Have you ever thought that umpires are a bit too willing to call strikes when the count is 3-0? Or, perhaps, you’ve noticed that umpires rarely call strikes when the count is 0-2? In this very clear paper, Etan Green and David Daniels from Stanford University use Pitch f/x data to answer questions about how the count (number of balls and strikes against a batter) help predict the chances that an umpire calls a ball/strike on the next pitch.
I was impressed with how the researchers wrote and presented so that everybody can understand their work. This paper is easy to understand and share with students in high-school, in my opinion. It simply takes a baseline understanding of the rules of baseball, basic probability ideas, and reading three-dimensional graphs.
How are umpires biased?
- 3 balls: P(called strike) rises by about 10 per
centage points above what happens overall.
- 2 strikes: P (called strike) reduces by as much as 20 percentage points below what happens overall.
- Last pitch called strike: P (strike) reduced by as much as 15 percentage points.
Is this isolated to a subset of umpires?
Let’s look at the 50% contour line of calling
a strike overall, When looking at pitches after 2 strikes, this contour contracts. The area between these contours is called a “band of reversal:” We found a lack of bias emerging for pitches called after a ball. But the ENTIRE distribution of strike thresholds is above zero for pitches after two strikes. IN short, EVERY UMPIRE IS BIASED.