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Rainbow sprinkles alert: Ben Lindbergh saw this one on Twitter, from currently shelved reliever Peter Moylan, who was traded to the Dodgers in the middle of last year after spending several years with the Braves. Mr. Moylan is currently recovering from Tommy John surgery, like everyone else in baseball.

Well, is it?

Warning! Gory Mathematical Details Ahead!
I found all situations from 2009-2013 in which a reliever was pitching in the seventh inning or later and where he faced a situation in which his team was either leading by less than three, tied, or down by one run, there were at least two runners on base, and he didn’t give up a run. If that’s not a Houdini act, I don’t know what is. I found the situations in which our magician reliever came back out for the next inning (and perhaps, the inning after that).

I controlled for the strength of the reliever and the opposing batter using the log-odds ratio method to calculate the expected probability that a plate appearance would end in one of several events (strikeout, walk, single, etc.). I also controlled for the reliever’s pitch count (maybe the reason that he got out of the jam was that he got himself into the jam to begin with) and whether or not he had a platoon advantage (a good reason that he might come out for the eighth is that he might be used as a LOOGY for one more batter). I ran a series of logistic regressions, looking again the same basic subset of plate appearances, a reliever pitching late in a close game (again, pitching team either winning by less than three, tied, or down by one) so that we’re comparing similar sets of contexts. I entered whether our reliever was a “returning Houdini” into the regression to see what effect it might have.

The results of those regressions were loud and clear in their message. For returning escape artists, strikeouts were well below expectations, as were outs in general. Walks, singles, and extra-base hits all increased, although home runs decreased (not enough to offset the other effects). The effect sizes were huge. As an example, take a situation in which we might otherwise expect a 20 percent chance of a strikeout. For a returning Houdini, the chances of actually striking the hitter out fell to around 12 percent. Other effect sizes were similar. Managers take note?

Not so fast. Consider the fact that one reason that a pitcher might have gotten himself to where he needed to escape was that he wasn’t really on his game that day. I further restricted our Houdini sample to those who faced (and conquered) a tough situation, but who had inherited the runners on base, meaning that while they escaped the mess, they had not been the ones to create it. Once I did that—again controlling for batter and pitcher quality overall, pitch count, and handedness advantage—the effects completely disappeared. It seems as though the reason that our Houdini pitcher shouldn’t bother coming out for the next inning is often that he just wasn’t having a good day to begin with.

Escape is Never the Safest Path
Moylan’s formulation makes intuitive sense. Everyone has had the experience of being in a “big” situation at whatever it is that they do, feeling that rush of adrenalin, and maybe even feeling rather wiped out afterward. But the idea that once the adrenalin goes away, some sort of edge has been lost is based on a misunderstanding of the body’s very complicated system for managing stressful situations. Adrenalin itself is only a messenger of what is known as the sympathetic nervous system. When a person is faced with a big situation, it activates the body’s “fight or flight” response system. Adrenalin goes and tells the various organs to prepare either for fighting or fleeing, telling (among other things) the heart to beat faster and the muscles to get ready for a lot of activity. It also tells the stomach, bladder, and bowels to cast aside all excess baggage, which is why people often report feeling like they will throw up or that they have to use the bathroom before a big event. People do have greater raw physical strength when they adrenalin is pumping, but baseball is a game of modulated physical strength, so that’s not always a good thing.

But once our pitcher has escaped, has run back to the dugout, and is sitting there with a jacket on to keep his arm warm, his brain recognizes that he is out of “danger.” The body activates the parasympathetic nervous system and its associated messenger chemical acetylcholine, which restores a resting balance. It takes a few minutes, but he probably has 10-15 minutes to sit there, and by the time he’s able to pitch again, he’s probably returned most or all of the way to a resting state. The reason that the body has such a system is that, physiologically, it can’t sustain the fight-or-flight changes for extended period of time without risking other negative consequences. That fading of the adrenalin rush might feel like a letdown, but it actually helps our Houdini reliever to go back out there for the eighth and not burn out.

In fact, the numbers show that our reliever is just as effective as we might expect him to be, given what else we know about him and his current situation. At least the average reliever is—there probably are differences between players as far as how much a pressure situation takes out of a pitcher, but I would argue that the burden of proof would be on the side that says that Smith absolutely needs to come out after an escape act.

The more important thing is that an escape act, while nice, seems more likely to be the sign of a couple of lucky breaks for a guy who was having a bad game. If a guy who pulled an escape act created his own mess, he probably should be replaced, or used with extreme caution. But if he was just a fireman who cleaned up someone else’s mess, he’s good to go if you need him.

Thank you for reading

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gweedoh565
4/22
Is that a Pearl Jam reference?

Great stuff, Russell!
therealn0d
4/22
Dissident. Off Vs.
Richie
4/22
Yes, excellent stuff. Thank you.
therealn0d
4/22
My immediate reaction before the second paragraph began was basically the conclusion that was drawn. Because it makes sense, and not just on days when you might say the reliever just had a bad outing, but in general. There's a good reason why pitchers get used in these roles, and it's because they're volatile and prone to untrustworthy outings, otherwise they would be closing out games. In short, they're really not all that good on a consistent basis. Now you know why you hate the way your manager uses his bullpen.
lichtman
4/23
Russell,

I can buy both premises - that there is a hangover effect AND that relievers have off days, but there is NO way that you could identify an off day by observing base runners in ONE inning and then have such a significant effect in the next inning. Do you have any idea of the variance that the "good days/bad days" would have to be in order for two base runners in one inning to result in that kind of a decreased performance in the next? Well, it is impossible.

So, something is wrong.

MGL
TangoTiger1
4/23
I concur with MGL. I'm not buying these results in the least:

"As an example, take a situation in which we might otherwise expect a 20 percent chance of a strikeout. For a returning Houdini, the chances of actually striking the hitter out fell to around 12 percent."

Not to mention that since these results are based on both groups of relievers, those who inherited runners and those who placed runners, and since Russell concluded that those who inheritied runners weren't affected (i.e., 20% before would also be 20% post-Houdini), that would mean that the other subset (those who placed runners themselves) would be far lower than 12% post-Houdini. Like a 5% or something.

Not buying it at all.

How can you have an entire article like this and not show the data? Seriously. It does not have to be in the article. Just put a link to the source data, aggregated by pitcher.

Oleoay
4/24
I had a different kind of question pop into mind. Do pitchers who return to pitch after extremely short innings (or long innings) time-wise tend to do better or worse? Whether it's adrenaline or acetylcholine or straight out muscle fatigue or what not, if we're talking body chemistry, how much does the length of an inning where the pitcher is sitting on the bench influences their effectiveness.

I also realize that's damn hard to measure.
lichtman
4/24
Nothing is really hard to measure. It is sample size that usually constrains us (from having much certainty in any conclusions drawn from the results).