Modeling the probability of a batter/pitcher matchup event: A Bayesian approach

We develop a Bayesian hierarchical log5 model to predict the probability of a particular batter/pitcher matchup event in baseball by extending the log5 model which is widely used for describing matchup events. The log5 model is simple and intuitive with fixed coefficients but less flexible than the generalized log5 model that allows the estimation of coefficients using data. Meanwhile, although the generalized log5 model is more flexible, the estimation of coefficients often suffers from a lack of data as a large sample of previous outcomes for a particular batter/pitcher matchup is rarely available in practice. The proposed Bayesian hierarchical log5 model retains the advantages of both models while complementing their disadvantages by estimating the unknown coefficients as in the generalized log5 model, but by using the fixed coefficients of the standard log5 model as prior knowledge. By combining the ideas of the two previous models, the proposed model can estimate the probability of a particular matchup event using a small amount of historical data of the players. Furthermore, we show that the Bayesian hierarchical log5 model achieves better predictive performance than the standard log5 model and the generalized log5 model using a real data example. We further extend the proposed model by including a new variable representing the defensive ability of the pitcher's team and show that the extended model can further improve the predictive performance of the Bayesian hierarchical log5 model.