Strike Zone Sizes Crouching Batters
We consider the strike zone a static area, although, in reality, it is a moving target. "As the batter is prepared to swing at a pitched ball," an umpire has to guess the height of the batter's letters and his knees. This moment is imprecise, yet PITCHf/x analysts must try to capture the top and bottom of the strike zone to get the most out of the PITCHf/x data.
As I see it, there are several ways to either directly observe or infer the parameters of the strike zone. One is to follow the work of John Walsh, Dan Fox, Ike Hall, Josh Kalk, Dan Turkenkopf, Mike Fast, Jeff Zimmerman, Ike Hall, and others, who all find the probability of a pitch being called a strike at any given location. It is helpful to know the edges of the zone without such rigorous analysis as these, as they necessitate large volumes of data. Instead, we know the plate is 17 inches wide. That serves just fine for the width of the zone. And we hope that we know the batter's height. Unlike weight, which varies year to year and is sometimes a touchy subject for athletes, height is consistent throughout a player's playing career, and should be fairly accurate. In some Pedroian cases, we'll hear that the guy is even smaller than listed. That's not the a big problem, though. The issue with using height, and height alone, is that batters have different stances. Fortunately, there are stringers at every game who mark what they believe to represent the top and bottom of the strike zone are for each batter. By linking the Retrosheet and Gameday databases, I found each batter's height and average top and bottom strike zone values.
Mike Fast has looked into the subject before, and I'm borrowing ideas from him, as well as an image from him below. The other guy whose data has proven useful to me in this study is actually the "Batting Stance Guy." BSG claims to offer "the least marketable skill in America," though, for me, it's quite useful.
You can estimate the top point of a batter's strike zone as 56% of his height, and the bottom as 26%. But I think we can do better. I took 130,000 pitches vs. RHBs that crossed over the heart of the plate, spanning a foot in width. Using the top and bottom strike zone values provided for each pitch, the average top and bottom strike zone values for each batter, the batter's height, and finally a regressed version using the 2nd and 3rd categories, I found the percent of pitches that agree with the umpire's ball/strike call.
It would appear that height is the best predictor, but certainly the values inputted by the stringers can add some value. Yet there are still outliers.
Toby Hall is one of the crouchiest players in baseball, and Batting Stance Guy demonstrates as much in this video. He also stresses the bent knees of Vernon Wells and Albert Pujols, whose crouches I can envision, but unfortunately they can't be fully captured in a regression. And Alex Rios has a big crouch, which was even commented on by Christina Kahrl in a past BP Annual. She wrote, "Alex Rios' stance reminds me of Von Hayes--spread low, slightly knock-kneed, and will he, like Hayes, always just be that slightly less than expected but still-good player," to which I say, bite your tongue, Christina Kahrl. Von Hayes is an icon.
Most of the batters who have higher strike zones than their height would indicate are pitchers. Many pitchers stand at the plate stiff as a board. As for position players, BSG accentuates the straight front leg in Adrian Gonzalez's stance. Jhonny Peralta's stance is unique, too. And Chase Utley also has an upright stance, which is somewhat notable, but more importantly, Batting Stance Guy also does an impression of the Von Hayes crouch in the linked Phillies video, and any time you have the opportunity to reference Von Hayes, it's a no brainer.