  Predicting batting averages for specific batters against specific pitchers is
a challenging problem in baseball. Previous methods for estimating batting
averages in these matchups have used regression models that can incorporate the
pitcher's and batter's individual batting averages. However, these methods are
limited in their flexibility to include many additional parameters because of
the challenges of high-dimensional data in regression. Dimension reduction
methods can be used to incorporate many predictors into the model by finding a
lower rank set of patterns among them, providing added flexibility. This paper
illustrates that dimension reduction methods can be useful for predicting
batting averages. To incorporate binomial data (batting averages) as well as
additional data about each batter and pitcher, this paper proposes a novel
dimension reduction method that uses alternating generalized linear models to
estimate shared patterns across three data sources related to batting averages.
While the novel method slightly outperforms existing methods for imputing
batting averages based on simulations and a cross-validation study, the biggest
advantage is that it can easily incorporate other sources of data. As
data-collection technology continues to improve, more variables will be
available, and this method will be more accurate with more informative data in
the future.
