Bayesball: Bayesian Integration in Professional Baseball Batters

Pitchers in baseball throw the ball with such high velocity and varying movement that batters only have a few hundred milliseconds to estimate whether to swing and how high to swing. Slight deviations in the contact point on the ball can result in weakly hit balls that do not result in opportunities for batters to score. Even before the pitcher releases the ball, the batter has some belief (an estimated distribution-a prior), of where the ball may land in the strike zone. Batters will update this prior belief with information from observing the pitch (the likelihood) to calculate their final estimate (the posterior). These models of behavior, called Bayesian models within movement science, predict that players will estimate a final ball position by combining prior information with observation of the pitch in a way that weights each information source relative to the uncertainty. Here we test this model using data from more than a million samples from professional baseball. Moreover, as predicted by a Bayesian model, we show that a batters estimate of where to swing is biased towards the prior when prior information is available ( pitch tipping), and biased towards the likelihood in the case of pitches with high movement uncertainty. These results demonstrate that Bayesian ideas are relevant well beyond laboratory experiments and matter for real-world movements.