## SSAC 14: What does it take to call a strike?

Difference between P(strike|S) and P(Strike|not S) for four different counts in baseball

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.

Every umpire shows bias for certain ball counts.