Abstract 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).

中文翻译：

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使用核密度和非参数回归估计来计算固有螺距值的贝叶斯方法

摘要传感器的部署可以在三个维度上表征球场和击球的轨迹，从而为根据其物理特性而不是其观测结果分配球场固有值提供了机会。我们通过使用贝叶斯框架来利用此机会，以学习从五维速度，运动和位置矢量到固有音高值的一组映射。核方法针对贝叶斯定理中的组件概率密度函数生成非参数估计，而非参数回归用于推导不受防御，球场和大气条件影响的球拍重量函数。交叉验证用于确定模型的参数。我们使用克朗巴赫（Cronbach）的alpha值来显示，固有音高值比基于结果的音高值具有更高的可靠性。我们还开发了一种方法，可以将各个音调级别的内在值组合成一个统计信息，该统计信息可以捕获一段时间内投手的音调集合值。我们使用这一统计数据表明，在一个赛季中胜过其内在价值的投手在第二年的表现往往会更差。我们还表明，与当前ERA或Fielding Independent Pitching（FIP）相比，该统计数据可为未来的平均运行平均数（ERA）提供更好的预测价值。我们使用这一统计数据表明，在一个赛季中胜过其内在价值的投手在第二年的表现往往会更差。我们还表明，与当前ERA或Fielding Independent Pitching（FIP）相比，该统计数据可为未来的平均运行平均数（ERA）提供更好的预测价值。我们使用这一统计数据表明，在一个赛季中胜过其内在价值的投手在第二年的表现往往会更差。我们还表明，与当前ERA或Fielding Independent Pitching（FIP）相比，该统计数据可为未来的平均运行平均数（ERA）提供更好的预测价值。