October 22, 2014
The Royals, the Strike Zone, and an October Surprise
Everybody’s been writing about the strike zone recently, and that’s for good reason. The strike zone is evolving, and for the first time in the history of baseball, we have the technology to directly record that evolution. Mostly, the bottom of the strike zone is dropping, and that plays some role in shaping the current pitching-dominated era (although exactly how much of a role is a matter of some debate).
What’s most astonishing about the strike zone’s changing definition is the rapidity with which we are witnessing the results. Year after year, the strike zone falls, and this year has been no exception. In this recent article, Jon Roegele chronicles the most dramatic drop in the bottom of the strike zone yet: In the last year, the zone’s real estate has increased by 16 square inches. But even without a rigorous statistical analysis of the zone, you could feel the impact of the strike zone’s accelerating fall in the numerous strikeout records which have been broken, and in the historic seasons of Clayton Kershaw and other pitchers.
On a whim, I recently looked at how the strike zone varies month to month. I figured that if the change in the zone had been so rapid year to year, maybe there had even been some change during the year.
A simple way to visualize this is with the average height of all the pitches which are thrown in MLB on a monthly basis. This statistic, pitch height, isn’t a direct measurement of the zone per se, but rather a way of seeing how pitchers perceive the boundaries of the zone. When the bottom of the zone drops, the pitchers will start aiming lower to take advantage of that drop.
This is the average pitch height of all MLB pitches thrown across the last three years. Reading left to right, one can see that it has declined in parallel with the evolution of the strike zone. Just as the zone has bottomed out, pitch height has fallen right along with it. Indeed, from a high of ~28 inches in April of 2012, the average height has dropped to a low of ~27 in June of this year.
Since June, the average pitch height stopped falling. On the year, the pitch height is still much lower than it was in 2013, but July, August, and September saw relatively steady heights of about 27.4 inches above the ground.
Now you get to October 2014 (circled in red), this year’s postseason. You might notice something very strange about the pitch height in this month: it is at the highest level it’s been since March/April of 2012. It’s changed more this month than in any other month on that graph. It’s essentially undone most of two years’ worth of zone expansion.
It’s reasonable to be skeptical that the increased height is a real change, as opposed to a small-sample size fluke (although other Octobers have not seen anywhere near as large a change in pitch height). There’s also the potential for confounding variables to affect the average pitch height, like the biased selection of a group of hitters and pitchers who make playoff teams. For example, playoff teams tend to have harder-throwing pitchers than regular teams, and perhaps those hard throwers are more likely to throw high. In addition, the number of ballparks is reduced, and the particular parks in this year’s playoffs tend to be home run suppressing, possibly changing pitcher approaches.
Here’s how we could go about testing whether the increase in pitch height is random variation or not. Let’s suppose, to begin with, that our October measurement is a small sample fluke. After all, as Ben Lindbergh (and others) have noted, all pitchers are somewhat inaccurate; they can’t control the location of their pitches perfectly, and so sometimes they might be aiming low in the zone, but the ball goes high.
Under this scenario, if we pluck 7,003 pitches from the year, we should see that sometimes we get an average pitch height roughly as high as what we are seeing in this odd October. To control for the fact that we are only seeing a subset of the pitchers in October, we can use a stratified sampling scheme. In plain English, Adam Wainwright has thrown 297 pitches so far in October, so we can sample 297 pitches from him throughout the year. We can repeat this process for each of the pitchers who have played so far this October, and then ask the following question: How often, in our stratified random samples, do we see an average pitch height as high or higher than the one we’ve seen this October*?
It turns out that we never see a pitch height as high as what we’ve observed in October. In 100 random samples, the highest average pitch height comes in at 28.01876 inches, just shy of the actual October pitch height of 28.01936. This suggests that October is a statistically significant (p<.01) deviation from what we expect. If it’s a fluke, it’s a very improbable fluke.
So far, I’ve just been looking at the behavior of pitchers, which might be an imperfect guide to the strike zone. Maybe they all collectively decided to start throwing their pitches higher in the zone to be sporting to those poor befuddled batters, and not because of some impetus from the umpires.
To examine this, we could look at how often pitches low in the zone get called strikes on a month-to-month basis. If the low pitches are getting called strikes less often, that suggests a calculated change in the geometry of the strike zone.
This is the proportion of pitches taken below 27.6** inches, and within a foot of the center of home plate, which are called strikes. Generally, this graph tracks the motion of the pitch height graph above. When lots of low pitches are getting called strikes, pitchers start aiming down in the zone. The correlation between the fraction of low called strikes and the pitch height, on a monthly basis, is R2 = .68, indicating generally good agreement.
Now look over to the right on this graph. You’ll notice that October 2014 has one of the very smallest proportions of low called strikes (the sixth smallest).
It appears, then, that there has been a change in the lower boundary of the zone, so that pitchers aren’t seeing the low strike calls they were used to earlier in the year. Hurlers are adjusting their pitch height correspondingly, throwing to a slightly higher level than in the regular season.
If these results are not simply the result of random chance (and they don’t appear to be), then we are left with some very awkward possibilities. Whatever your feelings are on the evolution of the strike zone as a whole, I don’t think there’s any reason it should change dramatically between the regular season and postseason within the same year. That kind of shift seems borderline unfair to the pitchers and hitters who became familiar with a certain kind of strike zone surface for 162 games, only to have it abruptly yanked away from them when the games count the most.
There’s an intriguing coincidence to these results, as well. During the regular season, I wrote about how the Royals had struggled mightily with low pitches, a notion I got from a Dale Sveum quote. Suddenly, the Royals are getting pitches which aren’t so low in the zone, and the very same hitters who struggled to meet their projections in the regular season (Billy Butler, Mike Moustakas, Eric Hosmer) have come roaring back with a series of clutch hits.
Perhaps the strike zone’s upward drift is a straightforward result of the league’s postseason umpire selection process, which rewards experience. Maybe more veteran umpires tend to call the low strike in a way that’s more consistent with what the strike zone was in the past.
Unfortunately, that appears not be the case. The umpires who have called balls and strikes in the postseason so far have not called the low strike any more frequently than umpires who haven’t been in the postseason (.338 to .335). What’s more, even the more aged postseason umpires didn’t call the low strike anywhere near as infrequently in the regular season as they have in October so far.
These results suggest that the pitch height aberration is not the result of uncommon player or umpire selection. Instead, there appears to have been a considered change in policy concerning the low strike. Looking carefully at the above graphs, one notices that pitch height reached its nadir in June of this year. Since then, pitch height has been increasing and low strike probability decreasing. If this change isn’t simply a statistically improbable coincidence or mass, catastrophic mis-calibration** of PitchF/X cameras, the league may have decided to shift their Zone Evaluation system at that point. Changing the definition of the strike zone in-season seems like a poorly-conceived idea, but it wouldn’t be the first time MLB made a terrible mistake.
Maybe this change in the architecture of the zone sheds some light on why this year’s postseason has been so topsy-turvy. The teams which were good in the regular season prospered, to some extent, on being the best able to cope with a brave new world of sub-27 inch strikes. Then the postseason happened, and the strikes migrated higher.
Then again, weird stuff happens in the postseason even when the zone stays constant. Regardless of whether there is an explanation for this change in pitch height, it happened, and the Royals and Giants were best able to cope with the resulting old-school zone. But let’s hope for sanity’s sake that the World Series doesn’t come down to a disputed call deep in the zone, in the now-ambiguous region which apparently varies not only by year, but by month.
*This also controls for consistent park effects, since e.g. Adam Wainwright will have thrown half of his pitches at his home park.
**So chosen because it’s the highest regular season average pitch height in a month. However, I see a decreased proportion of called strikes for a range of pitch height cutoffs going from about 24-30 inches.
***The playoff teams home parks saw pitch heights .2 inches higher than average, not enough to explain the .6 increase in pitch height between October and September. Only one playoff team’s home park—Baltimore—recorded an average pitch height as high as that observed league-wide in October.
What’s more, if the PitchF/X cameras were severely miscalibrated so that the height coordinates were uniformly increased, one would expect to see the strike probability change at the top of the zone as well—yet I observe no significant increase in called strike probability for high pitches.