From time to time, we’ll hear that a hitter was called out on strikes on a pitch that was “too close to take.” This statement implies that the pitch wasn’t a strike, but that it had a shot at being called one.

Well, actually, every pitch has a shot at getting a strike call. If you’re unconvinced, go peruse Ben Lindbergh’s latest catcher framing piece. The first pitch you’ll see in there is a fastball thrown by Max Scherzer that, after controlling for the situation, the pitcher, and historical data, had a 0.4 percent chance of receiving a strike call. That pitch is called a ball 996 out of every 1000 times, but catcher Bryan Holaday fooled home plate umpire Jeff Kellog into ringing up Jose Abreu.

Major leaguers are aware that umpires aren’t robots, and I’d argue that the game’s best hitters don’t leave close calls up to chance. That’s why we hear that “too close” phrase uttered so often, and it’s probably why we don’t think hitters should gamble on the strike zone twice in a row.

Last week, I explored the notion that a hitter shouldn’t take two fastballs on the edge of the strike zone in two-strike counts. I suggested that pitchers might get a bump on the second consecutive edge fastball, and that umpires make the correct call more often on the second pitch. I took a visual approach to the exercise, but I didn’t quantify the effect. Let’s do that first before going any further. To borrow Russell Carleton’s famous phrase: “gory mathematical details ahead” (followed by a few broad, sweeping conclusions).

In the chart below, I’ll group pitches by the likelihood each had of receiving a strike call. These called strike probabilities control for things like the count, the pitch type, and batter and pitcher handedness. All probabilities come to us thanks to the hard work of Harry Pavlidis and Dan Brooks, and they were used to build the fantastic catcher framing model you’ve all heard about.

The probability groupings you’ll see below align closely with the location of the pitch—obvious balls can be found in the 20 percent-zero percent range, and obvious strikes can be found in the 100 percent-80 percent range. Again, these called strike probability ranges account for changes in the size of the zone from count to count. So, while the location of the edge does change constantly, the way we define the edge is consistent.

Once I’ve grouped these edge fastballs by called strike likelihood, I’ll compare these rates to the actual rates we see in each situation. The difference between these two numbers is what we care about—and how we’ll define the impact of the previous pitch.

I should note that the one thing these called strike probabilities don’t control for is catcher framing. It’d be interesting to ask a major league catcher how much of an effect one close pitch on the outside edge has on his ability to frame the next one. Maybe that’s the missing piece to this puzzle, but I’d guess that the umpire’s reference point plays a larger role in influencing the next call. Anyway, without further ado (click to enlarge):

There appears to be a pretty consistent called strike benefit awarded to pitchers who throw consecutive fastballs to the outside edge. The first group of “slam dunk” strikes is notably smaller in size and also receives the smallest boost to its called strike rate. As I suggested last week, the greatest gains come for fastballs thrown to the border of the strike zone—the 60 percent-40 percent group.

These “toss-up” calls are much more likely to become called strikes after a fastball thrown to the outside edge. If the first edge fastball is thrown to the 60 percent-40 percent area, pitchers throwing to right-handed hitters see fewer called strikes than they should. But if the second one is thrown there (following any type of edge fastball), the actual called strike rate jumps to 3.4 percentage points higher than the expected rate for these pitches.

Let’s look at the outside edge for left-handed hitters. Last week, I suggested that pitchers generally don’t see a fair zone called here the first time around, but that they do get the calls they deserve on the second close fastball. That statement gains some traction here:

The outside edge of the zone looks to be pretty unfair to pitchers throwing to left-handed hitters for the first fastball; we see consistently large negative differences between actual and expected called strike rates. On the second fastball, though, the actual rates tend to align with the expected rates—suggesting that lefties begin to receive the calls they deserve.

In addition to receiving a large bump on “toss-up” fastballs against left-handed hitters, pitchers also see a huge lift for the 80 percent-60 percent fastball group. Despite being thrown well inside of the strike zone boundary, these fastballs received the call only 57.2 percent of the time the first time around (compared to an expected rate of 70.2 percent). After a close edge fastball, though, the percentage of called strikes bounces to a more reasonable 69.3 percent.

**The Effect of a Set-up Fastball**

We can press even further if we look at each combination individually. Thinking back to part one of this piece, I’ll evaluate C.C. Sabathia’s plan of attack in that Aviles at-bat. Can a pitcher “move” the called strike zone with a well-placed ball?

Instead of looking at all fastballs thrown to the outside edge, I’ll consider the effect of the exact location of the first pitch on the call given to the second pitch. These tables consider the impact that a first-pitch fastball thrown well off of the outside edge has on the next edge fastball.

This is a pretty specific situation we’re talking about here. The first pitch, a 30 percent-zero percent fastball, is usually somewhere between two and four inches outside of the typical zone boundary. That requirement narrows our sample size dramatically, and I’m not sure I’d buy into these exact percentages. Since we’re looking at larger categories, I decided to (once again) subtract out the average expected strike rate for each group. So, in essence, the “difference” field measures the gap between each group’s (situational) expected called strike rate and its actual rate.

Note that the percentage increase for each grouping comes *on top of* the boost that a typical second consecutive edge fastball receives—so, for left-handed hitters, a 30 percent-zero percent fastball could increase the called strike percentage of a “toss-up” fastball by as much as 15 percentage points (10 for following an edge fastball, and an extra five because that previous fastball was a few inches outside the strike zone). That’s an intuitive result, and one that should make left-handed hitters think about taking a close edge fastball that comes after an obvious ball.

**What Now?**

Color commentators clearly aren’t off base in claiming that an outside fastball can be used effectively to establish the edge of the strike zone. While I looked only at consecutive fastballs, I would guess that the effect might extend over a span of a few pitches. Maybe the last pitch isn’t the only one that can shift the strike zone—how about the pitch before it? The duration of this effect is worth looking into.

We also learned that the boundary becomes especially clear for the difficult-to-pin-down lefty edge of the strike zone. Both lefties and righties see a similar called strike breakdown after the first edge fastball, but it does take that first pitch for lefties to find equal footing. This holds true for all consecutive edge fastballs thrown within a few inches of each other.

The specific location of the first edge fastball also appears to influence the call of the next one. As expected, if the second pitch is closer to the plate than the first one, the likelihood of a strike call increases substantially. So, for example, if a pitcher goes for the outside edge and misses away in 2-1 count, he can feel more confident returning to the edge on a 3-1 count. If his next pitch is even an inch closer to the center of the plate, this pitcher is much more likely to get the call he’s looking for.

Many questions remain, though. For example: Does a set-up fastball impact the call of an off-speed pitch thrown after it? Can a pitcher use an off-speed pitch to “set the edge”? If an umpire blows the call on the first fastball, can we expect to see a similar shift in the zone for the next one? Is this effect contained to a single at-bat, or can the last call from a previous at-bat shift the zone for the first pitch in the next at-bat?

I think the most significant takeaway here is that pitch sequencing can have a large effect on the shape of the called strike zone. The type of pitch, its location, and its result certainly change an umpire’s perception of whatever comes next. Much of this work was done in an effort to quantify this pitch-to-pitch impact for one specific case (an edge fastball following an edge fastball), but there are surely other combinations of pitch types and locations for which the strike zone shifts. Future research on this topic will bring us closer to understanding what effective pitch sequencing looks like.

*Thanks to Harry Pavlidis and Dan Brooks for developing an amazing framework for understanding called strike probabilities.*