Ever since the PITCHf/x system debuted in the 2006 playoffs, people have been interested in what it says about the strike zone that the umpires call.

John Walsh and Jonathan Hale provided some of the seminal work on the topic. John observed how the umpires called a strike zone that was wider than the rulebook definition but not as tall and that it was shifted toward the outside for left-handed batters. Jonathan also looked at the umpire zones and broke down the results by umpire and pitcher.

Jonathan and recent BP addition Dan Turkenkopf built on this work by examining how the strike zone changed in a variety of situations: by inning, by pitcher age/experience, by pitcher control, by home/away team, etc.

More recently, John Walsh and J-Doug Mathewson raised the profile of the discussion with articles about how umpire zones change based on the ball-strike count and other factors. Jonathan Hale and Dave Allen had observed many of these effects previously, but John and J-Doug’s work got the attention of Rob Neyer, and with that attention came a lot of criticism of umpire abilities from Rob and others. Unfortunately, the focus was more on inflaming hysteria about bad umpiring than on thoughtful sabermetric questioning:

From Major League Baseball's perspective, it doesn't matter why it's happening. It shouldn't be happening, and we can only hope that something's being done. The strike zone should be the strike zone, regardless of the count. If the umpires call it the same way every time, the players will adjust accordingly. And it's worth pointing out that the games would go just a little quicker if umpires weren't consistently extending plate appearances based on the count.

Why would umpires be influenced to change their strike zones in so many different ways? What physical or mental factors influence them, and is there any evidence to support those theories? Are the umpires really as inconsistent as the data presented by the articles to date would suggest?

I have spent portions of the last couple years investigating the data about the strike zone and puzzling over those questions, mostly without finding answers I considered satisfactory, until recently, when a number of separate ideas coalesced into a theory about how umpires actually call the strike zone. Most of the ideas are individually well known in baseball and will not come as a surprise. What came as a surprise to me, however, was how they fit together to explain with one consistent theory a great deal about the data that has been observed about the umpire strike zone.

Individual Batter Zones

As mentioned above, several analysts have found that different pitchers have different strike zones called by the umpires. It turns out that batters also have their own individual zones. That this is true in the vertical dimension is not surprising, of course. Batters are of differing heights, from David Eckstein at 5’7” to Adam Dunn and Corey Hart at 6’6”, and their crouches are more or less extreme, leading to varying vertical boundaries even for the rulebook strike zone. However, individual batter strike zones, like individual pitcher strike zones, also vary by an inch or two on the inside and outside edges.

In aggregate, this shows up as the previously observed difference between left-handed and right-handed batters, but it also extends to differences among individual batters of the same handedness.

The first theory I examined as an explanation for this variance among batter zones was that batters who stood closer to the plate had their zones shifted outside as a consequence of the umpire using the batter’s body as a reference point. It is true that there is a correlation between batters who stand closer to the plate, as measured by how often they are hit by inside pitches, and those whose strike zones are shifted outside. However, the correlation is not perfect, and the counter-examples are particularly instructive as to the true cause of shifted strike zones.

For example, Jason Kendall hangs over home plate and is among the batters with the highest hit-by-pitch rates. Nonetheless, his strike zone was shifted almost an inch inside relative to the average right-handed batter. On the other end of the spectrum, Nelson Cruz has a very upright stance that keeps him away from the plate, and he is near the low end on hit-by-pitch rates. However, his strike zone was shifted almost an inch outside relative to average. What could be causing this disparity?

You might know that Kendall displayed the last vestiges of a power stroke during final years of the Clinton administration, while Cruz had a slugging percentage of .555 over the last three years. Despite Kendal’s tendency to crowd the plate, pitchers are unafraid to come inside and over the plate to him, whereas low and away is the favorite spot for a hurler confronting Cruz.

The typical pitch location seen by the batter has a strong correlation to the horizontal shift in his strike zone. Batters who see more pitches on the outside edge also see their strike zone boundaries shift farther away on both the outside and inside edges of the plate. Batters who see more pitches on the inside edge see their strike zone boundaries shift toward the inside.

The question, then, is whether the umpire calls the strike zone differently because the pitcher and catcher are aiming the pitches differently to the batter or whether the causality runs in the opposite direction. If the pitcher and catcher are adapting to an already existing umpire-specific zone for each batter, that still leaves us with the unanswered question of why the umpire zone differs from batter to batter, and batter positioning at best offers only a partial answer to that question.

I was unable to definitively answer the question of the direction of causality, but a mountain of circumstantial evidence points to the umpire zone being influenced by the location of the catcher’s target, rather than the other way around. Thus, I propose that the catcher target is the driving factor in how umpires call balls and strikes.

The Catcher Target Theory

In June 1993, Baseball Digest quoted Matt Nokes with his views on how umpires call the zone.

“Predictability is the key to getting borderline calls,” says Matt Nokes of the Yankees. “If the pitcher is consistent, then the umpire knows where to be looking. But if the catcher is jerking all around the plate and the ump does not know what is coming in where, it’s going to be harder for him to focus on those close pitches and you won’t get them. If the pitcher is throwing consistently where the catcher is setting up, he doesn’t have to be so fine. But if I set up inside and the pitch is on the outside corner, even if it is a strike, we’re not likely to get that call. Even if the pitch is over the outer half of the plate, it will be called a ball, because it missed the catcher’s target so bad. That’s just the way it is.”

If the umpires adapt their strike zones based on the location of the catcher target, it explains with one consistent theory many of the heretofore observed phenomena regarding the zone. If the catcher changes his target based on shifting umpire zones, these phenomena remain a collection of unrelated and unexplained oddities requiring a variety of unsubstantiated and sometimes contradictory theories about umpire motivations.

For example, as mentioned earlier, the zone for left-handed batters is shifted toward the outside. Do umpires have some bias against left-handed hitters? If so, why? Perhaps a more likely explanation is that they simply call more strikes outside to lefty hitters because that’s where the catchers are setting their targets, and the umpires are using the target as a cue. While right-handed batters see 58 percent of pitches outside of the midpoint of the plate, left-handed batters see 66 percent of pitches on the outside half. The average pitch to a left-hander is 2.4 inches farther outside than the average pitch to a right-hander, which dovetails nicely with John Walsh’s finding that the average strike zone for a left-handed batter was shifted 2.3 inches farther outside than the average zone for right-handed batter.

If umpires are influenced by the catcher target, it also explains why individual pitchers see such different zones. J-Doug Mathewson’s research placed Livan Hernandez and Felix Hernandez at opposite ends of the spectrum in benefiting and suffering from changing umpire zones. Look at where those two pitchers locate. (Pitches where the batter swung are not shown.)

Livan Hernandez aims toward the very edges of the zone, or even a little outside, both to righties and lefties, and it appears that the umpires give him the strike call when he hits the middle or inside of the catcher target. Felix Hernandez, on the other hand, aims closer to the middle of the zone. If he locates a pitch at the edge of the zone, he’s very likely to have missed his catcher target, and the umpires don’t give him the strike call in those cases.

Similarly, one of the variations in umpire zones that Dan Turkenkopf identified can be explained by variations in the locations that pitchers and catchers are targeting. Dan found that the older (or more experienced) a pitcher was, the bigger the zone he got from the umpires. It also happens to be true that the older a pitcher is, the more he pitches to the outside edges.

Why older pitchers pitch more on the outside edge is a question for further investigation, but it’s no accident that this affects the strike zone that pitchers see. This is another piece of circumstantial evidence that umpires are giving pitchers strikes on the edges when they hit the catcher target.

Catcher Framing

We can even look at pitchers who live on the edge of the zone and see some surprising differences among their receivers. Livan Hernandez got a bigger strike zone in 2008 with Joe Mauer behind the plate than he did when Mike Redmond was his catcher. In 2009, Hernandez got a bigger zone with Wil Nieves than with Omir Santos behind the dish. The effect is not huge, but it’s noticeable—the difference of a couple strikes per game. Other pitcher-catcher pairs demonstrate this effect, as well.

Compare the strike zones that Javier Vazquez saw with Jorge Posada and Francisco Cervelli catching him in 2010.

Vazquez saw a slightly larger zone on the outside edge to left-handed batters and especially to right-handed batters when Cervelli was catching.

Analysts such as Dan Turkenkopf and Bill Letson have looked at the issue of catcher framing using the PITCHf/x location data. They found dramatic and repeatable differences in framing performance among catchers, to the tune of 50 runs per season or more. Our catcher target theory of the zone would suggest, however, that a large part of this difference may be due to the typical pitch distributions thrown by pitchers and seen by batters. The differences in batter pitch distributions would probably mostly wash out over a season-size sample for a full-time catcher, but the pitcher sample for each catcher could remain highly biased and have a large effect on the framing measurement.

When Bill’s catcher framing numbers for 2008-2009 are normalized by pitcher, the best and worst catchers are around +/- 20 runs per season. This method could benefit from some additional fine-tuning, but at least the size of the effect is now in a range much more compatible with the size of the catcher ERA effect that Sean Smith found by studying catcher-pitcher pairs in the Hardball Times 2011 Annual.

This is an effect that has been observed at least far back as 1989, if not earlier. In The Diamond Appraised, Craig Wright discussed catcher framing skills.

Surprisingly, one of the key differences between the best and the worst is a mechanical factor. A catcher can get more strike calls on borderline pitches by not showing the umpire his glove as a target, or at least by drawing it back after the target is given. The best catchers—particularly the ones who call fewer walks in the matched innings—tend to give a full open-faced target to the pitcher and hold the glove closer to their body (watch Boone and Gary Carter). Holding the glove in toward the body is partially a physical reaction. Holding the glove perpendicular to the ground is a strain on the wrist and the forearm; holding the glove closer to the body eases the tension in the arm.

At first, the technique may seem counterproductive, giving a better target to the pitcher, but at the cost of losing the umpire by taking the glove out of his view. It would also seem to hurt your chances of getting a strike call by making you move more to go after bad pitches, particularly the low ones.

But that isn't the way it works. It's easy enough to handle the pitches around the strike zone with the glove held close to the body. The excess movement going after a bad pitch doesn't make a difference, because those are obvious ball calls anyway. It may even help emphasize to the umpire that if the catcher has to move a lot, it's a ball. Now consider the borderline pitch. Along with his natural judgment, the umpire is instinctively looking for clues. If he can't see the glove clearly, he may rely more on the catcher's movement; he didn't move, so it's a strike.

Not every strike zone variation can be explained by the catcher target theory, however. For example, there is a small but significant portion of the home field advantage (around 15 percent, according to Dan and J-Doug’s research) which derives from the strike zone. Average pitch distributions are very similar between home and visiting pitchers, implying that there is a different cause for the variation in umpire zone in that case.

The Effect of the Ball-Strike Count

Let’s dive in deeper on another source of strike zone variation that doesn’t seem to be explained by the catcher target theory: the changing strike zone by ball-strike count.

To recap, Jonathan Hale, Dave Allen, John Walsh, and J-Doug Mathewson have all observed that the strike zone is bigger in ball-strike counts that favor the hitter and smaller in counts that favor the pitcher. Since pitchers tend to pitch more to the edges in pitchers’ counts and more to the middle of the zone in hitters’ counts, our catcher target theory of the strike zone would suggest the zone should get bigger in pitchers’ counts and smaller in hitters’ counts. But that’s not what happens. What gives?

This is not a question to which I have an answer yet. However, it is instructive to look at the detailed location data by count. Though Dave conducted a regression that indicated that pitch type had no significant impact on the size of the zone at different counts, I found that pitch type and pitcher handedness did have a noticeable impact.

I compared mid-height pitches on the outside edge to right-handed batters at the 0-2 and 2-0 counts. The outside edge of the strike zone at 2-0 is about an inch and a half farther outside than it is at 0-2, as defined by the point where the umpire calls 50 percent balls and 50 percent strikes on average.

At this boundary, changeups were highly likely to be called strikes, especially from left-handed pitchers. Changeups made up about nine percent of the mid-height pitches on the outside edge at 2-0, but only three percent at 0-2. Sinking fastballs displayed a similar effect. On the other hand, sliders and curveballs were highly likely to be called balls, especially from left-handed pitchers. Breaking balls made up about eight percent of the mid-height pitches on the outside edge at 2-0, and 24 percent at 0-2.

Nonetheless, even if only four-seam fastballs are considered, the strike zone is still larger at 2-0 than it is at 0-2, still by about an inch and a half, and the reason for this remains unclear.

I did not find any significant bias in the sample of batters or pitchers between the 0-2 and 2-0 counts in terms of their pitch location distributions. The differences were less than one tenth of an inch, which is a small fraction of the observed effect.

Even if the sample of players is relatively unbiased, the PITCHf/x data itself may be biased. There is some error associated with all measurements, and though the PITCHf/x plate location measurements are highly accurate, they are not perfect. Umpire ball-strike calls give us some information about the likely direction of this measurement error. The effect is usually not large, but small distinctions can become very important at the edge of the strike zone. Thus, corrected PITCHf/x plate location measurements may be needed for some types of strike zone research.

I have previously speculated in response to the findings about the zone and the count that PITCHf/x measurement errors could be playing a role in the measured size of the zone. However, this effect turns out to also be a fraction of the observed effect. Moreover, it actually operates to exaggerate the difference in the size of the zone. After accounting for PITCHf/x measurement error, the actual strike zone edge is about 0.4 inches closer to the plate on the 0-2 count and about 0.2 inches closer to the plate on the 2-0 count.

A better understanding of how and why the zone changes size by count awaits the results of further research.

What’s Next?

Anyone researching the performance of umpires in calling balls and strikes is strongly encouraged to consider the catcher target theory. It does not fully explain every umpire variation, but it appears to be the primary factor in many cases.

Catcher framing is also an important topic in its own right. The specifics of what catchers do is worthy of further research with the PITCHf/x data. Noting that the catcher target affects the umpire zone is one thing; identifying and quantifying the effect of specific catcher mechanics is another. In any case, the ability to better quantify this aspect of catcher fielding is very important.

Whether baseball benefits from umpires adapting their zones to the catcher’s target is not necessarily a question with a simple answer. Umpires are rewarding pitchers for accuracy and command and penalizing them for being inconsistent and missing their target. Pitchers and catchers presumably expect this, and in As They See ‘Em, Bruce Weber argues that coaches and players in the dugout also judge balls and strikes in relation to the catcher target.

[Umpires will] say calling strikes is paramount, but they’ll withhold a strike call from time to time—if the pitcher badly misses the catcher’s target, for example, even if the ball might still graze the zone. If the catcher sets up outside and the pitch is up and in, the umpire ethos says the pitcher doesn’t deserve a close call for doing a poor job. Besides that, he’s made the catcher lunge; his glove probably moved out of the strike zone, which means it’ll look like a ball from the dugout, which means the umpire will be getting an earful if he calls a strike.

Is it a good thing or bad thing that some pitchers, like Livan Hernandez, are able to make a living by persistently targeting the edges of the zone? Similarly, some catchers can help their pitchers and their teams by gaining strike calls from the umpire through superior receiving mechanics. The umpire zone affects the career prospects of some players positively and others negatively. There is undoubtedly skill involved from both the pitchers and the catchers who are able to expand the strike zone. Such skill would be lost if the umpires were replaced with pitch-calling robots or were retrained to call the exact same size of zone for every pitch, regardless of the catcher target. Some people would find such fairness laudable; others would lament the passing of valuable baseball skills.

Even if it were desirable, it may not be possible for the umpires to cease using the catcher target as a physical reference point. It might be difficult for umpires to change that behavior, whether it is conscious or unconscious. The Zone Evaluation system, which is based upon PITCHf/x data and is used by Major League Baseball to grade umpires, takes into account the catcher target, according to statements made by Sportvision representatives at the 2008 PITCHf/x Summit. (The details of how catcher target is included in the umpire grading process were not given.  It may be similar to the process used with Questec data, which is described in As They See ‘Em, pp. 198-199.)

In the cases where the catcher target theory does not appear to explain the strike zone variation, it’s worth taking a deeper look to see if the mix of pitch types and pitcher and batter handedness are concealing instances of the catcher target theory in operation in canceling directions. Moreover, the pitcher, batter, or even catcher samples may be biased toward types of players who throw or see atypical pitch distributions.

Even if the sample of players is relatively unbiased, the PITCHf/x data itself has measurement error which may bias the results. Thus, corrected PITCHf/x plate location measurements may be needed for some types of strike zone research.

Umpire grading, whether individually or collectively in various game situations, is a tricky task. Umpires appear to call a zone that is very dependent on the location of a pitch relative to the catcher’s target. Sample bias and PITCHf/x measurement are also confounding factors. One may wonder how well Major League Baseball’s umpire grading accounts for these factors.

Many fans and writers rush to stick negative labels on umpires and to jump to conclusions of incompetence without carefully investigating the data. It’s not enough to throw up a PitchTrax graphic of the strike zone with a strike call shown outside the box in order to declare an umpire an incompetent idiot better replaced with a machine.

PITCHf/x data has been a great boon for baseball analysis, including the analysis of umpires and the strike zone, but it requires careful analysis if we are to come to conclusions that will stand up to scrutiny. The strike zone is an important topic, and the quality and motivations of umpires are worth investigating deeply. Let’s not stop with half answers and then delude ourselves that we are ready to sit in judgment of the umpires.

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{clap clap clap}

Fantastic research. If commenting is sparse today, it's only because the readers are stunned.
I agree Mike. This is phenomenal. I need more time to digest the findings.
Mike - Great work. Huge
"Stunned"? Not the adjective I'd use. "Feeling vindicated," maybe.

I thoroughly endorse Tom's "fantastic," and would take it a step further, to "long overdue." But you don't have to watch a lot of baseball to rapidly develop an intuitive sense that something like this has been going on. The question has been exactly what that "something" is, and this excellent study moves us closer to an answer.

I would also say, however, that if the results do stand up to scrutiny, they support the sense of outrage that I have come to feel about home-plate umpiring in the last decade. "Umpires appear to call a zone that is very dependent on the location of a pitch relative to the catcher’s target." Now where is THAT in the rule book? As Mike points out, there is two thing, and one thing only, that theoretically should affect the zone: the location of the space defined by home plate (which is fixed, after all) and the batter's shoulders and knees (which is variable). For it to be affected by a catcher's lunging, or other theatrics, moves baseball one step closer to pro wrestling.
Glah ... I can't type ... "there is two thing" should obviously be "there is one thing". Thought I'd fixed that!
I know some people feel that a changing zone is anathema. I don't know how I feel, but I do think it's important to recognize that it's a collective decision by baseball to call the zone this way--players and coaches are complicit--not some arbitrary decision imposed by fiat on an unwilling game by rogue umpires.

Also, changing the way the zone is called would have a substantial impact on the game. Some would say it would make it better, but it's not clear to me whether that's true.
Well, here's a scenario.

Last minute of the Super Bowl. The heavily favored New York Megaroids lead the Arizona Andro-Apes by two (2) points, but the Apes have the ball on the New York 35-yard line. Their rookie kicker comes in to attempt a field goal that, if successful, will produce the biggest upset in Super Bowl history. If he fails ... well, his name is Billy Goetz, so guess how history will remember him.

Mr. Goetz has the advantage of perfect field position, so he lines it up to go right down the middle. The snap is good, the hold clean, the blockers do their job. Goetz gets plenty of leg into it, but just VERY slightly hooks it. The ball grazes the left upright as it passes by ... on the inside.

The officials huddle as the crowd goes, well, ape. Someone has noted that the ball didn't go as straight and as true as it was supposed to. The kid missed his aim point, after all, by five feet, not just three inches! And the official stationed under the goalposts to make sure the kick went through had to move out of position.

And above all, he's a rookie.

After thinking about it, only one decision is possible. The referee waves his arms across his knees ...
To make your scenario more analogous to what actually happens in baseball, I'd say that they move the goalposts depending on the kicker. The officials do call field goals based on whether the ball actually goes through the goalposts, but not every kicker has the same goalposts. Where the goalposts are positioned for each kick depend upon where the kicker is kicking from and where he tends to kick to.

Right, that's a better analogy. However, the plate is there precisely for the purpose of defining the strike zone (side to side, anyway), just as the goal posts are there to define a field goal/PAT. The only difference is that it's far harder for an official to screw it up with goal posts, and consequently, an attempt by an official to redefine the "good" zone is vastly easier to detect. I submit, however, that that doesn't make the official's doing so any more egregious a violation of the role of the official than when an ump decides the strike zone isn't really what the rules say it is; it just makes the action more obvious, and harder to overlook.
If there were a like button here, I'd set up a macro to have it repeatedly clicked. This was terrific.
I would actually like to hear from umpires.

Specifically, will an umpire position himself more toward where the catcher is setup? If so, then he's got the "perfect" angle if a pitch comes that way, and he'll be offset at an angle if the pitch goes away from the catcher's target.

Ideally, the umpire is positioned directly behind home plate in line with the pitcher's mound. But, since the umpire may be moving left/right pitch to pitch, we've got a potential bias in play.
I used to umpire for local youth leagues -- so this is by no means meant to describe how MLB umpires do their work -- and we were trained to set up with our eyes right at the upper-inside corner of the strike zone for each pitch. That way you at least had the upper and inner boundaries down cold. By observation, that seems to be how they set up in MLB as well. At the same time, when you're an umpire wearing an "innie" chest protector (with the protector under your shirt), the catcher is your first line of defense from getting killed, so you see many umpires that subtly track where the catcher is -- shifting their bodies a bit to the outside if the catcher is outside, or lightly placing a hand on the catcher's back to move with the catcher. Essentially, if the catcher is set up on the outside corner, the umpire may shade his own placement that way and away from his typical set up on the upper-inside corner. That shift of position could explain a shift in the strike zone.

Relatedly, when umpires used "outie" chest protectors (the big balloon protectors), they set up in the middle of the plate with their eyes on the upper boundary of the strike zone. With the bigger protector, they're less reliant on the catcher for protection and can set up in the same place for each pitch.

Again, this is from my own amateur experience and observation of MLB, and an MLB umpire would offer infinitely better insight.
Best article I've read in months, good work.
Thank you all for the kind words. I'm glad you like it, and I'm glad I was finally able to spill all these thoughts out of my brain and onto the virtual page.
It's too bad the Pitch/fx wasn't around for the careers for Maddux and Glavine.
It was around for the last two years, 2007-2008. Glavine definitely pitched on the edges and took advantage of this. I was just looking at his data two days before publication. If I'd looked earlier I might have included him in the article. He wasn't quite Livan Hernandez-like, but he was very close, on par with Mariano Rivera in hitting the edges.

Maddux didn't appear to do anything special in expanding the zone, at least at the end of his career.
Too bad Pitch/fx wasn't around in `97 for the NLCS. It'd be cool to look at just how far Gregg was stretching the K zone, and where the catcher's glove was set.
This is the best baseball research article I've read in a long, long time. Bravo.
Excellent, Mike. The Livan/Felix graphic was a great choice.
This was an awesome article. Kudos to you, Mike. I am especially fascinated by the catcher-mechanics angle and would LOVE to see a study about today's catchers in terms of their glove mechanics and propensity of getting strikes. Also, intuitively, it seems to me that that facet might have an effect on the number of wild pitches/passed balls allowed by a given catcher.
Wonderful job, Mike! This is by far the best article I've seen on BP in a long time.

I'm 100% in the "uniform strike zone for all" camp, though. If the ball passes over any part of the plate between the batters knees and the letters of his uniform, the pitch should be a strike, period. I don't care who the pitcher batter, or catcher is, where they were positioned, or where the pitcher meant to put the ball. Bring on the robo-umps!
I disagree on robo-umps for a simple reason: If MLB did not have ball-strike arbiters, the quality of umpiring in the minors and amateur ranks would fall (nothing to aspire to) and consequently, those players would be less able to "learn the zone". So while we might get minor benefits in terms of pitch fairness in the pros, over time the ability of players (both pitchers and batters) to take advantage of that fairness would drop. Slowly at first, and gradually get worse.
Also, we would lose a big element of the game - namely, the quest of the pitcher to fool both the hitter and the pitcher with the breaking ball going in, then out of the zone. Hitters would start laying off those pitches more and more, hoping it misses the zone, thereby penalizing a pitcher for his duplicity and skill. Now, that pitch can also fool the ump, so laying off is not always the right call.
In short, better umpiring (especially of this end) may result in worse baseball.
That said, I definitely want video backup for all boundary calls and safe-out calls.
I have a theory that a batter checking his swing shrinks the strike zone. My logic is the batter moving the bat gives the umpire two things to decide - did he swing and was it a strike? The line of thinking is the umpire tendency is to not split the answer of those two questions, so if the batter did not swing at the pitch it is not a strike.
From anecdotal evidence I agree with you. I've looked into a some of the ball calls where PITCHf/x said the pitch was down the pipe, and they were either recording errors (data assigned to the wrong pitch) or check swings.
Problem I have is that we don't know where the umpire is positioned in relation to the pitcher and does his location stay constant for each pitcher. If the umpire is moving in regards to LHB and RHB, or even cheating to one side or another when a pitch is being thrown, there could be an effect on the ball/strike call.

In other words, the research is interesting but without the location of the umpire, the data is lacking a major component.
We know that the umpires position themselves on the inside edge of the plate, i.e., between the batter and catcher. Beyond that, though, we don't have a record. I would love to have a detailed record of umpire positions and stances.
Well done Mike. Seriously good stuff. Will admit to having to read a couple of paragraphs twice...
The two saves Koji Uehara "blew" last year -- against the Yankees, on home runs in the 9th -- were both preceded by could-easily-have been third-strike low-inside calls. In one case, at least, ARod made a comment to the umpire just before the non strike call. In both cases, Uehara's following pitch was a few inches toward the centre of the plate. Both became home runs. Has the data been analyzed to take into account the hitter, offensive team and opposing team? The Yankees caught a break both times. They were playing the last place team both times in games they were expected to win. It has long been said that veteran hitters are more likely to catch a break...
1. Batters do have an effect on the zone, and I talked about that in the article.

2. There does appear to be a home-field advantage in strike zone. I linked to Dan Turkenkopf's article on that topic, and J-Doug Mathewson wrote on that at Beyond the Boxscore and found the same size effect as Dan.

3. It still amazes me that thanks to Retrosheet, MLBAM, and Baseball-Reference, I can find the exact plate appearances you are talking about.

Nick Swisher's home run on September 8 was on a 2-0 pitch. It was in a decent location, on the black but thigh-high (-0.7, 2.4 ft), and followed a pitch that was very low and slightly more outside (-1.0, 0.9 ft).

Alex Rodriguez's home run on September 17 was on a 2-2 pitch that caught a more of the plate than Swisher's, plus it was on the inside half (-0.5, 2.3 ft). It followed a ball call on a pitch out of the rulebook zone but on the very margin of the real zone (-1.2, 2.2 ft). That pitch is called a strike to A-Rod less than 20 percent of the time.

It seems a stretch to say that the Yankees caught a break from the umpire in either of those two cases.
I should have also mentioned that the zone that A-Rod sees is very close to that of the typical right-handed batter.
I would think part of the effect would be the human desire to not call a 3rd strike on a questionable pitch.
That's what John Walsh suggested. That may well be part of it, but I haven't seen any proof of that in the data. There's nothing wrong with conjecture, and it can even be helpful, but we can't say we know on that basis. I'd like to know. There's more investigation to be done.
I've also seen (from the stands) an apparent trend towards giving the pitcher a break on 3-0, proportionally to the pitcher's experience. Does PitchFX show that?
Great stuff, Mike.
This is a really great article, and the useful images add so much more to the analysis than can be done with words. Nice work, Mike.
Early nominee for Article of the Year.

Great great work.
Just awesome stuff, Mike. As BillJohnson indicated, I think a few baseball fans intuitively know that there is bias in the pitch calling, but this is stunning in the presentation of the data and explanation of the most important interaction of the game.
Fantastic article Perhaps I missed this in the article, but it seems like this research assumes that the catcher on average is setting up at the centroid of the pitch clusters, yes? How can we be sure that is a valid assumption to make? If a pitcher tends to miss in the same direction consistently then there would be a bias in the presumed catcher location.
It seems reasonable to me to assume that the pitch clusters generally correlate with the catcher target. That much is common sense, and it's something I've validated by charting games from video. Whether the catcher target is exactly at the centroid of the cluster is another matter. I'm sure it's not always at the center. For one thing, most of the charts I presented are an amalgamation of ball-strike counts, and pitchers and catchers do vary where they aim and set the target. But also, individual pitchers may preferentially miss in the same direction from the middle of the glove, and individual catchers may set up the glove relative to the intended aim point in different ways.

If we wanted to be as accurate as possible in assigning a value to gaining strikes by pitchers and catchers, we'd have to account for those factors as best we could. For a first pass, though, I think it would be fine to assume the catcher setting up at the cluster center and see where that leads us.
I am overwhelmed by my love for this article.
First rate, Mike. Really, really good stuff.

Bring on the mechanized strike-calling robots. Watching a countless bad ball/strike calls every season is getting annoying.
IIRC, pitching guru Rick Peterson preached that pitches in the lower 1/3 of the strike zone have far lower BABIP than mid or high strikes. Does PitchF/X have any data on questions like this?
You might be interested in these articles by Dave Allen:

They address run value on swings, which is slightly different than BABIP like you asked about. PITCHf/x definitely has data that can be used to answer your question.
Thanx! Great article BTW
I'll add my voice to the chorus and say that this is really awesome stuff, the kind of thoughtful, well-researched article that will have people talking and linking back to it. It's also one of the many reasons I'm proud to write for BP--and maybe someday someone will think I'm the Mike that wrote this article :D
Another +1 for this article, both the original work as well as the thorough citations and links. A great primer for the discussion that I will bookmark since it collects and uses the various data so well. Looking forward to more.
Just want to add my own three thumbs up, Mike. I keep the third thumb in reserve for articles like this.
Thanks, Dave. That means a lot coming from you.
I concerned where your keeping that third thumb. Just kidding. Great research and article.
As a high school umpire, I can tell you that I'm not surprised by the results shown in this article. I think all umpires attempt to call the book zone, but there are things that can change your image of the zone. Among those would be movement by the catcher or batter - the catcher moving his glove through the zone, the batter checking his swing. Also, the fear factor when a catcher sets up outside probably has an affect. The best umpires for ball/strike calls are the ones that are affected the least, but I think all umpires would be affected somewhat.
Really great article. Thanks for sharing this info.
Wow, this is a phenomenal piece, Mike.

And as to the strike zone expanding/contracting based on the count, (I think tango hit on this one a while back) umpires generally want the players to be the ones to effect the game (this is even more true at the levels I've umpired Pony/Colt).
On the question of whether umpires are unwilling to end an at bat on a called 3rd strike, that shouldn't be that hard to test. The prediction is that the same pitch will be less likely to be called a strike when there are already 2 strikes, versus when there are not. (Might want to leave out 3-2 counts, to avoid conflating with the similar-but-different effect of feeling it is unmanly to not swing at a close pitch on a full count.)

You've alredy described the methodology and used it: cluster pitches by absolute location and handedness of batter (and any other features of the PA that you think might be important, such as batter height). Compare called strike rates within each cluster with and without 2 strikes. If the hypothesis is true, you should see a significant decrease in called strike rate when there are 2 strikes, independent of batter handedness or pitch location cluster.
The work has already been done by a lot of folks before me, and I listed them in the article. The size of the called zone definitely changes by count. The question is, why? I found some effect from pitch types, but the effect remained when only looking at fastballs.

I don't think we've ruled out that (1) something is biasing the sample of pitches that I/we haven't thought to consider, and/or (2) the umpires or catchers are doing something mechanically different based upon the count. For instance, catchers may (and do) take a different stance with two strikes in order to block third strikes in the dirt.

Until we examine more of these type of possibilities, I'm not comfortable simply chalking it up to an umpire philosophy of helping the underdog and considering the case closed.

One of the things that J-Doug identified needs more exploration: that the size of the zone changes with base-out state, and in favor of the party who already has the advantage. I haven't investigated that at all, but I'm hopeful that if we can identify the cause(s) of that, it may shed some light on what is causing the zone changes with the ball-strike count.
Mike- what about the observation that the zone for left-handed batters is shifted toward the outside. You don't addrfess this explicitly but it would seem that because all catchers are right-handed and wear their gloves on their left hand, that there would be a natural tendency to hold the glove a little left of center. Again consistent with your theory.
I mentioned in the article that LHB see more outside pitches than RHB. I didn't mention why this occurs, though. It's largely because LHB disproportionately face RHP, and they see a lot of changeups and fastballs on the outside half from RHP.

On the other hand, RHB face a closer to equal mix of RHP/LHP. Also, they tend to see fastballs on the inside half as much or more often than outside, and the sliders from RHP and changeups from LHP that they do see predominantly on the outside half aren't enough to tilt their location mix back to the outside to nearly the extent it does for LHB.
If I had time to watch every pitch, I'd be interested to keep track of the batter's reaction ... did he disagree with the ump's call? I'd bet plenty of batters are "whiners" ... and I'd bet we'd see some umps who get more whining ... and I'd bet we'd get some data which would further this conversation.

What makes me want robo-umps is the memory I have of watching the final out on Fernando's no-hitter ... my memory says the first pitch was outside, called strike 1 ... second pitch was further outside, called strike 2 ... third pitch was rediculously further outside called strike 3. I've been mad ever since ;-)
Why did I wait so long to read this article? Great stuff, I'm excited to see more research like this.