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We've already seen in my last post the tendency for batters to try to "cover the plate" when the count is in the pitcher's favor and be selective when the count is in their favor. Batters down 0-2 are much more likely to swing all across the zone than batters in a 2-0 count, for instance.

Another interesting property of the shifting Strike Zone is revealed by a sequential analysis. Consider that you're in a 2-2 count. There are different ways to have gotten there. At some point, though, the count was either 1-2 or 2-1. In other words, to get to a 2-2 count, you had to either have the last pitch you just saw be a strike or the last pitch for a ball.

How does this affect what you do on your next pitch? Well, as it turns out, if you took the last pitch for a ball, you're more selective in your 2-2 count than if you took the last pitch for a strike. That's right: your tendency to swing is influenced not only by the current pitch but the previous pitch. Maybe not too surprising that previous pitches influence future batter behavior, but perhaps surprising when you consider that these are plots taken from the same count, so presumably, hitters should be reacting in similar ways.

Here is the Subjective Strikezone profile when the previous pitch was a Ball. Warmer colors indicate "likely to swing", cooler colors indicate "likely to take":


And here is the profile when the previous pitch was a Strike:


You can definitely see a larger radius during the at-bats after an immediate strike than an immediate ball. If you measure the number of pixels in each plot above a .6 activation (roughly from "yellow" up on the colormap, the plot goes from 0 to 1), the 2-2 count immediately following a ball has 17891 above threshold pixels, and the 2-2 count following a strike has 21707 above threshold pixels - in other words, over a 20% increase in surface area of high-likelihood "swing-zone"!

One last note - the difference in average swing rates in a 2-2 count does not appreciably change following either a ball or a strike. Hitters swing around 66% of the time in one case and about 63% of the time in the other. What changes is the distribution of these swings - hitters in 2-2 counts in which the immediately preceeding pitch was a strike are more likely to chase than hitters in a 2-2 count in which the immediately preceeding pitch was a ball.