We have known for several years that right-handed and left-handed batters do not see the same strike zone in the major leagues. The strike zone for left-handed batters shifts about two inches toward the outside. This observation goes back at least to Dr. John Walsh’s analysis of PITCHf/x strike zone data in 2007.

In my analysis of the strike zone earlier this year, I suggested the following:

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.

Today, I want to investigate an alternative explanation, not because the above explanation is faulty or insufficient, but rather as part of the process of understanding the strike zone and how home plate umpiring works.

While researching hit batters, I observed that the umpire positioned himself differently on inside pitches to Chase Utley and Raul Ibanez. It turns out that changes in umpire positioning are not a rare event.

I decided to track the position of a home plate umpire’s head over multiple pitches. I began with the game from which I drew the original Utley-Ibanez comparison—Phillies at Cardinals, June 24, 2011, umpired by Mike Estabrook. I tracked the 27 pitches thrown in the first inning of that game, and here is what I observed. The horizontal dimension is from the umpire’s perspective.

Home plate umpires normally stand in the slot between the batter and catcher. When Estabrook does this, he is much closer to the plate with a left-handed batter up. With a lefty batting, he stands right in line with the edge of the plate. With a righty batting, he is about eight inches inside. In addition, when the catcher sets up for an outside pitch, Estabrook’s position is lower and usually a little farther outside.

I tracked the same data for two additional games in Busch Stadium, which has the advantage of a straight center field camera view. One game involved the Giants and Cardinals on June 2, 2011, umpired by Tim Welke. The other game involved the Blue Jays and Cardinals on June 24, 2011, umpired by Tim McClelland.

Welke’s position for left-handed batters is similar to Estabrook’s. However, he is much closer to the plate for right-handed batters, almost a mirror image of how he lines up for lefties.

McClelland’s technique was much different from the other two. Estabrook and Welke moved into position immediately after the catcher moved and were stationary prior to and during the entire flight of the pitch. McClelland started his move later and kept moving, following the pitch down lower in his stance, as well as laterally, all the way until it hit the catcher’s mitt. Moving during the pitch seems like a bad idea for consistent strike calls. Unfortunately, the facts get in the way of that theory. McClelland is one of the best-rated umpires according to the players and one of the best-rated home plate umpires according to my own measurements of percentage of correct calls. (Tim Welke is one of the worst-rated at strike calls, and Mike Estabrook is in the middle of the pack, though all the umpires are very close together in that measure of performance.)

Let’s look at the strike zones for each of these three umpires, first for right-handed batters, and then for left-handed batters, based upon pitch location data from 2010 and 2011. The black box shows the approximate left and right boundaries of the rulebook zone and the average top and bottom boundaries called by major-league umpires for a batter of average height. The perspective is from the umpire’s viewpoint.

You can see that McClelland does a good job of calling the rulebook zone left and right, while Welke and to some extent Estabrook have wider zones for right-handed batters.

All three of the umpires have zones shifted outside for left-handed batters, Welke the most, Estabrook in the middle, and McClelland the least. I chose McClelland and Welke because they represented umpires near the extremes in zones for left-handed batters (and because both had worked games behind the plate in St. Louis this year).

I had hoped that the variations in umpire positioning might explain the shifts in their strike zones. If so, it is not clear to me how, at least not from this sample of three umpires. Still, I found it interesting that umpires have predictable patterns of positioning based upon the positions of the catcher and batter.

I would like to touch on one other aspect of umpire strike zone evaluation. If you look closely at Estabrook’s plot for right-handed batters, you may notice something strange. Did he really call a strike on that pitch located at 2.96 feet high and 1.87 feet wide of the center of the plate? That is 14 inches off the edge of the plate!

If you believe the PITCHf/x data, then yes, he did, but it might be wiser to believe Estabrook than the data in this case. I reviewed the video of that pitch, and while it does appear to have been outside off the plate, it almost certainly was not 14 inches outside. By no means do I advocate video as an accurate method for judging strike calls. Relying on video leads to all sorts of problems, not least not being able to tell when the ball crossed the plate, even with a straight center-field camera view as we have for the pitch in question here. With those caveats, here is a still frame showing roughly where the ball crossed the plate.

From this angle, the pitch appears to be maybe five inches outside.

When I wrote earlier this year about the accuracy of PITCHf/x plate location data, I described a method for determining the error in the data. I happened to include Busch Stadium as the example, and you can see this game, the first of the 2010 season, as a prominent outlier.

I estimate that the PITCHf/x system was recording plate locations about four to five inches too far outside for the first two games of the 2010 season. That would make the pitch only nine inches off the plate, which still seems a bit much, both by the video and by the other strikes that Estabrook has called over the last two seasons. Perhaps the PITCHf/x plate location error was even bigger than I have estimated.

The PITCHf/x plate locations are generally within an inch or two of being accurate, but on rare occasions, they can be a lot worse. It is important to keep this fact in mind when evaluating umpires. Otherwise, you may find yourself thinking that Estabrook or some other umpire needs a seeing-eye dog on the field to assist with his zone.

The fact that the catcher target is set outside more often for left-handed batters may be the primary driver of the outside shift of the strike zone for left-handed batters. However, that would not seem to explain the bulk of the variation between umpires, who, over the course of several seasons, should see approximately the same fraction of left-handed batters and a diverse mix of pitchers. Variations in umpire positioning or other umpire mechanics would seem to be a natural explanation.

However, though I was able to identify unique positioning traits for the three umpires I investigated here, I could not correlate those variations to the variations in the umpires’ strike zones.