A new measure of baseball batters using DEA

Data Envelopment Analysis (DEA) is used to create an alternative to traditional batting statistics called the Composite Batter Index (CBI). Advantages of CBI over traditional statistics include the fact that players are judged on the basis of what they accomplish relative to other players and that it automatically accounts for changing conditions of the game that raise or lower batting statistics. Historical results are examined to show how the industry of baseball batting has matured and potential uses of CBI are discussed. The application of baseball suggests that random variation may have an effect on CBI. We investigated this effect by creating noisy data sets based on actual data sets and then compared the results, which revealed a negative bias in the majority of cases. We then present and test an extension to DEA for mitigating this effect of noise in evaluating a batter's true ‘skill’.