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Last week, we talked about Tim Lincecum's 148 pitch no-hitter and found that while there might be some consequence for a pitcher's next start due to such a long outing, it was relatively small and generally gone by the second start. So there's not much penalty in the short term for leaving a pitcher in to throw a lot of pitches; what about the penalty for taking him out?

It's an odd quirk of managerial strategy. Tim Lincecum would not have been in that game in the ninth (or eighth) inning if one of the walks that he had issued earlier in the game had been a hit. The score was 9-0. He would have gotten a pat on the back for seven strong innings and a trip to the showers. But Tim Lincecum was working on a shot at baseball immortality: the no-hitter. They don't make Sporcles for "guys who pitched seven innings and gave up one hit."

Had Bochy pulled Lincecum, even if every logical part of his brain said it was the right call, he never would have heard the end of it. Often, the explanation is that the pitcher would resent being deprived of his chance to finish off the feat. How often does any pitcher, even a good one, have a chance to approach that sort of moment? Maybe Lincecum would have sulked or for some reason taken it out on Bochy, and it would have affected his performance.

We don't know what would have happened if Bochy had given Lincecum the hook, and if he had, we might not have found out what happened in the clubhouse after. But in theory, we could design a study to look at whether pitchers pulled in the middle of a no-hit attempt show some dip in their performance afterward. The problem is that no-hitters that last even into the middle innings don't happen very often, and it's hard to get a decent enough sample size. So I decided to go for the closest thing that I could, the complete game shutout.

It's not a perfect analogy. You couldn't name everyone who's thrown a shutout this year. You could certainly list the no-hitters. There might be something special about a no-hitter (we'll talk about that in a bit) that a shutout doesn't have. But there are enough potential shutouts that happen each year that we can cobble together enough of a sample to take a look.

Warning! Gory Mathematical Details Ahead!
I found all cases from 2003-2012 in which a pitcher had made it to the end of the seventh inning and given up no runs, but had a pitch count over 95. (In this case, sending him out for another inning or two might give him a chance at a shutout, but it would also put him over the 100-pitch "limit" if he isn’t there already.) I did the same for the eighth inning. I coded whether the manager sent the pitcher back out for the eighth inning (or ninth, as the case might be). I wasn't concerned with whether the pitcher completed the shutout, merely whether his manager showed a willingness to break the rules a little for a guy who was approaching his own mini-milestone. If he loses the shutout, a pitcher might think, "That's on me." But if he loses it to the manager's hook, he might blame the manager for not trusting him.

I then looked at the pitcher's next start. And at his next five starts. And what he did for the rest of the season after that potential shutout. Using the standard log-odds ratio method for controlling for batter and pitcher quality (along with controls for current-game pitch count and platoon advantage), I plugged in the variable of whether or not the pitcher was allowed to continue in his quest for a shutout. Does that little feeling of trust (or seething, burning hatred about an opportunity stolen) have any effect on performance?

Nope. I looked at the decision after both the seventh and eighth innings. I looked over several time periods. I looked over a bunch of outcomes. There's no reason to believe that guys who are pulled out of a game, even though they were throwing a shutout through seven innings, perform better or worse than we might expect them to based on their seasonal stats.

Seeking a Peak
Let's first talk about what might happen in the clubhouse after the game. I'd caution anyone from making the leap from these findings to "Pitchers don't care if they're removed from a game when they are having a fantastic day." My guess is that most pitchers actually will feel a little miffed. But, not being fools, managers also realize that they might need to do a little damage control. A manager might call the pitcher in, give him an explanation of what happened, and build him up for the seven strong that he went. The pitcher might not leave completely satisfied, but hopefully he'd be okay with the explanation, and after some grumbling, he'd move on with life.

There might be other effects that we're not looking for. At contract time, the pitcher might remember that his silly manager mangled his one shot at glory based on some slavish adherence to pitch counts and decide that he doesn't want to sign. This might be a good thing, but a pitcher who is good enough to take a no-hitter into the seventh is more likely to be pretty good, and the kind of guy you hope might stick around. It’s also possible that the hook wouldn’t affect the pitcher himself, but his teammates (and players on other teams) could get the message that they won't get their shot at glory either.

And, as I hinted at earlier, a shutout is a poor analogy for a no-hitter. No-hitters are much more rare than are shutouts, but it's more than that. In about half of the cases where a pitcher took a shutout through the eighth inning, he did not go out for the ninth. No manager would ever do that for a no-hitter. It's because a no-hitter is what might be called a "peak experience." The psychologist Abraham Maslow suggested that human needs can be broken into five categories that must be met in order. There are basic needs like food and air, needs of stability and comfort, needs of companionship and belonging, needs of being thought well of by others, and finally, the ability to reach some peak experience. Some have interpreted Maslow's last stage in spiritual terms, that we are all seeking some greater connection with the universe, and maybe some people are.

I'd suggest that the idea of what constitutes a peak experience varies depending on what you're doing. For a bowler, it might be the last strike in a 300 game. For a world traveler, it might be getting to see the Taj Mahal in person. For a pitcher, short of a perfect game, what higher individual achievement is there than a no-hitter? (Please, spare me the lecture on how BABIP is random and the pitcher doesn't get dinged for the five walks he gave up… I know.) A shutout is a nice feather in the cap, but a no-hitter meets a basic human need for that one shining moment, and sometimes people (well, people other than Erik Bedard) do crazy and irrational things to get those types of places.

So we reach a philosophical question. While there doesn't seem to be much of a performance hangover from a huge pitch count, there might very well be an injury risk from throwing 140 pitches in a game. An injury will certainly affect a team more negatively than finishing up a no-hitter will help them, particularly if, as in Lincecum's game, it was 9-0 already. Finishing the no-hitter, assuming that even happens, will be a moment the pitcher remembers forever, although our imperfect evidence here suggests that there is nothing to be gained for the team from letting him do so. It's a classic individual vs. team situation.

Congratulations, Mr. Wannabe Manager. There is no correct answer. No matter what you choose to do, Twitter will eviscerate you. So, will you tell Lincecum to hit the showers or to stay warm for the ninth?

Thank you for reading

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Last year Johan Santana, not yet fully recovered from shoulder surgery, got a pseudo no-hitter (pseudo because an umpire called a clearly fair hit a foul ball). Manager Terry Collins let him destroy his own career, and the Mets's last two seasons, by keeping him a runaway ballgame to the very end. What's worse, Collins was entirely aware of his own stupidity!
Getting a no-hitter helps the team because there is more to baseball than wins and losses. Fans want a good experience, a chance to participate in something special. A pennant run is worth a lot even if you don't make it (unless you have a big lead and blow it, in which case it's a negative thing). No-hitters, All Star or Hone Run Derby appearances, hitting streaks, cone-from-behind or walk-off wins, and record-breaking or even near record-breaking performances all contribute to the value of the season for fans.

Sure it sucks when a star like Johan gets injured, but it's not like that performance changed the odds of injury from 0 to 1. The effect is relatively minor, statistically. The thing that would be interesting to look at it is if there's a measurable effect of these "irrelevant" events on things like ticket sales (that year and the next) or TV viewership, or team All Star votes, etc.
I'd like to know whether pulling the pitcher who's gone eight shutout innings and bringing in the 'proven closer' was (statistically) the right decision. Can you test for that?
Well, assuming that the game is close and the ninth really matters, would you rather have a really tired starter or a fresh and elite reliever in there. If it were a 2-hitter, there would be no question.
FWIW, Lincecum's next start against the Reds was horrible, but his 2nd start after the no hitter against the Cubs was pretty good, so maybe the rule based on miniscule sample size should be 'pull your pitcher unless his next start is against the Cubs'. On the other hand, Lincecum lost both games, so he might be seething anyway.