Abstract: Baseball players must be able to see and react in an instant, yet it is hotly debated whether superior on-field performance is associated with superior sensorimotor abilities. In this study, we compare sensorimotor abilities, measured through eight psychomotor tasks comprising the Nike Sensory Station battery, and game statistics in a sample of 252 professional baseball players. For this purpose, we develop a series of Bayesian hierarchical latent variable models that enable us to compare statistics across multiple professional baseball leagues. Within this framework, we find that sensorimotor abilities are statistically significant predictors of on-base percentage, walk rate, and strikeout rate, accounting for confounding variables such as age, position, and league. We find no such relationship for either slugging percentage or fielder-independent pitching. The pattern of results suggests performance contributions from both visual-sensory and visual-motor abilities and indicates that sensorimotor screenings may be useful for player scouting.