Model-based estimation of baseball batting metrics

We introduce an approach to model the batting outcomes of baseball batters based on the weighted likelihood approach and make use of our methodology to estimate commonly used baseball batting metrics. The weighted likelihood allows the sharing of relevant information among players. Specifically, this allows the inference on each batter to make use of the batting data from all other players in the league and, in the process, allows for improved inference. MAMSE (Minimum Averaged Mean Squared Error) weights are used as the likelihood weights. For comparison, we implemented a semi-parametric Bayesian approach based on the Dirichlet process, which enables the borrowing of information across batters while providing a natural clustering mechanism. We demonstrate and compare these approaches using 2018 Major League Baseball (MLB) batters data.