Biases When Calling Balls and Strikes

The source for this article:
What Does it Take to Call a Strike? Three Biases in Umpire Decision Making
Etan Green, David P. Daniels Stanford University,
Presented at the MIT Sloan Sports Analytics Conference, March 2014

Do umpires call balls and strikes solely in response to pitch location? If seems we do not. The study referenced in the research paper above analyzed all regular season calls from 2009 to 2011 in Major League Baseball – over one million pitches.

The Analytics

It found some very interesting analytics:
• The strike zone contracts in 2-strike counts
• The strike zone expands in 3-ball counts
• Umpires are reluctant to call two strikes in a row
It estimated each umpire’s aversions to miscalling balls and his aversions to miscalling strikes in different game states.
• For most pitches an umpire only needs to be 50% sure that a border-line pitch is a strike to call a strike half the time.
• However, the average umpire needs to be 64% sure of a strike to call strike three half the time.
• Even a strike-biased umpire still needs to be 55% sure of a strike to call strike three half the time.
• When the last pitch was a strike, the average umpire’s strike threshold rises to 60%.
• When the last pitch was ball (expect ball 3), the average umpire has a 50% chance of calling a border-line pitch a ball or a strike.

More interesting facts from the study

• Even though the umpire is not making his decisions based solely on the location of the pitch, this behavior actually helps him make more accurate calls.
• This is because the umpire has “expectations” about where he pitcher is going to throw at a certain count and whether the batter is going to swing.
• This is called “Bayesian updating” which is a fancy way of saying that the umpires are “statistically discriminating” – they use prior information beyond the exact location of the pitch.
• So, the umpire is calling the close pitches based on the pitch he would expect to be thrown.
The URL for this research paper:


An Earlier study

The following study was published in 2010 by The Hardball Times with the title “The Compassionate Umpire.”  It used Pitch F/X data to quantify the changing size of the strike zone.  By plotting the location of 200,000 pitches, the study determined that the strike zone can differ by more than a full qsquare foot depending on the count.  Overall, the more strikes a batter accrued, the smaller the strike zone became, reaching its smallest size when the count was 0-2.  At 3-0, the strike zone was at its largest.
More statistics from this study:
  • The 0-0 pitch favors neither the pitcher nor the batter.
  • The 0-1 pitch thrown on the edge favored the hitter 60.8% of the time
  • The 1-0 pitch on the edge favored the pitcher 55.1% of the time
  • The 3-0 pitch taken on the edge were deemed a strike 65.4% of the time
  • The 0-2 pitch favored the hitter 73.8% of the time