ABOVE AVERAGE IS OVER:

In a paper published in 2016, Daniel Chen, Tobias Moskowitz, and Kelly Shue report their findings in a study of all pitches tracked by Major League Baseball's Pitch f/x system, which tracked every pitch thrown in every game and recorded data like pitch location, vertical or horizontal movement, and release point, from 2008 to 2012. They looked at consecutive pitches that were "called" by the umpire--that is, not hit into play, hit foul, swung at and missed, or otherwise not adjudicated by the umpire--and found 900,000 such pairs. They also categorized all called pitches as obvious (that the pitch's status as a ball or strike was clear) or ambiguous (pitches on or near the edges of the strike zone). They report that 99 percent of "obvious" pitches were called correctly, while only 60 percent of "ambiguous" pitches were.

They began with the specific question of whether an umpire was more likely to call pitch 2 a ball if they had called pitch 1 a strike--that is, whether the call on the previous pitch biased their call on the next one. They found a small but significant effect on all pitches, where umpires were 0.9 percent more likely to call pitch 2 a ball if they'd called the previous pitch a strike, and the effect rose to 1.3 percent if the previous two pitches were called strikes. The effect was more blatant when the next pitch was "ambiguous," with biasing effects 10 to 15 times larger than those on "obvious" pitches.

The authors categorize this as a manifestation of the "gambler's fallacy," the errant belief that random or even semi-random outcomes will always even out in a finite sample. For example, gamblers may claim that a roulette wheel that has come up black five times in a row is more likely to come up red on the next spin because the wheel is "due"--which, by the way, you'll hear quite often about hitters who are having a cold streak at the plate, and which is equally absurd. They also cite the possibility of self-imposed quotas, where umpires might feel that they have to call a certain number or percentage of strikes in each game.

Anchoring effect, a different cognitive bias, provides us with a simpler explanation. Some previous piece of information independent of the next decision still affects that next decision by changing the mind's estimate of the probabilities of certain outcomes. The umpire's call on the previous pitch should have no impact on their call on the next pitch, or on their probability of getting the call right on the next pitch, but it does because the umpire's mind does not treat these two events as independent, even though the umpire may not be aware of this biasing. It could be a matter of an internal quota: "I called that last pitch a strike, so I should try to even things out." It could be a subconscious expectation:

"The last pitch was a strike, and the pitcher isn't that likely to throw two strikes in a row, so this pitch is more likely to be a ball." Whatever the cause is, the simplest explanation is that the umpire's mind is anchored on that last called pitch, and therefore the umpire's internal calibration is thrown off for the next pitch. That means they're less likely to get the next call right--and that's another point in favor of giving the job of calling balls and strikes to machines, not humans.

The anchoring effect was first proposed by Tversky and Kahneman back in 1974, in a landmark paper modestly titled "Judgment Under Uncertainty." The section title "Adjustment and Anchoring" begins with a statement that sounds obvious but contains multitudes: "In many situations, people make estimates by starting from an initial value that is adjusted to yield the final answer."

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