With two outs, Ben Zobrist batting, and Sean Rodriguez on first representing the tying run, Joe Nathan threw this 3-2, 82-mph curveball to end last night’s Rangers-Rays game and seal his 300th save:

And a million Rays fans (Are there that many Rays fans?) tweeted in terror and were suddenly silenced. With one called strike, the Rays’ win expectancy went from around 11 percent to zero.

I thought that pitch was outside. You thought it was outside. Brooks Baseball thought it was outside:

Joe Maddon thought it was outside, although unlike us, he might be suspended for saying so.

Joe Nathan, who benefited the most from the call, also thought it was outside.

And so, eventually, did home plate umpire Marty Foster, the man who made the call.

Sometimes when we talk about bad calls, we also talk about good pitch framing, but this isn’t one of those times. Pierzynski actually received the pitch pretty poorly, which may have contributed to the call. You can’t give the catcher credit for deceiving the umpire when his glove hits the ground.

So the question, really, isn’t “Did Foster make a bad call?” but “How bad a blown call was it?” The consensus on the internet in the immediate aftermath of the strike seemed to be that it was the worst blown call. (The internet isn’t known for its restraint.) After the game, I went on Facebook (a social media platform for popular people who have trouble keeping track of their many friends), and four of the five top posts on my News Feed were links to pictures or videos of the call, accompanied by comments expressing unfriendly feelings toward umpires. (The fifth post was a picture of a guy I talked to a couple times in college. He was riding a bicycle while wearing a big hat, and he wanted to share that with everyone.)

Was the internet overreacting? Well, let’s slow the pitch down a bit:

And now let’s stop it completely, at the very approximate point at which it crossed the plate:

It doesn’t look quite so bad now, and if I’d stopped it a frame earlier, which might have been just as accurate, it would have looked even better. (Because of how fast even a breaking ball travels, it's possible that no frame of video captured the ball precisely as it crossed the plate.)

There were at least three things, without looking at any other information, that made the call seem worse than it was:

  1. The offset center field camera, and the accompanying parallax effect
  2. The movement of the pitch after it crossed the plate, which made it look farther outside than it was when it mattered
  3. The fact that the call ended a close game

According to the raw PITCHf/x data, and Dan Brooks’ formula for determining distance from the center of the strike zone*, the pitch was 1.701 feet from center. What does that mean? Well, there were hundreds of pitches classified as called strikes from 2009-12 and recorded as crossing the plate farther from the center than that (not counting called strikes on 3-0, when the strike zone gets super-sized). Some of those—probably many of those—were PITCHf/x calibration errors or operator errors: pitches that weren’t as far from the strike zone as the measurements suggested, or pitches that were tagged as called strikes when really they were swinging strikes (or something else). I couldn’t watch them all if I wanted to, since not all the video is available, but let’s just assume that some calls in there, as recorded by PITCHf/x, were worse than Foster’s.

What if we narrow the sample to calls with two strikes? That’s much more manageable. The data says that 21 called strikes on two-strike counts in the past four seasons have been farther from the center of the plate than last night’s game-ending offering to Zobrist. I watched the first five, and the only one that A) is actually a called strike and B) looks like it might have been as far from center as the stats say was this one, a 3-2 pitch from Fernando Rodriguez to Cody Ross on August 21, 2011, with Fieldin Culbreth behind the plate:


That pitch, the numbers say, was 2.093 feet from the center of the strike zone. It doesn’t look like it’s that far, although the angle makes it tough to tell. (And it might not have been that far. Keep that in mind for a few more sentences.) But we’re splitting hairs here. Based on the raw PITCHf/x data, the internet was basically right, at least in its evaluation of last night's call, if not its response to it. That data suggests that while the strike to Zobrist wasn’t the worst call of the PITCHf/x era, it was on a fairly short list.

But. Raw PITCHf/x data isn’t park-corrected, and when we’re evaluating umpire calls, park corrections matter. As Mike Fast wrote a couple years ago, “Errors of an inch or two are sizable when grading umpire performance, and corrected location data would be useful in that application.” When we import PITCHf/x data into the BP database, we apply park corrections. And our best estimate of the PITCHf/x calibration error in Rangers Ballpark in Arlington last night is that the plate-x values were reported approximately two inches to the right (from the pitcher's perspective) of where the ball actually was. In other words, the pitch to Zobrist was two inches closer to the center of the plate than the raw PITCHf/x data indicated.

That’s significant. The margin of error of the PITCHf/x system is about an inch. The radius of a baseball is a little under 1.5 inches. And the park-corrected data suggests that the ball was only about half an inch outside the boundary of the typical left-handed hitter’s strike zone (which, remember, is shifted a couple inches outside to begin with, relative to the typical right-handed hitter’s zone). What that means is that it’s conceivable—not likely, but statistically possible—that some part of the ball nicked some part of the plate. If Foster were on trial, and the internet were trying to put him in prison for calling pitches poorly, his defense team could establish reasonable doubt that the pitch was not a strike.

Now, the pitch might also have been a bit low—again, it’s difficult to establish with certainty, for the same reasons. And because the pitch was both A) probably outside and also B) maybe a bit low, it was probably a ball and very likely to be called accordingly. According to Colin Wyers, the 50 closest pitches to the park-adjusted position of the pitch to Zobrist were called strikes 4 percent of the time. But 4 percent is not never. If not for the camera angle, the movement of the ball after it crossed the plate, the way Pierzynski received it, the importance of the situation, and the PITCHf/x park effects, this call might have been perceived as just regular bad, not a time to take out the pitchforks and torches.

(It’s also worth noting here that Foster’s strike zone is shifted even farther outside and down to lefties than the typical umpire’s:

All those colored rings outside the rectangle suggest that Foster is a good guy to have behind the plate when you’re a pitcher living on the outside corner to a left-handed hitter.)

So Foster’s call was very bad, but not historically so. Before you call for his head, I want to show you one other pitch. Some of you might take this as further evidence that umpires are awful. I prefer to take it as further evidence that calling balls and strikes correctly is really, really hard. I’m talking about the worst called ball of the PITCHf/x era:

This was a pitch thrown by Boone Logan to Joey Votto last May, with Larry Vanover behind the plate. It was 0.033 feet from the center of the strike zone—less than half an inch. It’s very difficult for a pitch to be more centered than that. And theoretically, it’s very difficult for a ball-strike call to be more clearcut than that. If you look at a still, it seems like an obvious strike:

But umpires don’t get to call strikes from stills, or by advancing video frame by frame. When we look at the pitch in motion, it’s not as obvious:

Yes, the pitch crossed the heart of the plate. But it was coming from an unusual angle, thanks to the LOOGY’s typical closed stride, so it was cutting across the plate rather than passing straight over it. Catcher Chris Stewart is a good framer, but he didn’t receive this pitch particularly well. And Votto led the National League in walks in each of the last two seasons, so if you’re going to give anyone the benefit of the doubt on what looks to you like a borderline call, it would be him. Oh, and the pitch was traveling at 94 miles per hour. It’s hard to track objects moving that fast. So even what should have been the simplest call of the past few seasons wasn’t as simple as it seemed.

Calling pitches isn’t quite as hard as hitting them—think about how often even the best batters fail to do that—but it’s still so difficult that in trying to do it, umpires are stretching the capabilities of human sensory systems. There are over seven billion people in the world, and the current crop of umpires probably doesn’t contain the absolute best of the seven billion’s umpire material, since not everyone in the world wants to be an umpire, or even knows what an umpire is. But the umpires we have are very, very good at umpiring, both because of their natural ability and their extensive experience. When they fail, it’s not because they aren’t trying, or because they’re unqualified. It’s because they’re human. Maybe they involuntarily blinked, or had to sneeze, or maybe their eyes were watering.  There’s no point in blaming the umpire for, basically, being one of us, but much better (at calling balls and strikes). Human beings didn’t evolve to play baseball, specifically, so we’re doing the best that we can.

If you like the “human element," presumably you’re pleased that a close game ended on a bad call instead of on the players’ own merits. (I’ve never been quite clear on how liking the human element works.) If you like the idea of “robo umps,” or supplementing the current system with some sort of technological aid, last night’s controversial call is another piece of evidence in support of your position. But as long as we’re operating under the current system, we have to accept that some small percentage of calls will be this bad, and some even smaller percentage of calls will be this bad and also potentially affect the outcome of a game. And then we have to decide whether we're enjoying baseball just as much as we would if we could count on all the calls. As it becomes increasingly clear that we no longer have to settle for uncertainty, the answer, for more and more of us, will be “no.”

* sqrt(px^2+abs(pz-2.575)^2)

Thanks to Dan Brooks and Colin Wyers for research assistance.