Of all of the recent advances in sabermetrics, catcher framing is likely the one with the greatest impact on our view of the game. Already, it has begun to affect our notions of player value, giving us a new respect for defensivelyminded backstops. But even beyond that, our new knowledge of framing reallocates a huge amount of the value we had implicitly assigned to the pitcher.
Catcher framing, and its effect on the game, are also difficult to measure rigorously. Fortunately, we are lucky enough to have Jonathan Judge, Harry Pavlidis, and Dan Brooks on the case. Their most recent article provided a precise framework for measuring much of the value due to catcher framing.
However, their work has been focused to date on examining the direct impact of the catcher upon the strike calls. Catcher framing quality to date has been measured only in the set of pitches which are not swung upon, whose value is determined by the umpire’s call. But there is another player present in the matchup in the person of the batter, and catcher framing may also impact the batters’ actions.
The batter suffers when there’s a good framer behind the plate, and prospers when there’s a poor one. A good framer expands the zone, making marginal pitches more likely to become strikes. Yet the batter is not a wholly passive observer in this process. If the batter behaves optimally, he must adjust his strategy to compensate for the framer’s quality, changing the pitches that ought to be swung upon.
For example, let’s imagine two batter/pitcher/framer trios in the same situation. In one, there’s a good framer behind the plate; let’s call him Jonathan Lucroy. In another, there’s a terrible framer, say, Josmil Pinto. The count is 22, and the pitcher laces a fastball that will land on the black, right at the edge of the rulebook strike zone.
As always, the batter is faced with that pivotal question of whether to swing. Given the location and the count, there is a decent probability of a strikeout if he leaves the bat atop his shoulder. On the other hand, a swing risks making poor contact.
The decision is further complicated by the framers. Lucroy dramatically increases the probability of a strike call, thus enhancing the downside of taking the pitch (increasing the probability of the strikeout). Conversely, Pinto decreases the same probability, making it more feasible to be patient. The batter, if they are taking framing into account, ought to be more likely to swing when Lucroy crouches behind them than when Pinto holds the mitt.
To be clear, the above situation only holds if the batter is 1) aware of the quality of the framer and 2) adjusts his behavior accordingly. So that’s the first question I’ll ask: Do batters adjust their swinging in accordance with the true called strike probability, as affected by the catcher’s framing skill?
Here’s how we can get to the answer. I built two models of called strike probability. In the first model, I considered only the raw coordinates of the pitch, horizontal and vertical, as well as the count. In the second model, I considered the above variables, as well as the identity of the catcher. The latter model, we know from extensive prior research, is more accurate because it incorporates the effect of the catcher.
For each model, I predicted the called strike probability for all of the pitches thrown in 2014. Then, I ran a logistic regression to predict whether a hitter would swing or not, based on the called strike probability, as reckoned by the two models, and the count.
You might have guessed at this already, but hitters, it turns out, are attuned to the skill of the catcher behind the plate. The second model, incorporating the effect of framing, fits the data significantly1[1] better than the first model. In plain English, what this means is that strike probabilities which incorporate framing better predict the behavior of the batter than those which rely only on the physical coordinates of the ball.
This result therefore implies that hitters are able to take into account the framer behind the plate in making the decision to swing or to hold, which answers the first pair of questions I posed. The batters are indeed aware, and they do seem to change their behavior, modifying the probability with which they swing in accordance with the catcher’s reputation. Not that we needed any more evidence in favor of the reality of pitch framing, but I do think that this result is a powerful piece of verification: batters have every reason to perform optimally, and they have clearly judged that to do so, they must consider the framing skill of the catcher in determining when to swing.
Leaving that aside for now, I want to push this line of inquiry a step further. Going back to the example I posed above, the hitter is more likely to swing with a good framer behind him. The swing itself negates the pitch from being counted as a positive outcome for the catcher, but there’s no denying that the catcher influenced the outcome of the atbat. Specifically, he forced the batter to make a swing he might not otherwise would have, at a pitch that was further from the center of the plate than perhaps the batter would have liked.
That’s important because I have shown before that the closer a pitch is to deadcenter, the better the quality of contact the hitter can make. For every inch one travels horizontally from the center of the zone, BABIP and SLG drop dramatically. So, one way in which catchers may be influencing atbats is by inducing hitters to swing at pitches from the center of the zone, thereby reducing the quality of contact that the batters make.
It’s one thing to posit that this effect may be present, and another thing to show it. Let’s take a look at Jonathan Lucroy, an excellent framer by any standard, and highly rated in particular by BP’s new metric CSAA (at 26 Runs/7k chances). For pitches when Lucroy was catching, the opposing batter swung 45.4% of the time. On average, those pitches were .53 feet from the center of the strike zone horizontally. The same batters, in the other atbats they saw, swung at pitches .518 feet from the center of the zone. That’s a significant difference[2] (p = .002). Against Lucroy, then, their swings got a little further from the zone’s center, consistent with the scenario I outlined above. The batters are forced, by Lucroy’s exceptional talents, to try to make quality contact with pitches a little bit further outside than they are normally comfortable with.
Now let’s look at the flip side of framing, at those stabbing, noisy receivers who cost their pitchers precious strikes. Last week’s analysis suggested that Josmil Pinto was an exceptionally poor receiver, so let’s look at his pitches. On average, when hitters faced pitchers Pinto was catching, they swung at pitches .51 feet from the center of the zone, near Lucroy’s number. When they faced all pitchers, they swung at pitches .516 feet from the center of the zone horizontally. That difference—.006 feet—is the reverse of what I noted for Lucroy. That is, they actually swung at pitches closer to the center of zone against Pinto, relative to other batteries they faced.
I went ahead and did the same calculations for a select few other framers marked by Jonathan, Harry, and Dan as either very good or very bad:
Name 
Framing Value (CSAA) 
Swing Distance With 
Swing Distance Without 
Difference 
29 Runs/7k 
.528 feet 
.519 feet 
.009 feet 

30 Runs/7k 
.532 feet 
.516 feet 
.016 feet 

23 Runs/7k 
.461 feet 
.515 feet 
.054 feet 
From these examples, you can see that a good framer increases the horizontal swing distance of the batter. Meanwhile, a poor framer, like Carlos Santana, can even decrease the swing distance quite substantially (granted, Santana caught relatively few pitches last year, so this number should be taken with a grain of salt).
The effect size is usually quite small, I should note: .12 feet is a bit more than an inch[3]. But also bear in mind that, like Lucroy’s framing, that modest effect is multiplied over many thousands of swings. Putting numbers to it, batters going against Lucroy and his pitcher swung 8691 times in 2014. Consequently, one way to think about it is that Lucroy forced his opponents to swing at pitches a grand total of more than 1000 feet (8691 swings * .18 feet per swing) further from the center of the strike zone than if a poor framer like Santana or Pinto had been behind the plate instead.
More concretely, Lucroy probably forced the opposing batters to swing at pitches they didn’t like just a little bit more, in thousands of separate instances. That has all sorts of negative effects, like increasing swinging strike rate, decreasing BABIP, and preventing hard contact. Fully accounting for all of these effects will wait for a later treatment, because it is by no means a trivial task. We would also need to adjust for all of the batters, pitchers, and parks involved, all of which is perhaps best accomplished within a formal modelling framework.
But what I have established here is that the effect of a good receiver extends beyond the pitches that batters let go by. A good framer, by changing the probability of a strike at the edge, causes the opposing hitter to modify their own behavior, causing them to swing at pitches a little bit further from the center of the zone. In addition to harming the batter’s chances directly, by flipping balls to strikes, a good framer changes the dynamics of the atbat indirectly as well. This effect suggests that the numbers we’ve generated to date for the value of framing are probably underestimates, which is good news for all the steady receivers of the world.
[1] AIC of the first model: 44819; AIC of the second model: 51459. Relative likelihood of Model 2 = 0.
[2] By permutation test.
[3] Also note that for this initial attempt, I’m only looking at the horizontal distance from the zone center. We would also expect the vertical distance to be affected, so these estimates of swing distance are probably too conservative.
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Great work.
 look at first pitch swings
 see of good framers have better LWTS (outcomes) than bad framers beyond what would be predicted by the count and other factors
I like the LWTS idea, that seems like a good way to go.
With that said, I wonder if perhaps the Brewers calibrated their downandaway philosophy to take advantage of Lucroy's particularly excellent skill. Generally, I think looking at how location/pitch type choices are affected by the framer seems like a good area for more research, one that we have been talking about.
As to whether the strategy might influence Lucroy's numbers, I will leave that to the framing experts. My guess is that it might affect his cumulative numbers, by giving him more chances to show off his framing skill, but I don't think it would affect his rate numbers, like the one I cited above.
I am not an expert on the various framing models (and to be quite frank the latest iterations of the BP models are beyond my math skills), so maybe they already factor in the latter case. However, from the articles I've read it seems to me that they mostly focus on the former  that every pitch that the catcher "steals" via framing is a mistake from the pitcher. This study is the first I've read that seems to touch on the latter. I would be very interested to see if this can be quantified  how many runs are batters worse when faced with a larger strikezone? That would kind of be a complement to the current framing work, quantifying framing from the perspective of the batter. I'm curious how closely the numbers would match.
Related to this, do you know if anyone has tried to look at whether catchers on opposing teams of excellent framers show larger than normal strike zones in these games? In other words, if Lucroy stretches the zone for an umpire in a game, is the umpire somehow conscious of this and relaxes the zone a little for the other team as well? I suppose the answer would be no, at least my understanding is that framing is accomplished in a way that the umpire doesn't recognize that he is calling the zone any differently.
Perhaps that study would put the framing ability of a catcher in a proper context.
"Lucroy is catching, I'm not going to let him trick me" could lead to a much smaller strikezone this season. Interesting one to watch.
a bad framer will always be a bad framer, on the other hand....
What I'm getting at here is something I've argued before: the idea of there being any single thing that is "the strike zone" is incorrect. Better, at least in my humble opinion, to average over all of the zoneS that exist, in showing the effect of someone like Lucroy. In this way, we avoid the problem of picking some arbitrary threshold which may or may not reflect the actual zone, which as we know moves, grows, shrinks, and changes shape depending on many factors.
The other thing is that this ought to affect more than just that fraction of pitches which paint the black. In fact, pitches well inside are sometimes called strikes, and I would bet that they are more often called so when a good framer is receiving than a poor one. So the batter can't rely on his framing knowledge only when the pitch is doubtful, he has to be thinking about it always.
One thing I saw you hinted at towards the end of the article, but some considerable consideration has to be placed on the batter and his K/BB rate. If he's a free swinger, he's already more likely to take a hack at the .53ft pitch. Conversely, if he's more patient, it's more probable that he sits on one.