The reliability of basketball shooting tests with binary outcomes

This paper addresses distinct questions related to the reliability of basketball shooting tests: (i) how to appropriately model data from tests with binary outcomes, (ii) how many shots are needed for the tests to be reliable, and (iii) can additional information from shot trajectories (shot hit location and entry angle) improve the reliability of the shooting tests? We designed a Bayesian statistical model that takes into account the binary nature of the outcomes and can be used to model test data for multiple individuals simultaneously. We demonstrated the utility of our approach with a simulation study and on a real-world example with 27 basketball players and 7309 shots across 4 different shooting tests. Results showed the practical importance of modelling data as binary and the relatively large sample sizes required for the tests to be reliable. We also showed that additional information from shot trajectories provides valuable insights into an individual's shooting, but we were unable to achieve a meaningful improvement in the estimation of shooting ability.