The Zone with Two Strikes

Today a friend at Stanford sent me an article, Do We Shy Away from Pivotal Calls?, about research a couple of business-school students have done to quantify how an umpire's strike zone changes when there are two strikes against the batter. According to the study, which won second place at the MIT Sloan Sports Analytics Conference, umpires prefer not to call a batter out on strikes if the pitch is borderline. In fact, according to the charts below, umpires will only call strike three on a pitch down the middle of the plate 70% of the time.

The image on the left shows a typical strike zone when there are 0 or 1 strikes against the batter. The image on the right shows the typical zone with two strikes.

The revolution in baseball analytics has resulted in several different kinds of discoveries. First is the eye-opener, where new evidence dispels a long-held notion about the way the game should be played. The guys Michael Lewis profiled in Moneyball demonstrated, for example, that a high on-base percentage (OBP) is as valuable or more valuable than batting average (AVG). Sabermetricians have also shown that the sacrifice bunt is unwise in most situations. Both of these arguments challenged the status quo and were highly controversial, at least for a while. (Sacrifice bunting, actually, is still a topic of debate.)

The other kind of sabermetric revelation has the opposite effect, providing statistical evidence to support a pillar of received wisdom. Even a casual observer notices that umpires' strike zones change according to the situation. How could they not? Put yourself in the ump's shoes. Imagine calling a borderline pitch strike three to end the World Series. What if you got it wrong? Thankfully, the new MLB instant-replay regime does not allow for review of ball/strike calls, but still, isn't it just more prudent, from the ump's perspective, to err on the side of caution?

Not really. Umpires are paid to be objective. Ideally -- and I'm sure umps would tell you they strive for this ideal -- a ball is a ball and a strike is a strike regardless of the count. The Stanford study suggests not only that this isn't happening, but that this kind of objectivity is not possible. Think about it. If a major-league umpire can't be objective, who can?