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

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.

About roughlynormal

I have been a math/statistics teacher for 25 years. I currently teach at an independent school in southern California. I also coach teaching fellows for Math for America - Los Angeles chapter. I love my career, my colleagues, and my friends & family.
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