June 27, 2017
The Pendulum Swings Back
A pendulum consists of a weighted object tied to the end of a string. It is a simple physical property of pendula that if you lift one to a certain height and let it swing on the string without adding any force to it, the weight will not make it all the way back to its previous height when it swings back. The system loses a bit of energy in the process. This means that if you constructed a pendulum and let the weight go just a bit away from your nose, there is no way that the weight can return back and bop you on your snout. To do that the weight would have to come all the way back to where it started and a little bit further to get to your nose, and that is physically impossible.
The funny thing is that you can give someone that exact explanation and then set up an actual pendulum with the weight starting right by their nose, and as it swings back ... they flinch. Why? That makes no sense. They were just given an explanation about how the weight couldn’t physically hit them!
What if instead, you had skipped the lecture on pendulum physics altogether and tried something else? What if you talked to our unwitting volunteer about the emotional reaction that he was about to feel? You tell him that it’s common for people to experience a bit of panic when they see something coming toward them that looks like it’s going to hit them in the face. This is normal, but you have taken steps to make sure that he has nothing to fear. When you set up the pendulum again a bit away from his nose, he probably isn’t as likely to flinch.
By focusing on his emotional needs in the situation, rather than explaining the situation logically, you’re more likely to change his behavior. Humans are not logical creatures. They are emotional ones. If you remember nothing else today, remember that.
Pitchers throw to first base to check on runners an astonishing number of times, compared to the actual benefit that they get from doing it. Pickoffs are rare and most throws aren’t even that close, but they still do it. Yes, pitchers are just “keeping the runner honest,” and if they didn’t throw over runners would get the wrong idea and stray too far, but after a while shouldn’t the pitcher look over, see that the runner is only two steps off, and just say, eh, forget it? What’s this throw really gonna do?
Not so fast!
We know from previous research that when a runner tries to steal, if he does so after the pitcher tries to pick him off (unsuccessfully, obviously), he is actually less likely to nab the base than if he does so without a check-in throw. This effect holds even when accounting for the quality of the runner and the catcher and the game situation, and it’s worth about five percentage points of success rate. There’s also an effect on success rates for runners going first-to-third on a single after they’ve received a check-in throw. It’s not huge, but it’s there.
It’s worth asking why this is, although here I have to get into a bit of speculation. Let’s say that a runner on first is thinking about swiping second if he gets a chance. He’s got to cover 90 feet between first and second, although he’s probably leading by a few feet off the bag. He’s taking a lead for the most obvious reason that there is. If he tries to steal, it’s easier to run 80 feet than 90 feet.
Even bad runners cover the 90 feet between home plate and first base within 4.5 seconds. That’s an average of 20 feet per second. We know that he’s not running at an even speed of 20 feet per second. There’s acceleration to think of, but laying that aside, if he can cover 90 feet in 4.5 seconds, he can cover 80 feet in 4.0 seconds. The possibility of a throw to first means that he has to think about a quick dash in the other direction, so he has to balance his desire to get to second with his need to take cover at first, if need be.
Here’s the thing, though: The runner has some idea of where that balance point is based on his own baserunning abilities and the pitcher’s tendencies and move, and so he selects how far he leads off based on whatever calculus he does on the subject. In theory, after a pickoff throw that does nothing more than annoy the crowd, he has a little more information.
Let’s say that he took a lead of 10 feet initially, and was able to get back when the pitcher threw over. He now has a very recent data point that says he is capable of recognizing the pitcher’s pickoff move and getting back to first base from a lead of 10 feet. In fact, he just did exactly that. Whatever calculation went into his initial 10-foot lead, it seems that he just validated it. If he changes anything in the next 15 seconds, perhaps it should be taking a 10.1-foot lead. It makes no sense to go backward to a nine-foot lead. Why retreat?
Game broadcasts will sometimes show a live readout of how large a lead a runner is taking, showing off the capabilities of the Statcast system. Alas, this data is not publicly available, but it would make for an interesting study in human behavior. Is it possible that runners take a shorter lead off first base after a pickoff throw than they do before it? (It would be the perfect A/B test. It would be the same pitcher, same runner, same game situation, and even the same count. The only difference would be the pickoff throw that didn’t get him.)
After a pickoff throw, a runner has a new piece of evidence to consider. He knows that the pitcher is willing to throw over, although it seems unlikely that he didn’t have that thought already in his head when he first started sneaking away from the first baseman. I mean, the fact that the first baseman was on the bag ready to receive a throw should have been a giveaway. That the runner survived the initial pickoff attempt is evidence that he was able to read the pitcher’s move and respond correctly. Therefore, whatever go/stay response bias he has calibrated in his mind is working, and if anything, he might have evidence that he could even be a little more liberal with it.
If logic is prevailing, our runner should take at least the same lead that he had before the pickoff throw, and keep the same go/stay response bias. Maybe he should even be a tiny bit more aggressive. If he were the same distance from first (or a bit further) and was a little more likely to go, then all else equal, we should see a slight uptick in the success of any stolen base attempts. But we don’t. We see the opposite. Humans are not logical creatures. They are emotional ones. To understand why, let’s instead re-frame the non-successful pickoff throw as an emotional experience.
There are plenty of low-frequency events that people are still invested in looking out for, because while they might be low-frequency, they aren't no-frequency and they are of high value. People hold out hope for winning a big prize in a raffle, even knowing the remote mathematical odds. If the event that we’re talking about pops up at random intervals, it fits to what psychologists call an “intermittent reinforcement schedule” and psychologists know that if you want to get someone invested in a particular behavior, you should set up an intermittent reinforcement schedule for that behavior. Slot machines work this way. You play, and sometimes you win, although at random intervals without warning, enough to keep it in your head that the next spin might be a lucky one.
You can turn that logic around. A runner on first base knows that most pickoff throws don’t actually pick the runner off, but he also knows that sometimes they do. It happens rarely, but when it does, it’s an awful event. An out is recorded for your team, a runner is removed from the bases, and in front of 30,000 people you have to do that awkward jog back to your dugout where you look straight ahead because you don’t want to acknowledge in any way that you just did something stupid. Even if it doesn’t happen on this throw, it could happen on the next one, if you’re not being careful.
And the throw over to first base activates that little moment of doubt. That doubt might not last very long, but it doesn’t have to. It’s really only going to be a few seconds before you’re going to have to take a lead again. It doesn’t have to be a huge amount of doubt, nor would the runner necessarily recognize it as doubt. Its effects wouldn’t necessarily be visible to the naked, untrained eye. The effect size on stolen base success rate is about five percentage points, after all.
Consider for a moment that a stolen base attempt is effectively going to come down to a race between the runner’s foot speed and the pitch-catch-throw-tag sequence of the defense. The runner usually tries to take off as the pitcher is mid-delivery, and the sequence from the release of the pitch to the tag is around 3.5 seconds. Call it a total of 4.0 seconds flat. Let’s say that our runner hesitates an extra tenth of a second–less than the blink of an eye–on the pitcher’s delivery. Let’s say he also takes a lead that is two feet–half a step–shorter. If he covers 20 feet per second, that’s roughly going to mean an extra tenth of a second that he’ll need to make his journey. He’s lost two-tenths of a second (give or take) but there’s only four seconds allotted (give or take). That’s going to turn some fraction of would-have-been-stolen-bases into caught stealings.
In 2016, there were 1,471 times that a runner tried to steal second base after the pitcher had made a non-successful throw over to first base, or 49 per team. If throwing over to first is worth a five-percent drop in stolen base success rate, that means that the average team “lost” 2.5 stolen bases. The value of changing a caught stealing into a stolen base (or vice versa) varies with how many outs there are. Just based on a simple run expectancy table for 2016, it’s worth about 0.8 runs with no one out, 0.55 with one out, and 0.3 runs with two outs. Let’s split the difference and call it half a run per instance. There’s also some small effect on first-to-third success rates. It means that the average team loses a run or two each year to their emotional selves.
It might seem a little disappointing to have come all this way for a run or two, but beyond the cliché “every little bit helps” it probably wouldn’t be all that hard to re-claim that value. The point is how you’d go about doing it. This isn’t a time to be beating people over the head with run expectancy charts. Sure, that’s the backbone reason of why you do it, behind the scenes, but if you want people to change their behavior, you have to take care of their emotional needs as well. And maybe there are other areas of the game where the solution can be re-framed. Maybe the solution isn’t more logic, but a candid look at how a strategy might be experienced emotionally.