Validation of ball spin estimates in tennis from multi-camera tracking data

The purpose of this study was to examine the accuracy of methods to estimate ball spin rate and spin axis direction using multi-camera tracking technology. The method implemented by Hawk-Eye and a theoretical ball trajectory model were assessed for their accuracy against high speed-vision. A theoretical ball trajectory model was found to estimate ball spin rate and the spin axis direction more accurately than the method used by Hawk-Eye. The superior performance of the ball trajectory model was indicated by a lower mean bias and standard deviation (2.92 ± 222.76) than Hawk-Eye (-100.01 ± 542.44), as well as narrower limits of agreement and a 327.63 RPM lower RMSE. Spin rates less than 4500 RPM were estimated with the highest accuracy, but neither method was able to consistently and accurately estimate spin rates >4500 RPM. The application of a trajectory model to multi-camera ball tracking data provides a practical and non-invasive method to accurately estimate the spin imparted when hitting, allowing for large-scale collection of spin rates during matches.