  We develop the SEAM (synthetic estimated average matchup) method for
describing batter versus pitcher matchups in baseball. We first estimate the
distribution of balls put into play by a batter facing a pitcher, called the
empirical spray chart distribution. Many individual matchups have a sample size
that is too small to be reliable for use in predicting future outcomes.
Synthetic versions of the batter and pitcher under consideration are
constructed in order to alleviate these concerns. Weights governing how much
influence these synthetic players have on the overall estimated spray chart
distribution are constructed to minimize expected mean square error. We provide
a Shiny web application that allows users to visualize and evaluate any
batter-pitcher matchup that has occurred or could have occurred during the
Statcast era (specifically 2017-present). This methodology and web application
could be used to determine defensive alignments, lineup construction, or
pitcher selection through estimation of spray densities based on any input
matchup. One can access this web application at
https://seam.stat.illinois.edu/. The computational speed with which the method
calculates the spray densities allows the app to display the visualizations for
any input almost instantly. Therefore, SEAM offers distributional
interpretations of dependent matchup data which is computationally fast.
