A Bayesian method for computing intrinsic pitch values using kernel density and nonparametric regression estimates

The deployment of sensors that characterize the trajectory of pitches and batted balls in three dimensions provides the opportunity to assign an intrinsic value to a pitch that depends on its physical properties and not on its observed outcome. We exploit this opportunity by using a Bayesian framework to learn a set of mappings from five-dimensional velocity, movement, and location vectors to intrinsic pitch values. A kernel method generates nonparametric estimates for the component probability density functions in Bayes theorem while nonparametric regression is used to derive a batted ball weight function that is invariant to the defense, ballpark, and atmospheric conditions. Cross-validation is used to determine the parameters of the model. We use Cronbach’s alpha to show that intrinsic pitch values have a significantly higher reliability than outcome-based pitch values. We also develop a method to combine intrinsic values at the individual pitch level into a statistic that captures the value of a pitcher’s collection of pitches over a period of time. We use this statistic to show that pitchers who outperform their intrinsic values during a season tend to perform worse the following year. We also show that this statistic provides better predictive value for future Earned Run Average (ERA) than either current ERA or Fielding Independent Pitching (FIP).