November 25, 2013
The Corner-Outfield Inefficiency
On Friday’s episode of Effectively Wild, listener Matt Trueblood emailed the show to ask Ben and Sam a fascinating question. Why is it that teams do not have their left and right fielders switch places more often, particularly if one of them is a better fielder than the other? We know that some players like to pull the ball, while others like to hit to the opposite field. Why not put the better fielder in the place where it’s more likely that the ball will be hit? It’s a fascinating question because there is no rule that prohibits it from happening. In the era of the infield shift, why hasn’t anyone tried this?
Teams will often shift an outfielder from left to right (or the reverse) within a game if they make a defensive substitution, and no one minds. Sometimes players bounce back and forth and back again. Other than the fact that box score makers would hate it, why not within an inning as the batter changes?
Hey look, it’s the #GoryMath signal!
Warning! Gory Mathematical Details Ahead!
My data set is all events from 2003-2012. I started with all fly balls, pop ups, and line drives that were fielded by either the left or right fielder and coded whether that was a product of a ball being hit to the batter’s pull field or the opposite field. Home runs were not included, since you can’t defend a home run (unless, perhaps, you’re Carlos Gomez).
Hitters were more likely to hit the ball to the opposite field (55-45) than to the pull field, and this held true for right-handed hitters (54.5 percent opposite field) and left-handed hitters (55.4 percent opposite field). Strangely, this turns out to be the most important finding in the study. Hold on to it.
There was a split of 58 percent fly balls and 42 percent line drives overall, but when hitters pulled the ball, they were more likely to hit a line drive (54-46) than a fly ball. On balls to the opposite field, there was a 68-32 split in favor of fly balls. Line drives are more likely to fall for hits than fly balls, so when hitters pull the ball, they’re more likely to hit something that’s going to do some damage. It’s tempting to think then that it’s better to put the better fielder in the pull field, because that’s where the rockets are going to be headed. It turns out that that’s wrong.
There’s an interesting fact to note about pulled balls vs. opposite field balls. Opposite field flies are easier to catch. Defenders caught 65.1 percent of opposite field balls, but only 44.2 percent of pulled balls. Some of that is due to the fact that more of those pulled balls are line drives. But the effect survives even after controlling for the type of batted ball. For fly balls, 80.1 percent of the pulled variety ended up in a fielder’s glove, while 85.4 percent of opposite field flies were caught. For line drives, 13.9 percent of pulled line drives ended up as outs, while 21.6 percent of opposite field line drives ended up in gloves. A pulled ball is more likely to end up falling in for a hit. So, why aren’t we putting the good fielder out there and the bad fielder in the opposite field? Read on.
Let’s see what happens to those balls. Not surprisingly, because pulled balls are more likely to be line drives, and therefore hits, they produced a bigger bang. I assigned run values to each event (single, double, triple, out) based on the linear weight values that we use here for such things. I found that the average pulled ball was worth .206 runs for the hitting team, while an opposite field ball was worth .022 runs. Offensive teams want hitters to pull the ball. So shouldn’t the team in the field try extra-hard to defend against pulled hits?
Well, no. The secret to why we don’t want to put the good fielder in the pull field is this. Let’s look at the value of the hits that happen when the fielder doesn’t catch the ball. We know that pulled balls are more likely to be line drives than fly balls. Surely enough, those pulled balls end up as a single 59 percent of the time and as an extra-base hit 40 percent of the time. (There were some cases where the batter got TOOTBLANed, if you’re wondering where the extra one percent is.) Opposite field balls went for singles 66 percent of the time and extra-base hits 33 percent of the time. Balls that were pulled and fell for hits had an average run value of about .584 runs. Balls that were hit to the opposite field went for .567 runs. It’s a little more important to prevent the types of balls that fall for hits in the pull field, but not by much. And since the value of the out is pretty much the same, changing a hit into an out in the pull field has essentially the same marginal effect as changing a hit into an out in the opposite field.
Now, let’s talk about our two fielders. One is better than the other and everyone knows it. In 2012, the best left fielder at catching fly balls (min. 100) hit near him (Alex Presley) did so at an 89 percent rate. The worst (J.D. Martinez) had an 80 percent success rate. In right field, top honors went to Jose Bautista (89 percent) and a participation trophy went to Michael Cuddyer (75 percent). Results for line drives had a similar spread, about 15 points in either direction. We’ll be conservative and say that our good fielder is five percentage points more likely to catch a ball in the air than is the bad fielder in both left and right field.
The value of changing one marginal ball from a hit to an out in the pull field is worth roughly the same as in the opposite field. Therefore, you simply put the better fielder where more balls will be hit: in the opposite field. Remember the finding I told you to hold on to? Yes, percentage-wise, more balls fall into the pull field, but they have the same value as do the ones in the opposite field. The point is not to have a balanced defense, and you won’t get one here. If 85 percent of fly balls in the air to the opposite field are caught now, compared to 80 in the pull field, it’s tempting to reflexively use our five-percentage-point upgrade to balance that out. But that’s the wrong way to think about the problem. The better strategy is to put your assets where they will have the most marginal impact.
What sort of effect might this have on a team? From 2003-2012, the left fielder handled 51.3 percent of outfield flies not hit to the center fielder. Our left fielder and right fielder are pretty good at sharing. There’s also evidence that both are decent at fielding. Right fielders caught 83.8 percent of the fly balls hit their way and 17.7 percent of the line drives, while left fielders caught 83.3 and 16.6 percent respectively. (The fact that that adds up to 99.9 percent is a coincidence.) Right fielders appear to be slightly better fielders, although they handle the slight minority of the traffic. That means that the lesser fielder is slightly more likely to have a ball headed his way than the better one. But for now, let’s call it even.
If we always had the better fielder in the opposite field, it would mean that 55 percent of the time, we would have a better fielder in position to catch the ball (compared to 50 percent now). We also assume that he would be five percent better than the other guy at catching balls, and that the value of turning a hit into an out is about 0.8 runs. So, for each fly ball to either left or right, the benefit of always making sure to station the better fielder in the batter’s opposite field is .002 runs. From 2003-2012, the average team had 1,114 such balls over the course of a season, meaning that this strategy would be worth about 2.25 runs over a season. If the fielders were 10 percentage points apart in their ability to catch fly balls, the strategy would be worth four and a half runs. We’re starting to get into “half a win” territory, simply by having the left and right fielder change places every once in a while. And it costs nothing.
Ah, But the Assumptions
We may also have a situation where the two outfielders involved vary in their arm strength. One might have a noodle, and the other a cannon. The only real instance where there’s a difference between throwing from left and right comes on a play at third. In 2012, the best guy at keeping a runner from going first to third on a single (or throwing him out) was Jeff Francouer (72 percent) while David DeJesus had a mere 46 percent success rate. That play happened an average of 84 times to each team in 2012, and the difference between first-and-second and first-and-third is worth .25 runs (with one out). If we assume that our two outfielders differ in their ability to hold or throw out the runner by 10 percentage points, and that the stronger arm will be in left some of the time, that’s suddenly worth about a run in lost value (although you might get some of it back when the single is to left field). So, switching the left and right fielders back and forth works best when both have comparable arms. If there is separation, it will mean that some of the value that you worked so hard to create will disappear.
One other issue that was brought up on the podcast was how far both fielders would have to run if they were constantly swapping places. It’s an interesting question. Take a look at this diagram, which will give us something with which to work. Let’s assume that the left fielder and right fielder are both standing about 300 feet from home plate and offset from the foul line by about 15 degrees, using a radial measurement. We can connect the two dots for the left and right fielder and both of those dots to home plate. Since the angle formed by the two lines radiating from home plate has a measurement of 60 degrees, and the lines are of equal length, we have an equilateral triangle. The left and right fielder will need to jog 300 feet or so each time they change spots. In 2012, the average team would have made eight of these switches in an average game, so our two corner outfielders would add an extra half-mile or so, spread out over three hours, to their workout that night. If they took the jog at a four-mph pace (not too hard), they could traverse 300 feet in about 50 seconds. That’s going to add to game time.
Under Ideal Circumstances…
In addition, my shifting was based entirely on the batter’s handedness. An enterprising team could do better calculations around individualized spray charts and could tailor their strategy to how that night’s starting pitcher might pitch to each hitter. Maybe they wouldn’t want to betray any of that information, except for the fact that “Our scouting report tells us that you are left-handed.”
But there’s another force at work here. In United States culture, it’s not nice to look like you’re trying too hard, especially for such a small reward and when you look weird doing it. As the infield shift has become more and more popular, I find it interesting to hear some of the reactions from teams that don’t shift. Usually, they have moralistic underpinnings. We’re gentlemen here. We don’t shift. We could, but that’s for the riff-raff to do. Brian McCann would totally shoot this down. Still, they’re leaving runs on the table. I have to wonder at what price come pride and tradition.
So, should the left fielder and right fielder changes places as the batter changes hands? Yes. They should, under ideal circumstances. The payoff would be a couple of runs per year and this would not solve all the world’s problems, but it would make teams a little better. And probably get them laughed at a little.