There are two very important things to notice in these graphs:

• As the sample size (number of at-bats) increases, Harper's simulated performances vary less from his assumed ability 0.273. This is an example of the law of larger numbers.
• As the sample size (number of at-bats) increases, it is less likely for a hitter with an ability of 0.273 to have a performance of 0.500 or greater by random chance alone