...that area over home plate the upper limit of which is a horizontal line at the midpoint between the top of the shoulders and the top of the uniform pants, and the lower level is a line at the hollow beneath the knee cap. The Strike Zone shall be determined from the batter's stance as the batter is prepared to swing at a pitched ball.
But although the definition is inflexible, the zone itself is a living, breathing, amorphous thing. Since PITCHf/x data was first released to the public, an army of studies have captured its many moods and sizes. Here's an article showing how the strike zone has grown to conform to the rulebook strike zone since the introduction of PITCHf/x, and here's an article from the end of the season showing that the expansion is still going strong. Here's one from this year's Sloan Sports Analytics Conference detailing how the strike zone varies with respect to count, and here's one modeling the strike zone as an ellipse, not a rectangle.
But few of these studies have looked at what effect, if any, the type of pitch thrown has on how umpires define the strike zone. Perhaps the best investigation of this is Jon Roegele's Baseball Prospectus piece from last year, but Roegele did not control for the effect of count in his study. Since we know that umpires can be influenced by subtleties such as how a catcher receives the pitch, why shouldn't they also be influenced by the break and speed of the ball?
If real, these effects would be important. Teams planning for a big series against a division rival could adjust their starting rotation based on the umpires behind the plate, putting the young flame-thrower up with the ump who gives you the high hard one, and saving the crafty veteran for the umpire who likes the curveball on the outside corner.
First, we need to see if different pitches are called differently. We begin by compiling all pitches taken (both balls and called strikes) from the 2014 regular season, grouping them according to their PITCHf/x classification, the count on which they were thrown, and whether they were thrown to right-handed or left-handed batters. Even after removing pitchouts, intentional balls, and pitches that the system couldn't label, we are left with a sample of over 200,000 pitches thrown to righties, and 170,000 thrown to lefties. The breakdown for right-handed batters is shown below, with warmer colors representing more common pitches.
By dividing the strike zone into one-inch squares, and assigning each pitch to the appropriate bin, we can draw contour maps of the strike zone. This first example compares four-seam and two-seam fastballs seen by RHB on 0-0 counts. The numbers listed are the likelihood that a pitch in each bin was called a strike, with the dark red representing 100%, dark blue representing 0%, and white representing bins with no pitches.
Already we can draw a couple of inferences. First, we can see that the brightly colored areas (i.e., those where a strike is called more than half the time) are approximately the same size. And second, we can see that even in this case, with tens of thousands of pitches to fill our bins, there are still a large number of empty bins. Sample size is going to be a problem.
We can see this problem even more clearly in this second example, comparing four-seam fastballs with curveballs. Here, even more bins are empty, but we can again see that the red and yellow areas are about the same size, and in the same location.
To compare the relative sizes more effectively, let's look only at the 50th-percentile contour. Everything inside this contour is called a strike at least half the time; everything outside it is usually called a ball. Here we have overlaid five of the most common pitch types -- four-seam fastballs, two-seam fastballs, curveballs, changeups, and sliders -- on 0-0 counts, and we can see that their contours almost perfectly overlap.
What about the strike zone to LHB? If we compare these contours to the previous set, we can see evidence of the "lefty strike," the extra few inches off the outside corner umpires typically give to pitchers against left-handed hitters. But the lefty strike is not dependent on the pitch type: Outside curveballs get the same amount of leeway as outside fastballs.
Sample size issues prevent us from looking at the effect of count on individual pitch types -- note, for example, that not one batter took an inside changeup all year -- but we can get around this by using Brooks Baseball's pitch categories to combine similar pitch types. Here we compare the strike zones seen by RHB and LHB, respectively, on different categories of pitches in an 0-1 count.
Even in this broader case, there are still sample size issues on the inside part of the plate. But, as we can see from the previous and the next graph (derived from all 1-0 counts), pitch type is not a factor in how the strike zone changes according to count.
This consistency is also consistent over time. Below, we see the relative zones for all 0-0 counts in 2008. As we'd expect, the strike zones for hard, breaking, and offspeed pitches are all smaller than their 2014 counterparts, but all three strike zones are at least equivalent to each other.
To Major League umpires' credit, we can conclude that, no matter how the strike zone fluctuates, it does not fluctuate according to the type of pitch thrown. This conclusion floored me when the evidence first presented itself. And yes, I know that ideally the strike zone shouldn’t vary based on pitch movement (#robotumpsnow). But for a human being to track where the ball crosses some imaginary plane, at blink-and-you-missed-it speeds, at an angle, with a catcher and batter in the way, and with 40,000 people screaming for your head?
. . .