  Standard measures of batting performance such as a batting average and an
on-base percentage can be decomposed into component rates such as strikeout
rates and home run rates. The likelihood of hitting data for a group of players
can be expressed as a product of likelihoods of the component probabilities and
this motivates the use of random effects models to estimate the groups of
component rates. This methodology leads to accurate estimates at hitting
probabilities and good predictions of performance for following seasons. This
approach is also illustrated for on-base probabilities and FIP abilities of
pitchers.
