In-season prediction of batting averages: A field test of empirical Bayes and Bayes methodologies

Abstract

Batting average is one of the principle performance measures for an individual baseball player. It is natural to statistically model this as a binomial-variable proportion, with a given (observed) number of qualifying attempts (called ``at-bats''), an observed number of successes (``hits'') distributed according to the binomial distribution, and with a true (but unknown) value of $p_i$ that represents the player's latent ability. This is a common data structure in many statistical applications; and so the methodological study here has implications for such a range of applications. We look at batting records for each Major League player over the course of a single season (2005). The primary focus is on using only the batting records from an earlier part of the season (e.g., the first 3 months) in order to estimate the batter's latent ability, $p_i$, and consequently, also to predict their batting-average performance for the remainder of the season. Since we are using a season that has already concluded, we can then validate our estimation performance by comparing the estimated values to the actual values for the remainder of the season. The prediction methods to be investigated are motivated from empirical Bayes and hierarchical Bayes interpretations. A newly proposed nonparametric empirical Bayes procedure performs particularly well in the basic analysis of the full data set, though less well with analyses involving more homogeneous subsets of the data. In those more homogeneous situations better performance is obtained from appropriate versions of more familiar methods. In all situations the poorest performing choice is the na\"{ı}ve predictor which directly uses the current average to predict the future average.

arXiv commentPublished in at http://dx.doi.org/10.1214/07-AOAS138 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (1)

• In-season prediction of batting averages: A field test of empirical Bayes and Bayes methodologies

Cited by in corpus (28)

• In-season prediction of batting averages: A field test of empirical Bayes and Bayes methodologies
• Nonparametric empirical Bayes and compound decision approaches to estimation of a high-dimensional vector of normal means
• An empirical Bayes mixture method for effect size and false discovery rate estimation
• Interval Estimation for Messy Observational Data
• Hierarchical Bayesian Modeling of Hitting Performance in Baseball
• Optimal shrinkage estimation of mean parameters in family of distributions with quadratic variance
• Nonparametric Empirical Bayes Estimation on Heterogeneous Data
• Nuclear penalized multinomial regression with an application to predicting at bat outcomes in baseball
• Optimal shrinkage estimation in heteroscedastic hierarchical linear models
• Solving the Empirical Bayes Normal Means Problem with Correlated Noise
• Nonparametric empirical Bayes and maximum likelihood estimation for high-dimensional data analysis
• On nonparametric estimation of a mixing density via the predictive recursion algorithm
• Sharp regret bounds for empirical Bayes and compound decision problems
• A Bayesian analysis of the time through the order penalty in baseball
• Empirical Bayes, SURE and Sparse Normal Mean Models
• Introducing Grid WAR: Rethinking WAR for Starting Pitchers
• Approximate nonparametric maximum likelihood inference for mixture models via convex optimization
• A General Framework for Empirical Bayes Estimation in Discrete Linear Exponential Family
• Group-Linear Empirical Bayes Estimates for a Heteroscedastic Normal Mean
• Nonparametric Empirical Bayes Estimation and Testing for Sparse and Heteroscedastic Signals
• Empirical Bayes Selection for Value Maximization
• Optimal Estimation of Change in a Population of Parameters
• Estimating the Mean and Variance of a High-dimensional Normal Distribution Using a Mixture Prior
• The Efficiency of Density Deconvolution
• Compound decision in the presence of proxies with an application to spatio-temporal data
• Improved Multiple Confidence Intervals via Thresholding Informed by Prior Information
• Improved Component Predictions of Batting Measures
• Asymptotically optimal nonparametric empirical Bayes via predictive recursion