Baseball Therapy: The Knee

Last week, Major League Baseball announced a proposed change to the strike zone. In response to a zone that continued to sag downward, MLB’s competition committee has recommended that the definition of the bottom boundary of the strike zone be changed from the hollow under the kneecap to the top of the knee. It doesn’t seem like much. That’s maybe two inches of space, although the actual called strike zone has always differed somewhat from the rulebook strike zone, but if the changes are put into effect for 2017, then pitchers might be feeling a little more squeezed next year.

There are those who blame the low strike for ushering in an era of depressed offense and depressed fans who don’t like watching 2-1 games. Perhaps this will make baseball fun again. In fact, research by Jon Roegele has suggested that if baseball could have turned back time to the strike zone that it had in 2009, it would have resulted in 1,000 extra runs being scored league-wide, enough to give every team an extra two-tenths of a run per game. Not bad.

But I think we need to explore a little bit beyond just looking at pitches at the knees. The law of unintended consequences clearly states that… there will be unintended consequences. When you change a part of a system, you change the whole balance of the system. I suggest that to really understand what might happen next year if the rule change is put into play, we need to think a bit deeper.

Warning! Gory Mathematical Details Ahead!

Thanks to PITCHf/x, we have some rather helpful data to help us answer this question. One thing about setting the boundary of the strike zone to correspond to a part of a person’s body is that people come in different shapes and sizes. Thankfully, PITCHf/x tells us where the bottom (and top) of each individual’s strike zone was. Because the width of the strike zone is governed by the ever-constant home plate, we can at least know whether a pitch fell into the regulation strike zone (if not the effective one) on a case-by-case basis.

One thing that we do know about pitchers is that they throw a lot of pitches to the edges of the strike zone. This shouldn’t surprise anyone, but in 2015, about a quarter of all pitches crossed home plate within two inches of the regulation strike zone and a shade under 40 percent were within three inches. Consider that a standard baseball has a diameter of about three inches, and suddenly, you have a slightly better appreciation for what umpires do on a nightly basis. It makes sense as a place for a pitcher to throw. The strike zone is—in theory, anyway—the box in which a hitter should be able to hit a ball well, and if he doesn’t swing at it, well then he’s just wasting everyone’s time. The edges of that zone are the places where the batter is going to have the least (comparative) abilities, so if a pitcher can locate on the edge, just inside the zone, he’ll get a strike if the batter takes and not have to bear the risk of throwing one down the middle.

People have differently shaped knees, but raising the strike zone in the way that MLB has proposed will effectively raise the strike zone about two inches for the average hitter. So, let’s take a look at those two inches worth of strike zone to see what happens when we turn them from “strike” to “ball” territory. I looked at all pitches from 2015 which were horizontally in the strike zone (that is, they were over home plate). Then I looked for those that fell in the two inches below the bottom of the strike zone, the two inches that would be affected by the transition (the former “low strike” zone, the future “just missed low” zone), and the two inches that would become the new bottom of the strike zone.

In the affected zone in 2015, hitters swung at 61.2 percent of the pitches placed there and made contact on 83.5 percent of their swings. When they made contact 57.2 percent of the time, the ball went into fair territory. When the ball went into fair territory, hitters had an OBP of .331 (batting average is, by definition, the same as OBP for this subset of balls), and a SLG of .513.

It’s worth noting that these are league averages. Individual hitters have their own strengths and weaknesses and pitch locations will be tailored to try to take advantage of those fault lines. Similarly, pitchers have different talents in their abilities to execute certain pitch locations, but this at least gives us an aggregate look at what to look for. But we’ll throw the disclaimer on these numbers that they only apply to the mythical “league-average hitter” facing the mythical “league-average pitcher.”

Here’s a table showing the numbers for each of those three zones:

Now, consider what a pitcher is often trying to do when he paints the bottom of the zone. He might want to throw a pitch that the batter will read as “in the zone” but it will dive out of the zone and he’ll have to reach a little further to hit it than he wants to. We can see that right now, when a hitter does swing at a pitch in that (current) just-out-of-the-strike zone area, he swings and misses about 12 percentage points more often than in the current low-strike area (the zone that would be affected by the rule chance), and if he does make contact, the pitcher gets a foul ball 5 percent more of the time and even the fair ball outcomes are about 90 points of OPS worse than those in the two inch slice directly above it. Not bad. The pitcher could also be trying to freeze the hitter by throwing something that the hitter thinks will dive down below the hollow of the kneecap, but actually nicks the bottom of the zone for a strike.

It’s all a risk-reward calculation for the pitcher. If he’s going to play on the edges, the line between the zones separates a called ball from a called strike with the obvious costs and benefits that go with that. But if the batter swings, the expected results are quite different in the two zones, enough that he might be willing to take that chance (especially if he feels confident that he can execute the pitch). Now… where to locate the pitch?

The proposed change in the strike zone, though, changes that risk-reward calculation. The pitcher is still weighing a ball vs. strike, but the line dividing those two zones from each other now corresponds to two zones that aren’t quite as separated from each other as they used to be. Trying to work just below the bottom of the new zone still means leaving the ball in an area where hitters can still get some good licks in. In theory, that’s exactly what MLB is trying to do. If the pitcher wants to work at the edges of the zone, he’s going to be working in zones where the expected outcome is higher than it used to be. That will drive up offense in addition to giving the pitcher less of a target to notch ever more strikeouts.

That’s what it does in theory, anyway. The catch is that there’s no rule on the books that says that the pitcher has to throw to the bottom of the zone as often as he previously did. What’s interesting about this particular change in the rules is that—for a pitcher who wants to play at the edges—it pretty much leaves the other three edges unchanged. Want to go to the outside corner? Want to work the top of the zone?

So, let’s see what happened when pitchers played at those edges in 2015. First, let’s look at the top of the zone. It turns out that pitchers don’t actually often throw a pitch that’s just over the top of the strike zone, but they do throw plenty of high strikes (within two inches of the top of the zone). I’m going to show you the same numbers as above for the high strike and insert them into the table that I created above.

Let’s go back to the decision that the pitcher needs to make. Right now, if he wants to play along the edges of the bottom of the zone, he is working in two zones where the expected contact percentages are 83.5 and 71.2 percent. To put it another way, the swing-and-miss rates are 16.5 percent and 28.8 percent. Instead, he could try to throw a high strike, an area which has a high swing-and-miss rate of 22.1 percent, roughly in the middle of the two zones that he’d have to work in at the bottom of the zone. Expected OBP (.331 and .310 at the bottom of the current zone and slightly under it, .320 for high strikes). There’s a decent case to be made that throwing high in the zone is roughly equivalent to throwing low in expected outcomes.

Now, not everyone works high in the zone. In fact, it’s probably a select set of pitchers that do. We can see from the SLG rate for those high strikes that if a hitter does get ahold of one, it can travel a very long way. And for some guys, trying to work up there would be downright silly. Still, if you have the stuff to work up there, you are thinking about these sorts of numbers when deciding where to locate your next pitch.

But now look at that table again, and see what those incentives look like when the strike zone moves up those two inches? (Focus on the first row, and then a comparison to the third and fourth rows in the table.) Suddenly, if the pitcher wants to work at the bottom of the “new and improved” strike zone, he’s working in areas where the expected contact percentage is above 80 percent in both cases. It’s only 78 percent for high strikes. The expected OBP at the bottom of the zone (and just below it) are .353 and .331. It’s only .320 for a high strike. Even the SLG associated with high strikes (.546) doesn’t look so high any more compared to the .513 and .577 in the two “low” zones. Now, faced with the decision to throw a high strike or to play around with the bottom of the zone, the numbers seem to favor throwing it high. Throwing high strikes (again, assuming you have the stuff to throw it high) is simply a better bet compared to those two “low” zones. In the current strike zone, the two are about equal.

Don’t feel comfortable throwing high strikes? You can always start working the inside and outside edges of the plate. Sure, they have their own risks, but with the risks of trying to work the bottom of the zone going up, those risks will also start looking more appetizing as well. Why should a reasonable pitcher still continue to work the bottom of the zone?

The answer to that question gets into game theory. If all a pitcher does is throw high, unless he has unhittable velocity, the hitter is going to be looking there, so to keep him honest, he’ll have to throw low once in a while. We could re-run the same sorts of analyses for pitchers who want to play the horizontal edges, but the point is that changing one part of the strike zones changes the incentives for a pitcher to throw there. A perfectly logical response would be for him to shift his pitch selection away (not completely, but most certainly substantially) from that area.

Why Should I Do That?
Let’s sum this all up in one sentence. “If to get a low strike, I’m gonna have to come that high up, I’m just gonna find a different way to attack this guy.” That’s not how it will work for every pitcher. Some guys have to work down. It’s also not going to work on every hitter. Down might be their only identifiable weakness. Those pitchers will be negatively affected (and those hitters will love the new rule), but in time, those pitchers are in danger of simply being replaced by others who have a skill set that aligns more with the incentives present in the ecosystem.

If you change one part of the strike zone and leave the rest essentially unchanged, then you’re probably going to just drive traffic to those other parts of the zone, and you’re going to adversely affect certain types of players. If MLB wanted to promote offense by shrinking the strike zone, they could instead narrow home plate a bit (and thus, narrow the strike zone horizontally) and drop the top of the zone. Maybe the idea is that they feel that low-strikers have benefited too much from their negligence in enforcing the rulebook zone as is, and they want to take away that advantage. At this point, we’re arguing aesthetics of who the “correct” types of players are.

Perhaps there is some Nash equilibrium where an initial refusal to work down in the zone lets hitters focus on the other three “edges” and thus makes the bottom of the zone a little more palatable for a pitcher to throw to because he has the element of surprise on his side. The important thing to note is that the effect is not going to be as simple as “all the pitches that have been thrown to that area will continue to be thrown there.” Even assuming that pitchers will continue to throw low, just not quite as low, at the same frequency as before is suspect. Pitching is always risky, but pitchers can (and probably will) move at least some of their risk into comparatively safer harbors.

Maybe MLB is really mostly interested in restoring the effective strike zone as the hollow of the knee (what the actual rulebook says now, though data show that the effective zone runs a lot lower). Asking for C when you really want B is a time-honored negotiation (and parenting) strategy, though they might want to be careful what they wish for. If the rule change goes into effect, but the actual result of implementation is that the zone is called where the current zone was supposed to be called all along, MLB will probably face pressure to call the strike zone as its rulebook states. I wonder if they want it that high. Before you know it, people will be complaining about all the 15-14 games again, and lamenting various topographical impossibilities.

Moving the strike zone upward probably will put upward pressure on offense. Jon Roegele’s research shows at least a correlation (if not causation) between the falling strike zone over the past few years and the downturn in scoring. Maybe MLB really does just want to make baseball fun again. But I’m left to wonder if this isn’t brain surgery with a butter knife. The result of this new policy isn’t just “fewer called low strikes.” It’s a change in the ecosystem, and maybe a change in the game itself.