how fast the ball is spinning, e.g. 2400 1 revolutions per minute (rpm), and a direction defined by the spin axis and the right-hand rule as shown in Figure 2. A pitcher controls the spin axis with the orientation of his hand and fingers when he releases a pitch. The direction of ω can be represented by the unit vector ω = ω/|ω|. b Figure 2: Spin axis and spin vector direction The magnitude of the Magnus force [8] is given by 1 |F | = ρAC |v|2 (1) M 2 L where ρ is the air density, A is the ball cross-sectional area, and CL is the dimensionless lift coefficient.