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January 21, 2013

Baseball Therapy

Pitchouts and My Underage Gambling Problem

by Russell A. Carleton

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Last week, my colleague Sam Miller ran a few numbers on the pointless, yet poignant play that is the pitchout (a billion points to whomever catches that reference) and concluded that pitchouts are actually a net loser: they cost the defense/pitching team more in runs than they gain. Sure, individual pitchouts sometimes nab a would-be base stealer (and that's a good thing), but overall, managers guessed wrong so often that the expected payoff wasn't high enough to justify the strategy. Rule number one of strategic thinking is that just because you got lucky on a stupid bet, it doesn't negate the fact that it was a stupid bet.

Sam's math is relatively simple. He points out that pitchouts increase the likelihood that a runner will be caught from about 25 percent to 50 percent. Since the swing in value from a stolen base to a caught stealing is roughly .63 runs, if the manager has guessed right and the runner really is going on that pitchout, the gain is 0.158 runs. To do this, the manager must sacrifice a ball in the count, often meaning that the pitcher will either fall behind or sacrifice the advantage in the count for which he had worked so hard. Sam cites work by our own dearly departed Dan Turkenkopf (congrats Dan on getting hired by a team!) who found that changing a strike to a ball is worth .118 runs. Because about 63.7 percent of pitches go for strikes (I believe he speaks of non-contacted balls... adding in balls in play would change the calculus here, but also would negate the whole point of why we're discussing pitchouts), the manager is sacrificing a 63.7 percent chance at a strike, which is worth .075 runs.

Would you pay 75 cents for a chance at 158 cents? It depends on how good you think the odds are of winning. To figure out what the correct mathematical answer is, let's calculate the break-even point.

Oh yeah, by the way...

Warning! Gory Mathematical Details Ahead!
Cost of giving up a chance at a strike is 0.075 runs

Potential gain of guessing right and increasing the chance of a caught-stealing is 0.158 runs

There's no real gain or loss if the runner isn't going.

We calculate the break-even point this way:

0.158 * prob + (1 - prob) * 0 = 0.075

Solving that, we get a break-even point of 47.5 percent.

For the pitchout to make sense, a manager needs to guess correctly that the runner is going about half the time. As Sam showed, in real life, managers are actually successful about 20 percent of the time, and teams are leaking runs as a result. Pitching out could be a good bet if managers were better at figuring out when that guy on first was about to break, but major-league managers just aren't up to the task.

On its face, it seems that pitching out is a silly strategy. But what if there's more to it? One thing that I've come to learn about baseball is that when a seemingly pointless strategy is in use, there's always a reason. It's not always a good reason, but there's a reason.

And so I went in search of the reason for the pitchout in the numbers.

Who gets a pitchout?
One thing that made me do a double take on this topic was the fact that in the past, I've found that another seemingly silly play, the pickoff throw to first, is actually a wonderfully effective strategy. It rarely actually picks off a runner, and even when it does, that's generally counterbalanced by the fact that the ball could go sailing past the first baseman. But, runners who had a check-in by the pitcher were significantly less successful in their attempts at stealing. Perhaps pitchouts also would have some sort of deterrent effect?

One thing I wanted to look at was a potential obvious bias. A manager is going to pitch out only if a runner is on first whom he thinks will steal. This is generally a fast guy who likes to run. And while he may or may not admit it, calling for a pitchout is also not really a ringing endorsement of the catcher's arm, either. To test for this, I calculated the number of plate appearances there were in which a runner was on first and no runner was on second. If a runner singles to lead off an inning and then stands there watching as his next three teammates all make harmless outs, he has had three chances to steal second. I calculated both the percentage of times that the runner tried for second in this situation and the percentage of times he was successful. I did the same for the catcher: how often did he face a runner on first with second open, how often did the runner try to steal, and how often was that runner successful.

I ran a few logistic regressions predicting whether or not a manager would call for a pitchout, given the runner and catcher stats calculated above. Sure enough, a runner who liked to go for it and who was successful more often drew more pitchouts. A catcher who was seen as an easy mark, both in terms of how often he was tested and how often he allowed a stolen base, was more likely to take a step outside the catcher's box to catch an unannounced intentional ball.

Keep this in mind. We have a biased data set, and we need to correct for this. This will become important later on.

Are managers bad at guessing when runners will go?
Not really awful, and actually, not altogether bad. As we see above, they aren't as good as they need to be, but let's put a 20 percent success rate into context. For one, managers have to pick not only the at-bat in which the runner would be going, but the exact pitch. Consider that from 2003-2012, there were about 1.36 million pitches thrown in situations where there was a potential steal of second and about 33,000 attempts on second base. The runner goes on roughly 2.5 percent of pitches (Note, because someone out there will pull out a calculator: I'm doing some rounding here. And yes, that includes runners going on three-ball counts, where a pitchout is pointless.) If managers were just picking pitches at random for pitchouts, we'd expect them to get it right 2.5 percent of the time. They are eight times better than that!

Managers also aren't stupid. 92.1 percent of pitchouts are thrown with the count either even or the pitcher ahead, and almost never (1.9 percent) with a two-ball count. It's one thing to draw the count back to even. It's another to intentionally put your pitcher in a hole.

Managers know that the most common time for a runner to try for second is the first pitch of an at-bat (26.9 percent of such attempts). The plurality of pitchouts are on the first pitch as well (40.1 percent) Not surprisingly, runners are more likely to go on a 1-0 pitch (14.4 percent of attempts) than an 0-1 pitch (12.5 percent of attempts), while more pitchouts are thrown on 0-1 counts (22.0 percent) than 1-0 counts (6.1 percent). Both managers know the rules of the game and are adjusting their strategies accordingly. However, when the count is even, the game is more likely to be afoot!

But let's look at managers (in general) from the point of view of signal detection theory. In a perfect world, every stolen base attempt would be met with a pitchout. If you have 100 percent certainty that a runner is going, even factoring in that it's not a guarantee that he will be thrown out, the gain in probability of a caught stealing outweighs the cost of the ball. If you are 100 percent certain that the runner is not going, there's no point in giving up a ball to the hitter. Signal detection theory looks at how good someone is at detecting when a target event (a stolen base attempt vs. no attempt) will occur and consequently making the correct decision (pitching out vs. not). In reality, there are two types of errors that a manager can make. He can pitch out while the runner stands at first and mocks him for wasting a ball (false alarm), or he neglect to pitch out even though the runner is going (miss). Signal detection theory tells us how good a manager is at figuring out when the signal (detectability or d') is there and which error he is more likely to make (response bias or beta).

From 2003-2012, managers as a whole had a d' = 0.841 (for the uninitiated, that's not too shabby... not great, but not horrible. For this number, higher is always better.) But they had a response bias of 6.95 (yikes! A perfect score here is 1.0, no higher, no lower). The fact that the number is over 1.0 means that managers err on the side of pitching out much more than they should. This is how we can say that managers are pretty good at figuring out when the runner is going, and at the same time, far too itchy in hitting the pitchout button.

Is pitching out a deterrent later in the game?
My first thought when I read Sam's article was that he wasn't taking the game theory aspect of pitchouts into account. Perhaps pitching out is a bad decision at the micro level, but we need to take into account what other effects it might have. Suppose a team pitches out in the third inning. Whether they are successful is irrelevant for the moment. In the fifth inning, will the opposing manager, faced with another decision about the runner on first, be a little more hesitant to send him? Because... well, they've shown that they are willing to pitch out. They might do it again. A pitchout is a way to keep the other team honest. And maybe that reduction in the other manager's willingness to steal means that the other team becomes a little more afraid to take chances that would actually be to its advantage.

For all possible stolen base situations from 2003-2012, I coded whether there had been a pitchout earlier in the game against that team. I started with very simple logistic regressions predicting whether the presence of a pitchout earlier that day would be associated with a drop in stolen base attempts and, when there was an attempt, success in stealing. The answer was that a pitchout (regardless of its success) earlier in the game made the offensive team more likely to send a runner, although no more or less likely that he would succeed.

But wait, remember that one of the reasons that a pitchout is thrown in the first place is that you have a fast runner and a weak-armed catcher. I controlled for both factors (using the natural log of the odds ratio for their seasonal numbers) to discern which direction the relationship flowed. Even after controlling for these things, the findings held. Managers were more likely to click "send," and it didn't affect success in either direction.

What about if the pitching team had previously not only thrown a pitchout, but had done so when the runner was actually going? (Again, the runner need not have been thrown out.) Surely this would scare the manager on offense as he realizes, "The other guy is in my head..." Actually, once you control for both catcher and runner tendencies, there is no effect on behavior later in the game. The manager sends the runner just as often as we would expect, and he's successful no more or less often. There are no after-effects of a "successful" pitchout.

The manager who pitches out might be trying to "send a message" early in a game. He just might not be sending the message that he wants to send, since it does not deter the running game of the other team, and indeed makes his opponent more brazen. The manager who calls for a pitchout might want to say, "We're watching...", but instead he telegraphs, "Yeah, my catcher doesn't throw out a lot of runners and I'm willing to sacrifice a valuable commodity (a ball) for the off-chance that I might catch your speedster. I'm clearly worried about how your team's running game is going to affect my chances of winning here."

At the micro level, pitching out is a fool's strategy. At the macro level, it doesn't do anything helpful. So why does the pitchout still exist?

Why My Trip to a Casino as a 14-year-old Explains the Pitchout
I am currently 25 cents up on the American gambling industry. And I intend to keep it that way. When I was 14, my family took a trip to Black Lake, Michigan, which is way up at the top of the glove. On our way home, we stopped off at a tribal nation casino. I still have no idea why. I was, of course, too young to gamble at the time, but I gave my father a dollar and asked him to deposit it into the nearest quarter slot machine, pull the lever four times, and bring me whatever was in the tray afterward. He struck out on the first three pulls, and on the fourth try, hit for five coins. I'm proud to say that with the proceeds, I bought a copy of USA Today for the purpose of looking at the box scores of the day before. And a cookie.

I was rather proud of myself for having beaten the casino gaming industry, despite the fact that a) it was luck and b) gambling is a tax on people who are bad at math. Still, I felt a strange sense of accomplishment. Looking back, it wasn't just the 25 cents that I made, it was the thrill of having beaten the system (and at such a tender age!) The system is apparently still bitter, as no one from the gambling industry has ever called me since.

A manager might know that he's placing a losing bet by pitching out. (If he doesn't, please show him this article, and he will.) But let me suggest that there's a hidden prize in pitching out that might make it all worthwhile. Just like at the casino, sometimes, you come up the winner, and that feels really good. The payoff from a successful pitchout guess is not just 0.158 runs, it's the chance to say, "Ha, other manager! I can read your mind." And if you guess wrong... well, it's only a ball, and the game just rolls along. If there's a common thread that runs through a lot of the inefficiencies in baseball, it's the male pack animal tendency to try to display dominance behaviors over other males. My 14-year-old self would have appreciated that.

The problem is that pride can't be cashed in for anything on the scoreboard. Balls, on the other hand, can eventually be exchanged for first base. Or for a big fat fastball later in the at-bat.

Then there's the issue that traps people who have gambling problems. Once in a while, you get a nice reward, and habits (like gambling... or pitching out) that are rewarded intermittently are actually harder to break. If you got a cookie every time you hit the button, you could rationally calculate whether hitting the button was worth it. But if you got a cookie once every five times (or so), there's the thrill of the anticipation of whether or not you might win this time. And that thrill is what hooks you.

Major-league managers probably are smarter than the average bear when it comes to figuring out when the other team is going to run. In fact, our signal detection analyses show that they do a decent job. But even if they were twice as good as the historical record shows that they have been, they'd still fall short of what they needed just to break even. Therein lies another cognitive weakness that people fall into. Managers do better than random chance and probably would do better than all the callers into talk radio who swear that they can do a better job, but talk radio callers are the wrong baseline for comparison. For anything.

What's frustrating is that it's mathematically possible to be good enough to make the pitchout a worthwhile strategy. And every gambler believes that he's just one little tweak in his strategy away from beating the house. In truth, the pitchout, just like going to the casino, is a losing proposition. Some days, you'll get lucky and beat the house, but in the end, you will lose. The rational manager should realize that he's being tempted by a game which he can not ultimately win or more correctly, which he is not good enough to win. Then he should take the next logical step and stop playing the game. Problem: if something is impossible, there's no shame in not being able to do it. But in American culture, and again in American male culture, it's not allowable to say "I'm not good enough." There's that overly male tendency rearing its ugly head again.

And so, next season, expect a few pitchouts.

Russell A. Carleton is an author of Baseball Prospectus. 
Click here to see Russell's other articles. You can contact Russell by clicking here

Related Content:  Managing,  Strategy,  Tactics,  Pitchouts,  Gambling

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