Regardless of what team they follow, what league they favor, baseball fans seem to be united by one common cause: they all seem to think that umpires don’t know how to call balls and strikes. That would be problematic, of course, seeing as how often umpires are called upon to do that and how important it is to the game of baseball.

The latest cause for outrage was a pitch Lance Berkman took for a ball, which he would then follow up with a double on Thursday night in the Yankees' victory over the Twins in Game Two of the American League Division Series. Twins manager Ron Gardenhire got thrown out of the game for arguing the call of that pitch. And throwing fuel on the fire is TBS’s graphical display of pitch locations:

Screencaps of Lance Berkman's at-bat.

That animation in the lower right-hand corner of the screen is PitchTrax—different broadcasters come up with different names for it, but it’s all a nice graphical display of the same PITCHf/x data powering Gameday. And according to PitchTrax, that pitch caught just enough of the strike zone to be called a strike.

Did it?

Let’s put on our deerstalker caps and Inverness capes and play a game of “What did they know and when did they know it?”

And let’s start things off a little close to home.

What did you know and when did you know it?

What fans at home have to go off when judging balls and strikes is primarily the view provided by the center-field camera.  (We’ll discuss PITCHf/x in its various forms later on.)

There are a lot of things conspiring against you being able to judge balls and strikes off of video. You can sum it up broadly like this—your brain is a magnificent thing, and it takes the two-dimensional images you’re seeing on your television and reconstructs it so that you think you’re seeing it in three dimensions. It’s a marvelous process, and if you stop to think about it, it’s pretty amazing.

What it is not, however, is perfect.

In order to present the view that you see, the camera is positioned in the outfield at an offset, and then zoomed in to magnify the picture. This is, in essence, an act of deception—you are made to feel like you’re watching a little ways from behind the pitcher’s mound, when in reality you’re watching from the outfield bleachers.

And what the offset does is it distorts the view of the strike zone you have—it’s the phenomenon of parallax. You can observe this yourself, if you just go out to your car and check the gas gauge from the passenger’s seat and then from the driver’s seat:

Illustration of parallax using a car's gas gauge.

You also have problems with depth perception—essentially your brain is “guessing” the depth based upon visual cues in the image. This is difficult enough under the best of circumstances—there are really, really good reasons human beings have two eyes instead of one. Cyclops would be a terrible baseball player. You can get some idea of how this works just by covering one eye and trying to judge distance, then doing it with both eyes open.

The camera offset works against us here as well—it distorts our perception of the distances between the pitcher and the plate, for instance, as well as how we perceive the break of the pitch.

But the act of zooming the lens in has some consequences here as well. The most obvious effect of increasing the focal length of a lens is to increase the magnification and reduce the angle of view—you get a “closer” look. But that’s not the only effect. As you zoom in, lenses will tend to magnify more distant objects more than closer objects, like so:

Two cones at different levels of zoom, from a distance.

Now a different angle on the cones:

A top view of the same cones.

By zooming in on the cones, we make them seem to be closer to each other than they are. The same is true of the pitcher and the batter (and thus the pitch as it travels between them).

The act of recording a pitch on video significantly changes how it looks compared to how it really is. This is why if you’re watching on TV, and the umpire calls a close pitch in a way you disagree with, it is far more likely that the umpire is right than you.

(And of course, the exact offset and the amount of magnification changes from park to park and sometimes batter to batter. Some camera setups are going to make it look like more pitches are inside than they really are, others may make it look like pitches are lower than they are, and so on.)

What did Ron Gardenhire know?

I’m guessing not much. MLB dugouts are not well-positioned to give you a good view of the strike zone. After getting tossed, he could have gone into the video room and seen… the same video the rest of us saw. I doubt it does anything more for him than it does anyone else.

What did PITCHf/x know?

Of course, now we have PITCHf/x data (and before that, Questec). These systems use special cameras positioned in the stadium to record every pitch, and from there use computers to extract an estimated path of each pitch.

Now, we’ve already talked about the problems with using cameras to track pitches—but assuming you have good data on where the cameras were located relative to the field and the optical qualities of the lenses being used, using some advanced math you can get to a pretty accurate reconing of the pitched ball. Sportvision, makers of PITCHf/x, report that a properly calibrated PITCHf/x system is accurate to within a half an inch at the front of home plate.

But is the data we’re seeing coming from a properly calibrated system? Remember—the accuracy of the system is based on having accurate data on the location of the cameras and the properties of the lenses. In order to do this, PITCHf/x operators calibrate the cameras based on a set of landmarks placed upon the field before the start of the game. The key here is “before the start of the game.”

The game in question, for instance, had an announced attendance of 42,035—that’s a tickets sold count, not a turnstile count, but for a playoff game I imagine they’re pretty close. The average adult weighs something like 175 pounds (at least, that’s what they claim). What this means is that between the time the PITCHf/x system was calibrated and the time the first pitch was thrown, roughly 3,680 tons of baseball fan was introduced into Target Field, not counting seat cushions, signs and rally towels. And each one of those baseball fans was somewhere around 98.6 degrees Farenheit and radiating heat. All that weight and heat causes the stadium to actually move, and the cameras move with it.

In this case, I asked Mike Fast to look at the data and come up with an estimate of how far out of alignment the cameras at Target Field might have been that night. Estimating the error is difficult—in smaller samples, you have to contend with noise; in larger samples, you may miss changes that happen out of time.

PITCHf/x reported the pitch at .67 feet away from the center of home plate as it crossed the front of the plate; according to Mike’s corrections, it was probably .72 feet away, with a margin of error of .06 feet (accounting for the random error in pitch location measurement, plus the estimated error in the correction.) The edge of the zone (in other words, the edge of the plate) extends to .71 feet from the center of the plate in either direction. Now, PITCHf/x is giving us the center of the ball—if any part of the ball catches the plate, it’s a strike. So the effective zone extends to roughly .83 feet from the center of the plate.

So we think that pitch was probably a strike, given what we’ve seen with PITCHf/x—but we’re not entirely certain. (Remember, standard error means a 68 percent chance outcomes occur within the MOE.) It is, essentially, a borderline pitch.

And it is far easier for us to judge the accuracy of PITCHf/x’s estimate of the horizontal strike zone than the vertical—the position and width of home plate is fixed. The top and bottom of the strike zone moves with each batter, and if a batter shifts his stance, the top and bottom of the zone move as well. PITCHf/x operators manually record the strike zone (defined at the belt for the top and at the hollow of the knee) at the start of each at-bat; of course the batter is free to move around in the meantime. So when using the F/X data to judge whether or not a pitch is in the zone, you need to account not only for measurement error in the pitched ball, but the operator’s estimate of the strike zone as well.

This is why it is expressly unhelpful to go to your favorite PITCHf/x website, pull up a scatterplot from a single game, and use it as evidence the umpire did a bad job. The responsible thing to do (and this is what MLB does when using PITCHf/x to grade umpires) is to correct for these calibration errors and to look at a larger sample of data.

This is also one reason it’s infeasible right now to use PITCHf/x to call balls and strikes in a live game. (There are others—timeliness is one, of course. Another is operator error—game scorers are just as human as umpires, and they sometimes make mistakes in associating the PITCHf/x data with the right pitch in the game, for instance.)

What did the batter know?

I do want to make one last note—Hunter Wendelstedt isn’t the only person who thought the pitch was a ball. Berkman probably did as well, otherwise he would probably have swung at it.

What’s interesting to note here is that Berkman and Wendelstedt were the two people (besides possibly the catcher) with the best view of where the pitch crossed the plate. They’re also two people that have been selected for their ability to judge balls and strikes.

(An interesting side question—if a batter and an umpire disagree on a close pitch, which is more likely to be correct? I don’t know the answer to this. I mean, I’ve seen how Milton Bradley reacts on a called strike three, so I know how he feels about the answer. And he may even be right, in the case of Milton Bradley. But in general—I don’t know. I think it’s interesting, though.)

So I don’t think we’ll ever know, for sure, if that was “really” a ball or a strike. But in order to play a baseball game, you need to know the answer to that question—and Wendelstedt is the man entrusted to provide that answer. As Christina Kahrl so aptly put it, human umpires are the worst ways to determine if a pitch is a ball or a strike, except for the alternatives.