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

By Lawrence D. Brown. 2008

123 citations recorded by the source corpus.

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 naive predictor which directly uses the current average to predict the future average. One feature of all the statistical methodologies here is the preliminary use of a new form of variance stabilizing transformation in order to transform the binomial data problem into a somewhat more familiar structure involving (approximately) Normal random variables with known variances. This transformation technique is also used in the construction of a new empirical validation test of the binomial model assumption that is the conceptual basis for all our analyses.

Subfields: Economics and Econometrics, Nature and Landscape Conservation, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/bb3ec2eeb6714de0f3e3632e6dd44810afc193d5

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Citations in the corpus

Empirical Bayesball Remixed: Empirical Bayes Methods for Longitudinal Data (2017, methodology): “Our approach is related to recent work by Weinstein, Ma, Brown, and Zhang (2015) on grouped patterns of heterogeneity in the normal mean model, although the longitudinal data structure here permits estimation methods that are considerably more general.”
Improving Transparency and Replication in Bayesian Statistics: The WAMBS-Checklist (2017, unknown): “Finally, data-based priors can be derived based on a variety of methods including maximum likelihood (see, Berger, 2006; Brown, 2008; Candel & Winkens, 2003; van der Linden, 2008) or sample statistics (see, e.”
A Bayesian Approach to Multilevel Structural Equation Modeling With Continuous and Dichotomous Outcomes (2015, methodology): “Within this context of data-driven priors, it is common to use ML estimates (or akin) to inform the prior distribution (see, e.g., Berger, 2006; Brown, 2008; Candel & Winkens, 2003; van der Linden, 2008).”
NONPARAMETRIC EMPIRICAL BAYES AND COMPOUND DECISION APPROACHES TO ESTIMATION OF A HIGH-DIMENSIONAL VECTOR OF NORMAL MEANS (2009, background): “This choice was studied in our simulations and also in Brown (2008) and Greenshtein and Park (2007), where real data sets are explored.”
Group-Linear Empirical Bayes Estimates for a Heteroscedastic Normal Mean (2015, methodology): “We use the popular baseball data of Brown (2008), which contains batting records for all Major League baseball players in the 2005 season.”