March 29, 2016

Baseball Therapy

It Worked Last Time

by Russell A. Carleton

There’s an endless game of cat and mouse to be played among pitchers and batters. Ted Williams famously said that hitting a baseball was the hardest thing to do in all of sports, but what makes it so hard? Sure, hitting something that small traveling that fast with a blunt instrument takes Olympian levels of reaction time, hand-eye coordination, and raw strength, but put even a decent minor-league hitter up against a pitching machine that is “throwing” 95 mph and eventually, he’ll start squaring it up every single time.

The problem in baseball is that the collision between bat and ball needs to take place within a particular (small) area of the bat and it needs to be at the right time during the flight path of the ball. Otherwise, someone’s going to be walking back to the dugout after having popped out to second. The problem – at least from the batter’s point of view – is that the pitcher never has the decency to throw the same pitch over and over again at the same speed and to the same location. Hitting is timing and pitching is upsetting timing and all that (quoth Warren Spahn).

So pitchers play games with hitters. They change speeds. They throw balls that curve and dip and bend and zwurvle. Otherwise, they’ll end up with the ERA of that batting cage pitching machine. And they throw those pitches in sequences that try to exploit weaknesses so that batters will make that collision at just the wrong time or angle. That pop out to second would be really nice right now. Still, there’s a bit of an edge that batters have if they are paying attention. Baseball is a game of repetition. Perhaps a pitcher was able to zwurvle his way into an out with this at-bat, but in about 45 minutes, he’ll be facing off against the same batter. The one who has seen the zwurvle before. Does our brave pitcher have another trick up his sleeve? Does he need one?

It’s been said that strike one is the most important pitch in baseball. There’s evidence to back that up. A plate appearance that starts with strike one (rather than ball one) is much more likely to end up as a strikeout and less likely to end up as a walk, if for nothing other than obvious reasons. Suppose that when Smith faces Jones in the first inning, he starts him off with a fastball on the outside corner, and it works! Jones swings and misses. In the third inning when they meet again, the incentives are still the same. Smith would rather start the at-bat with a strike, but he has a decision to make. He knows that a fastball on the outside corner did the trick last time. Will he try the same strategy? If it worked once, it might work again… but does Jones know that he’s thinking that and will he alter his approach to anticipate that? But does Smith know that Jones knows? But does Jones know that Smith knows that Jones… I have a headache.

The point is that there’s always a certain amount of game theory in baseball. But even within the game theory, there’s an interesting question to be asked. If “stuff” is all you need, once a pitcher has found something that works, why not just do it over and over and over and over. Even if a hitter knows that something is coming, sometimes it’s so filthy that he can’t really do anything about it. Please consult the collected works of Mariano Rivera on the subject. But perhaps there’s more to this game than just “stuff.”

Why don’t we ask the pitchers what they believe? Not with a tape recorder. Let’s look at what they actually do.

Warning! Gory Mathematical Details Ahead!
I used PITCHf/x data from 2015. I specifically focused on the first pitch of each at-bat for the twin reasons that a) everyone gets one of those and b) we don’t need to worry about the pitch that came immediately before in the at-bat. I coded each pitch as a “success” if it produced either a strike (whether by a called strike, a swing and a miss, or a foul ball) or the batter was put out. I then looked what happened the next time that the pitcher and batter met. (I ran the model both with the stipulation that the second encounter had to be later that day and later took that restriction away. The results were largely the same both times. I will report the same-day findings.)

After a successful “strike one” pitch, does a pitcher go back to the same strategy the next time they meet?

I first looked at pitch type (fastballs and changeups and such). When a pitcher has success in getting strike one, he throws the same pitch for the first pitch to the same batter in the next encounter 36.4 percent of the time. If he hadn’t gotten strike one? He throws that same non-effective pitch 35.4 percent of the time. The sample size is big enough that this is significant (by a simple chi-square, if you’re scoring at home), but significant just means “pretty sure it’s not zero” and not necessarily “something we need to make a big deal out of.” Here, we don’t see much of an effect. But let’s be a little more methodologically rigorous. I first wanted to control for the fact that we might see a lot of matching pitches because a lot of pitchers rely on a first-pitch fastball.

I controlled for how often a pitcher throws that particular pitch as the first pitch in at-bat. If he always starts off with a fastball, we shouldn’t be surprised if he goes fastball again, no matter what happened last time. I placed this control variable (expressed as a natural log of the odds ratio) into a logistic regression and added in the “success last time” variable. The significance of the effect disappeared. It doesn’t seem that pitchers are influenced in their pitch selection by what happened the last time. If this is true, it suggests that pitchers are resisting the temptation to just go with what worked last time, at least at the aggregate level. Then again, if word got out that this is what they were doing, then they’d be done for. So, let’s give pitchers some credit. They know that they can’t get too predictable.

But maybe there is an effect that we’re missing. There’s more to a pitch than whether it zwurvles. Perhaps pitchers don’t change what they throw, but where they throw it. I divided the strike zone (and the parts outside the strike zone) into inside, middle, and outside. Perhaps a pitcher doesn’t think “I got him with a fastball last time, I can get him with a fastball this time” but he does think “I got him with a ball away last time, I can get him with a ball away again!”

When a pitcher has success (again, strike one or the batter put out) on the first pitch of the last at-bat, on the first pitch of the next at-bat, he goes to the same space 41.3 percent of the time. When he wasn’t successful last time, he goes there 48.1 percent of the time. That’s both statistically significant and a little surprising. A pitcher is more likely to go back to a part of the plate that wasn’t successful last time than he is to chase success!

Again, to add some more methodological purity, I controlled for the likelihood that a pitcher just likes to throw inside or outside on the first pitch in general, but the effect was still significant and still in the direction of a pitcher being more likely to fish in a hole where he hadn’t caught a fish before than one where he had.

It Might Not Work Again…
Let’s give the starting pitchers of the world some credit. They’re facing the best hitters in the world and they know that they’ll have to do so a few times within the same two-hour period. And they know that they’ll have to be unpredictable. The evidence shows that, as a group, they succeed in that, at least as far as first pitches go. In fact, if nothing else, we see that they aren’t overly reliant on what worked before, but specifically want to try something different. That makes sense in that the batter, coming up for the second time, has proof positive that he has a weakness and may be taking steps to compensate for it.

I think that this also shows us something important about pitch sequencing. Pitch sequencing has commonly been thought of in terms of pitch types--for example, the effectiveness of a fastball that follows a curveball. But what we see in these findings is that the effect that we see is that while pitchers don’t tend to change what they throw, they tend to change where they throw it based on past results. What a pitcher “has” on a given night might vary. He might have a night where he has good command over his fastball and feels more comfortable with it, but have no feeling for his zwurvle. So, the question of how to hold his hand around the ball might be made for him in some sense. But where to throw the ball is another story. Pitch sequencing is one of those things that no one’s got a full accounting of, and as we continue in this work, it’s wise to think about the issue of location of the pitch, both in terms of how pitchers actually select where they throw it and what effect it has once the ball gets there.

One other interesting angle that comes from all of this is the idea of the times through the order penalty. A couple of weeks ago, I suggested that the “penalty” such as it was had more to do with fatigue than it did with some sort of learning effect. This might be part of the reason why. If pitchers are properly varying their sequencing and mixing things up, there’s less to be able to learn. While a pitcher can’t fight the laws of fatigue, he can do his best to make sure that there’s no pattern to follow from at-bat to at-bat.

If nothing else, it should give us an appreciation for how difficult a starting pitcher’s job really is. He’s got to be able to throw all of the types of pitches that would make for him to not be predictable. And if he’s any good at it, you can see why teams would want to keep him around, even at the cost of an eight-figure yearly salary.

Russell A. Carleton is an author of Baseball Prospectus. Follow @pizzacutter4
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