Next time you're following a major-league baseball game on television, watch a few at-bats closely. You might just see the strike zone expand or contract from pitch to pitch.
That's the conclusion that two Stanford PhD candidates have reached after watching every pitch thrown in the course of three consecutive seasons.
In an academic paper they're preparing to submit to an economics journal, Stanford's Etan Green and David Daniels contend that umpires are more likely to err on the side of caution when the fate of a plate appearance is in their hands, whether it's a walk or a strikeout.
Specifically, when there are two strikes on a batter, they say umpires are more likely to call a borderline pitch a ball rather than a strike. And when there are three balls on a hitter, the umpires are more likely to call that same borderline pitch a strike.
"Given a choice between a pivotal decision and an inconsequential decision, the umpires tend to err on the side of the inconsequential decision,'' Green said in a recent telephone interview, "unless they're absolutely sure the pivotal one is right.''
What about close 3-and-2 pitches taken by the batter? They said the strike zone still shrinks some but that it's not as egregious as with any other two-strike count.
To reach their conclusions, the Stanford duo analyzed more than a million pitches from the 2009, 2010 and 2011 seasons, using data that is publicly available thanks to Major League Baseball Advanced Media's PITCHf/x tool, which tracks the speed and location of every pitch.
The Stanford duo's findings did not come as a surprise to the Mets' Dillon Gee, a control pitcher who makes his living by hitting the corners of the strike zone. He thinks recent technological advances have led umpires to be extra careful when it comes to called third strikes.
"I'm sure they don't like to go back and see they sent three guys down on pitches that were out of the strike zone,'' Gee said. "I'm sure they're just probably more locked in on making sure it's a strike. They're not ending someone's at-bat on a questionable pitch. I think that's probably why.''
The results also were of interest to Mets catcher Travis d'Arnaud, who has received rave reviews from Mets pitchers this season for his ability to frame pitches -- move close pitches ever so slightly back over the plate for appearance purposes.
"I haven't really been paying attention to that,'' d'Arnaud said of the potential strike zone changes based on the count, "but I'll start looking.''
Major League Baseball, however, doesn't need to start looking. The performance of plate umpires has been something league executives have been studying through technology for more than a decade, and the league has a different take than that of the Stanford guys.
The league's current program, called Zone Efficiency, has been in use since the start of the 2009 season, and it's based on the same PITCHf/x data the Stanford guys used for their study.
However, MLB senior vice president for baseball operations Peter Woodfork, who oversees the umpires, said the league uses the PITCHf/x data "as the starting point'' in its system.
Although Woodfork declined to reveal the ultimate findings, calling it confidential, he said they "strive to make sure we are consistent throughout all at-bats, no matter the count.''
"Since we started using advanced technology to help grade plate scores, umpires have continued to improve in calling balls for pitches off the plate,'' Woodfork said. "However, we walk a fine line as we also do not want umpires to go too far and then start incorrectly calling balls.''
Joe West, the 36-year major-league umpire who is the president of the World Umpires Association, did not return a call seeking comment.
To be sure, Gee said he, as a pitcher, isn't bothered by the Stanford duo's findings. He said part of his job is to figure out what strike zone he's pitching to on a given day and then do his best to take advantage of whatever leeway he can get.
"Every guy is different back there, too,'' Gee said. "Some guys might give you an inch or two away, but not in. I think it just depends on the guy, too. That's part of pitching, too, knowing what zone you're throwing to.''
But ultimately the strike zone is a set standard in a rulebook, and its evolution over time -- as seen through the eyes of umpires -- has historically been something of interest to the baseball world.
And now everyone has access to at least some form of advanced technology to help see what the umpires are looking at.
"There's a larger question we're after,'' Green said. "Are umpires aware they're doing this? And I think that's a matter that's up for debate.''