Hierarchical Bayesian analysis of racehorse running ability and jockey skills

Abstract In this paper, we proposed a new method of evaluating horse ability and jockey skills in horse racing. In the proposed method, we aimed to estimate unobservable individual effects of horses and jockeys simultaneously with regression coefficients for explanatory variables such as horse age and racetrack conditions and other parameters in the regression model. The data used in this paper are records on 1800m races (excluding steeplechases) held by the Japan Racing Association from 2016 to 2018, including 4063 horses and 143 jockeys. We applied the hierarchical Bayesian model to stably estimate such a large amount of individual effects. We used the Markov chain Monte Carlo (MCMC) method coupled with Ancillarity- Sufficiency Interweaving Strategy for Bayesian estimation of the model and choose the best model with Widely Applicable Information Criterion as a model selection criterion. As a result, we found a large difference in the ability among horses and jockeys. Additionally, we observed a strong relationship between the individual effects and the race records for both horses and jockeys.