### Which On-Base Percentage Shows the Highest True Ability of a Baseball Player?

#### Abstract

This article looks at the true on-base ability of a baseball player given their on-base percentage. Unlike a typical proportion estimation problem where one is able to make an analysis based on knowing the number of successes and number of trials, this problem only gives us the proportion of successes rounded to three decimal places. This article presents two different Bayesian models for finding the highest true on-base ability. The first Bayesian model considers modeling the distribution of times on base, plate appearances and probability of being on base as a prior distribution and then finding a posterior distribution given an observed on-base percentage. The second Bayesian model looks into the distribution of hits, walks, hit-by-pitches, plate appearances and probability of getting on base and then creating a simulation of baseball players to see their true ability given a particular on-base percentage. After implementing the two models, it turns out that the highest reasonable on-base percentage that shows a player's true ability is around .4.

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