Combining Radar, Weather, and Optical Measurements to Model the Dependence of Baseball Lift on Spin and Surface Roughness

Abstract

We develop a new method for characterizing the lift force on a baseball. The methodology addresses this task from the novel perspective of considering a large set of radar measurements acquired outside of a laboratory setting. The reduced degree of standardization in the measurements is countered by several elements of the approach. A new optimization method is developed that incorporates domain knowledge and constraints derived from optical measurements. The optimization accounts for the uncertainty in the different data sources while exploiting the size and diversity of the radar measurements to mitigate the effects of systematic biases, outliers, and the lack of geometric information that is typically available in laboratory experiments. Fine-grained weather data is associated with each radar measurement to enable compensation for the local air density. By applying this methodology to a set of over two million trajectory measurements, we achieve unprecedented accuracy in the characterization of the lift force. We show that the lift coefficient is more than six percent greater than measured by previous laboratory experiments. We also demonstrate the ability to predict increases in the lift coefficient in response to changes in seam height on the order of a thousandth of an inch. Previous methods based on smaller sets of laboratory measurements have been unable to discern changes in the lift coefficient in response to changes in seam height of 0.02 inches. We demonstrate the statistical significance of the results. This work benefits several important application areas including the monitoring of sensor calibration systems and the definition of ball specifications that constrain trajectories to acceptable ranges.