Is an .833 hitter better than a .338 hitter?
This article considers the problem of using batting average alone to estimate a baseball player’s chance of getting a hit. This problem differs from typical proportion estimation problems because we know only the observed proportion of successes rather than both the number of successes and the number of trials. Our information is also restricted because the observed proportion of successes is reported to only three decimal places.We solve this problem in the context of present-day major league baseball by first developing a model for the joint distribution of hits, at bats, and chance of getting a hit. We then treat that model as a prior distribution and update the prior based on the observed batting average. One interesting result is that among batting averages likely to occur in practice, .334 leads to the highest posterior mean for true ability.
|Main Author:||Frey, Jesse.|