Baseball Hacks

Significant Number of At Bats

How to choose a threshold for a statistically significant number of at bats.

Here’s a good trivia question for you: of all players who have played more than 15 seasons, who had the highest batting average? The answer is Michael Stanton. Yup, that’s correct: lefthanded pitcher Mike Stanton (relief pitcher for the Braves, Mets, and Yankees between 1989 and 2005) had a career batting average of .421, making him the greatest batter of all time, better than Ted Williams, Babe Ruth, and Barry Bonds.

Obviously, I’m kidding; Stanton was not the greatest batter of all time. He got 8 hits in 19 at bats over a 16-year career, making him lucky. This is a problem with a lot of baseball statistics: how can you tell if they’re significant? This hack explains how to think about this problem, and it shows a few things about baseball statistics that I think are remarkable.

Major League Baseball uses two thresholds to decide which players qualify for titles such as Highest Batting Average. (In case you’re wondering, these are actually part of the Official Rules; see rule 10.23, if you’re curious.) For batters, they require that a batter had an average of 3.1 at bats in every game of the season (that’s about 502.2 at bats). For pitchers, they require that the pitcher pitched an average of one inning in each game played over the course of the season (that’s 162 innings). Are these reasonable assumptions?

But often, baseball teams and announcers use less-stringent criteria ...