There’s a meme that I occasionally see floating around about how having a “cheat day” when on a diet is actually a good thing for those trying to lose weight. There’s probably something to that. Dieting requires a level of commitment and discipline that can be hard to sustain, and if knowing that you have a “cheat day” keeps you from giving up entirely, it might end up being a net-positive to have one. But the meme goes further to say that if one cheat day is positive, imagine what seven cheat days would do.
Lately, I’ve been writing a lot about the infield shift. I’m not a fan. I’m not one of those people who screams “play the game the right way!” If it worked, I would gladly encourage teams to do it. I’m just not fully convinced that it works as well as thought. The problem seems to be that while the shift does a good job at converting balls in play into outs, it comes with side effects. It changes how pitchers pitch. With the left side of the infield short-staffed (against a left-handed hitter), they tend to shy away from the outer-third of the plate where the batter might be tempted to poke it to the left side, and as a result, they throw more balls than they otherwise would. This seems to lead to the obvious side effect of more walks, but also puts the batter in a more advantageous count more often. It’s not a total effect. Pitchers still do go toward the outer-third, but the effect is big enough to have some real consequences for the game, and—importantly—it seems to allow more walks than it prevents in singles.
Last week in this space, I found that the “walk penalty” isn’t a static effect. There appear to be certain types of hitters and pitchers who appear to be more immune to it. In particular, pitchers who get a lot of swings-and-misses seem to do better (from their perspective, meaning more outs). On the flip side, batters who make a lot of contact seem to get better results (meaning fewer outs). But knowing that there were things that might change the magnitude of the “walk penalty” meant that there was a chance that some cases were OK to shift in. Even if the walk penalty was brought just a tiny bit below the benefit from the extra infielder on the right side, it’s still net-positive, and so a team should do it.
Well … let’s see if we can find those shifts that are worth saving and … maybe a few surprises in the math as well.
Warning! Gory Mathematical Details Ahead!
Once again, I’ll be working with data downloaded from Baseball Savant detailing events from 2015-2019. The data have an indicator for each pitch of whether the defense was lined up in a shifted formation. They note two different types of shift (in addition to a standard formation) of a partial shift and a full shift. Previous research that I (and others) have done shows that these partial shifts aren’t really all that effective at suppressing singles, and as such, I exclude them from the data set.
I used a regression to create a model of what the expected outcome would be for a given set of circumstances, with and without the shift on. Teams have to make the decision about whether or not to shift before they know the outcome, and the batter has the added benefit of knowing that decision before stepping into the batter’s box. Teams should make the best decision that they can. I used wOBA coefficients (located conveniently in the data set) as my outcome measure. I created a regression which included both the batter’s average wOBA contribution, and the pitcher’s, per PA over the course of that year, along with some key situational variables (is the batter left-handed, is the platoon advantage in effect?) and some batter and pitcher statistics, including swinging strike rate, ground ball rate, pulled ground ball rate, and called strike rate for batter and pitcher.
(As a check, I ran mostly the same analysis using whether the plate appearance ended in an on-base event or not, and got the same basic model and answers to the subsequent questions below.)
The regression I used was stepwise, so that the model could pick the most influential variables. Not surprisingly, batter and pitcher wOBA per PA rates were the most strongly correlated (with … wOBA itself). I first used all plate appearances which did not feature a shift and entered the rest of the variables to generate an equation that would predict the expected outcome in wOBA terms. Platoon advantage, and whether the batter was left-handed entered in. I did the same for all PA involving a shift. On that one, in addition to the same variables as above, how often both batters pulled their ground balls and how often pitchers had their grounders pulled (for obvious reason) and how often pitchers got swinging strikes, which we saw last week was an important piece of the puzzle.
Once I had the two equations, I could estimate—independent of what actually happened—the expected value of shifting and not shifting. If a team could do likewise, the correct answer is to pick the one with the lower value.
First, I ran a simple frequency of how often shifting made sense and found that … 40 percent of the time it made sense? (I told you that there’d be surprises…) Huh?
Here’s a different question: Among the shifts that actually happened, how many of them were supported by the model? The answer: 61.8 percent. You can be a cynic and say that 38.2 percent were not good ideas. Or in statistical parlance, teams reacted to a non-present signal, which is a Type I Error.
But wait a minute, I thought that the data said that shifting overall was a bad idea. It is, even though the majority of shifts were actually supported. When you look at how big a penalty those “bad idea” shifts had versus the average gain in expected value from the “good idea” shifts, the bad ones had a magnitude that was about 1.5 times greater than the good ones. The shift is still a net-loss for the defense, but … the data suggest that the best cure isn’t deleting the shift altogether, but cutting back the bad ones.
And now a question even I had never thought to ask. I’ve looked at cases where the shift was employed and found overall that the effects were actually bad for the defense. What about the cases when a team didn’t shift? What happened there? The answer was that 33.4 percent of cases where a team should, have shifted, according to the model, they didn’t. (For the initiated, they made a Type II error.)
In a sentence that makes no sense but is perfectly correct, the shift is both over-used and under-used. Put a little more succinctly, teams aren’t necessarily shifting the wrong amount, but they are shifting in the wrong situations.
There is one problem:
These are the percentages of shifts that teams “got wrong” according to the model. As the use of the shift as a strategy has been increased (with a blip dip in in its use between 2017 and 2018), teams have actually been loading up on more “bad” shifts (Type I errors). Over that same time period, they did cut down on the percentage of times when they didn’t shift, but should have (Type II errors), but the Type I errors outpaced the reduction in Type II errors.
What gives? I isolated all shifting situations and then split them by whether the model thought kindly of them or not. I compared the overall statistical characteristics of both batter and pitcher in the situations that the model liked and the ones that it didn’t like, and found … nothing that interesting. And then, in a throw-away analysis, I looked at the two variables that I’d included in the regression that were categorical: whether the batter was left-handed and whether the platoon advantage was in effect.
Among shifts that did happen, if the batter was left-handed, the model thought it was actually a good idea 84.1 percent of the time. Among shifts that happened against right-handed batters, the model had a favorable opinion 1.6 percent of the time. That’s not a mis-print. One point six percent. The model clearly thought that the secret to the shift was simply noting where the batter was standing. Could it be that simple? I looked at the situations where the shift didn’t happen and found the model telling me the same things. Shift the lefties. Don’t shift the righties.
(Here I’m going to pause and send you to read (two) something(s). There’s an amazing Sabermetrician who found this a year and a half ago whose name is Russell. It just isn’t me. It’s Russell Eassom at the blog “Bat Flips and Nerds.” Go read those.)
Once I had Eassom’s findings in hand, I pulled out the analysis code that I have used in the past concerning the effectiveness of the shift, and quickly paneled the data by batter handedness. For a quick recap, this takes hitters who had more than 50 non-shifted PA and sets their results from those PA as their expectation for when they are shifted. For example, if a hitter gets 20 singles in 100 non-shifted PA, if the shift is a better defense, we would expect to see singles in fewer than 20 percent of the same batter’s shifted PA. Small sample sizes will overwhelm the analysis of an individual hitter, but if you pile everything together, this can give us an idea of what’s going on in the aggregate. Data are once again from 2015-2019.
|Change from baseline for outcome||Left-handed batters||Right-handed batters|
|Strikeouts||+ 2.2%||– 4.7%|
|Walks||+ 1.1%||+ 0.9%|
|HBP||– 0.0%||+ 0.0%|
|Single||– 2.0%||+ 0.2%|
|Double/Triple||– 0.0%||+ 0.3%|
|Homerun||+ 0.0%||+ 0.4%|
|Out in Play||– 1.3%||+ 2.8%|
|On Base Event||– 0.9%||+ 2.0%|
|BABIP||– .016||– .006|
|Linear Weight Runs (per PA)||– .007||+ .018|
This is where I sheepishly say, “Yeah, why didn’t I think of that?”
The shift does seem to “work” for reducing BABIP for everyone the way that it’s supposed to, a little better for lefties than righties, but profit is profit. The walk penalty is still a real thing. We see that walk rates do go up in front of the shift, on both sides of the plate. What differs is that the shift also seems to increase the number of strikeouts among left-handed batters as well, while having the completely opposite effect for righties. Righties also see an increase in their extra-base hits and their home run output, while for lefties, it’s mostly flat. Handedness is clearly the key variable. (I broke the numbers down further to see if the handedness of the pitcher made a difference, and it did, but the result was still the same and the handedness effects for the pitcher are confounded with the platoon effect.)
With lefties, the shift does steal back more outs than it gives away in walks, though surprisingly, in the form of strikeouts. It seems that pitchers go for a style of pitching which favors a lack of contact, which does produce more walks, but also more K’s. Considering everything, the shift is a net positive against lefty swingers. Not so much for righties, where the ball tends to go into play more with destructive results.
Which brings me to this chart which makes me feel a little better about myself, even though I totally got things wrong:
|Year||Percentage of LHB Shifted||Percentage of RHB Shifted|
Major-league teams have been increasing the rate at which they have been shifting everyone, left and right. While they’ve been increasing their proportion of shifts on left-handed batters, on which they accrue value, they’ve also been increasing their percentage of shifts against right-handed batters, which are toxic and cancel out much of the benefit that they would have gotten by just sticking to shifting the lefties.
Major League Baseball didn’t see it either.
It means that much of my own writing on the topic has been conflating two different effects. The walk penalty is a real thing, and I stand by it. I assumed that this was what was driving the finding that the shift was a net negative. It certainly doesn’t help, but what seems to have been driving the bus is that somehow, shifting against right-handed batters somehow supercharges them and reduces their interest in strikeouts. Even though the majority of shifts are done against lefties, the negative effect of shifting against righties is much greater than the effect of the benefit of shifting against lefties, so the net effect of these “missing” righty strikeouts (and the fact that some portion of them became extra base hits and home runs) was turning the shift into an overall negative. Teams were doing something right and something wrong at the same time.
I just sort of assumed that if the shift worked (or didn’t) against lefties, it would work (or not work) the same way against righties. I assumed that it was all a mirror. I feel a little foolish making that assumption now. There’s the simple geography that if you shift a lefty, the one infielder on the left side can play in the shortstop hole and probably at least sorta defend a broader area of fair territory than the lonely first baseman who has to stick close to first base to receive a throw on a potential ground ball out. There’s the reality that most pitchers (and batters) are right-handed, so it was more likely that a right-handed batter was facing a same-handed pitcher, while a lefty was facing an opposite-handed pitcher. Same vs. opposite-handed pitching involves two different sets of strategies and the ball breaks differently from the batter’s perspective.
I looked in that mirror and didn’t realize that I was the one who was backwards.
Before I go, I want to tease one possible implication of this finding. I don’t feel fully confident to recommend this yet, but the data are at least suggestive. I admit it. I’m hedging.
The data that we saw above say that left-handed hitters should almost always be shifted. Somehow—and until I really can understand the “how” on this, I want to be careful—a shift changes either the pitcher or batter in such a way that more walks happen, but also more strikeouts. Maybe it’s as simple as the pitcher still feels a little antsy about letting the ball go into play and there being a silly single to the left side, and so the pitcher goes to the strikeout bag of strategies. Whether that’s part of the shift or something that could be altered by just realizing that it was happening and changing behavior, I don’t know. But according to these preliminary data, left-handed batters should almost always be played in a 3-1 formation. Righties should be played 2-2.
I’m someone who gets worked up over words. I find that when there’s a concept that doesn’t have a word, there is often opportunity. (I call them groffles or “unspoken words.”) I (and others) have written about baseball evolving toward what might be called “positional anarchy.” When the shift first came to prominence, there were chuckles when a ground ball to the 34 hole found the third baseman in short right field, and the scorecard said G5-3 as a result. But we all understood that it was just part of a special strategy that was used against special hitters. Now it seems that the special lefty might be the one that doesn’t get shifted. What do we call it when the third baseman playing in short right field is now standard practice, at least when a lefty is up? What happens when the third baseman spends a third of the game nowhere near third base and that’s just an accepted part of the game. Nothing weird about it.
We might end up needing to create a new word for that player.
Thank you for reading
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