August 25, 2015
Interaction Effects and Credit
Last week, we discussed the baseball team as a jigsaw puzzle. How the pieces fit together (or don't) can make a real, tangible difference to a team. How much difference depends on what we're talking about. The way a defense fits with the pitcher on the mound could make a big difference; given some modest assumptions, on the order of half a win. But is that the only difference a good infield defense makes?
One thing that at least makes intuitive sense is that a pitcher who is standing in front of four really good infielders might think to himself that it's okay if he gives up a ground ball, because it's more likely to go for an out. The mere presence of those infielders changes the way that he approaches an at-bat. But does stuff like that actually happen?
Warning! Gory Mathematical Details Ahead!
On top of that, using the log-odds method—which looks at the pitcher, batter, and league rates of some event happening and then generates an expected frequency for that event—I figured out the chances of a ground ball happening or a ball in play happening. This serves as a control variable.
Now the tricky part. A pitcher generally plays for the same team all year and probably spends a lot of time in front of the same four fools for a lot of it. He generally knows that he's getting roughly the same service most of the time, whether that's a good defense or bad defense behind him. Last week, we saw that in 2014, the Rays had the worst infield defense in baseball while the A's had the best. Sonny Gray made all of his decisions safe in the knowledge that he had good backup while Chris Archer made all of his knowing that the guys behind him were a little dodgy. Maybe if they switched bodies (or at least switched uniforms), they would have been completely different pitchers (or at least somewhat different pitchers).
To correct for this, I took the weighted average of the "average" defensive efficiency rate for infielders that the pitcher normally played in front of. To make an absurd example for illustration, suppose Sonny Gray pitched to 10 batters all year, nine of them in front of a defense that never ever converted a ground ball into an out, and then the 10th in front of an absolutely perfect defense. He would have an "average" infield defense conversion rate of 10 percent. For each plate appearance, I then looked at how far away that particular infield was from his "average" infield. If Gray is pitching in front of the "bad" A's infield, he might be less willing to let the ball be put into play than normal.
I constructed a binary logistic regression looking at a simple outcome: Was the ball put into play or not? To control for pitcher and batter tendencies, I used the control variable described above and then used the difference in infield efficiency. Data were for 2010–2014 and only pitchers who faced more than 250 PA were asked to attend the party.
The results were maddeningly wishy-washy. After controlling for the pitcher-batter matchup's likelihood of producing a ball in play, there was an effect for pitchers giving up more balls in play when pitching in front of a more efficient infield (at least compared to what they usually got), and it had a p-value of .10. Those familiar with the joys of fudging the p-value will appreciate this little sweet spot. If a p-value is below .05, all is good. If it's below .08 or so, you squint and say it's close enough. At .10, you can kinda know that something is in there intuitively, and there's just enough that you don't sound absolutely crazy advocating for it, but …
It's possible that some pitchers, though not others, really do adjust their style to favor a more pitch-to-contact approach when in front of a good defense, and that's just enough noise to fuzzy up the regression. This is the difficulty of large-N research. Some pitchers may adjust their game plans on different variables, and since we're talking about pitchers as one big undifferentiated whole, there may be a differentiating factor that makes a difference.
Then again, maybe I'm just trying to justify why my regression didn't work. Even if it had worked, I looked at the effect size and found that moving from an infield that is 10 percent better at picking up ground balls is worth an extra 0.2 percent chance (so, we'll call it a deci-Jonah) of a ball being put into play. Over a full season, that might be one or two extra ground balls.
I did run some moderational analyses to see whether things varied if a pitcher was a ground-ball guy or a ball-in-play guy more generally. Maybe pitchers who are pitch-to-contact guys in general are a little more wary of the four fielders standing behind them and adjust their style accordingly, but guys who aren't pitch-to-contact guys might not care. They're aiming for strikeouts anyway.
The answer there also came back in that maddeningly "close but not really" range. It did point toward pitchers who were already pitch-to-contact guys allowing more balls in play in front of the good infield than the bad one, but again, the pointing was not very strong. It's possible that the differentiating factor is that some guys think about these sorts of things and others don't and we have no way to really measure that.
One thing was clear. I ran similar analyses predicting whether or not a better infield than usual made for pitchers getting more ground balls when the ball went into play. The answer was most certainly not. So, pitchers don't tend to turn on the sinking action in front of the good defenders in an attempt to get ground balls, but there is (weak) evidence that they are okay with the ball going into play more often.
I did the same basic thing for fly balls and outfield defense. It turns out that the effects were actually pointing toward a good outfield defense predicting pitchers being less willing to let the ball go into play, but the coefficients were not significant.
But Who Gets the WAR?
But here's a question I asked last week that I think deserves a little more reflection. Who gets the WAR for the ground ball that happens because the pitcher felt more comfortable in front of a good infield defense? What "caused" the ground ball was the pitcher changing his approach to induce more contact. But the reason that he did it wasn't because of anything that defense did, but because of what they might do. Still, at the same time, the pitcher has to get some credit for noticing (or being told?) that the infield behind him was really good, so he should throw that sinker a little more. And then being willing to do it. It's not something that he normally would have done, but the circumstances dictated it and he adapted. Maybe the pitching coach should get the WAR for suggesting that course of action in the pregame meeting. Maybe the GM gets some credit for realizing that pairing a ground-ball machine with a bunch of Hoover infielders was a great idea.
Of course, the answer is that everyone deserves some credit; at least, intuitively, it makes sense that everyone gets some credit. But they don't get it in the way that we normally assign credit. The scoresheet sees the grounder to second and gives the pitcher credit for getting the batter out. It might credit the second baseman for a good play, or just gently pat him on the head for a ho-hum grounder that he adequately handled. But WAR can't really see the thing that didn't happen.
We lack a name for this sort of effect. The value the fact that the pieces are sometimes more than the sum of their parts, even if only slightly so. I'd like to call it eWAR: emergent WAR. The idea that a group of parts can come together to form a coherent whole that is beyond the explanation of simply the parts themselves. I don't know whether there's a bunch of value to be had here or just tiny little slivers. But as we learn more about the game, there are going to be things that don't fit neatly into our idea of WAR that all the credit for everything must somehow be parceled out to one person or another. There's room for the idea that not everything is so neat.