A mixed effects multinomial logistic-normal model for forecasting baseball performance

Prediction of player performance is a key component in the construction of baseball team rosters. As a result, most prediction models are the proprietary property of team or industrial sports entities, and little is known about them. Of those models that have been published, the main focus has been to separately model each outcome with nearly no emphasis on uncertainty quantification. This research introduces a joint modeling approach to predict seasonal plate appearance outcome vectors using a mixed-effects multinomial logistic-normal model. This model accounts for positive and negative correlations between outcomes, both across and within player seasons, and provides a joint posterior predictive outcome distribution from which uncertainty can be quantified. It is applied to the important, yet unaddressed, problem of predicting performance for players moving between the Japanese (NPB) and American (MLB) major leagues.