Sensitivity of batted-ball speed to swing speed models

In baseball and softball, batted-ball velocities depend strongly on bat speed prior to contact. The purpose of this study was to characterize the sensitivity of hit. ball speed to swing speed models. A pitching machine was used to project balls at varying speeds considered to be age appropriate for female fastpitch softball batters ranging from 9 to 24 years of age. Participants swung bats of varying moment of inertia and high-speed video was used to measure bat and ball kinematics for each hit. Several power law swing speed models were compared, including a generic model for all participants, age-specific models and participant-specific models. In addition, an exponential Gaussian process regression model was used. Estimates of batted-ball speeds were obtained by coupling the swing speed models to a model of the bat-ball collision. The root mean square error of model estimates ranged from 2.3 to 5.0 rad/s for swing speed models and 3.6 to 8.5 m/s for batted-ball speed estimates. The Gaussian process regression model performance was similar to the participant-specific models (swing speed root mean square error = 2.4 rad/s; batted-ball speed root mean square error = 3.7 m/s). The correlation of the Gaussian process regression model with field measurements was surprising given the limited number of inputs, which warrants further investigation. Agreement between all power law models and field measurements improved when the bat moment of inertia about its instantaneous center of rotation (rather than about the knob) was considered. This information will be of use to players and coaches to improve batting performance and bat selection.