A Variance Decomposition of Individual Offensive Baseball Performance

This paper considers a variance decomposition of offensive baseball performance. Estimating the variance components of offensive baseball performance allows one to determine how much of the variability in performance can be accounted for by differences among teams and how much of the variability lies at the level of individual differences within teams. In addition to variance components, this paper examines the reliability estimates of the true team means in offensive baseball performance. Using offensive baseball data from the 2000 season, and replicated again for 2003, intra-class correlations and parameter reliabilities are obtained under the correct probability model for the performance measure in question. The results show that most of the variability in offensive baseball performance lies at the individual level with only a small number of measures where a sizeable amount variance is accounted for by differences among teams. Changes in the variance components and parameter reliabilities are observed from 2000 to 2003. Team level predictors are added to demonstrate the flexibility of the modelling approach. The paper concludes with a summary of the findings and implications for examining the contextual effects in baseball.