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December 26, 2013

Baseball Therapy

Rest an Extra Day to Keep the Doctor Away?

by Russell A. Carleton


Last time we met, we contemplated the curious case of the fifth starter. He is, somewhat by definition, worse than the other four guys who might otherwise be starting tonight’s game. Yet there he is, standing out there for the next 3 1/3 innings until he inevitably gets chased after giving up his sixth run. Why not just skip this exercise in futility and let the other (better) guys pitch the game? Last week, we saw that pitchers didn’t suffer much from going on three days’ rest. It was a high pitch count in his last outing that was a problem. If pitchers have, historically, performed just as well on three days’ rest as four, why is baseball so afraid to go back to the four-man rotation?

I’m a believer that if something exists in baseball, there must be a reason for it. It might not be a good reason, but there’s got to be something. Maybe it’s that the five-man rotation, while it does bleed away value in starts given to a glorified long reliever, is actually a hedge against injury.

A team’s ace starter in the standard five-man system makes about 34 starts a year. In a four-man rotation, he’d probably notch 40—assuming that he was healthy enough to finish out the season. Maybe teams went to a five-man rotation because of a simple cost-benefit analysis. Yes, you give starts to an inferior starter, but lowering the injury risk for the other four guys by not overworking them is worth it. We know that pitchers who threw a lot of pitches last year are at risk of being injured this year. So adding a fifth starter is, hypothetically, a way to hedge against injury risk for four separate spots on the roster. Could it be that the potential lost productivity from injuries is greater than the price of giving extra starts to no. 5 (and let’s be honest, nos. 6, 7, and 8)?

Warning! Gory Mathematical Details Ahead!
I want to look at this with the same historical perspective that I’ve been using over the past few weeks. While injury databases exist for the past decade or so, injury reports from the 1950s and ’60s are harder to come by. We’ll need a proxy. For all pitching appearances in a game from 1950-2012 (all of them), I calculated how many days came between them. For this one, I did not distinguish between appearances as a starter or in relief, so if a pitcher relieved on Tuesday, then started on Saturday, the database is aware that he had Wednesday, Thursday, and Friday to rest. For the first appearance of a season, I didn’t bother, because there are six agonizing months between the end of one regular season and the beginning of the next. I then excused all relief appearances from the data set.

I looked for cases in which a pitcher went 20 days or more without pitching in a big league game. At that point, we know it’s more than just skipping a start. However, to try to guard against guys who came up to make a spot start and then were sent back down, I required that he had started at least 50 games before I started looking at his data points. At that point, he’s established himself as a starter who’s good enough to get a season-and-a-half’s worth of starts.

Additionally, I looked for cases in which a pitcher’s last appearance came before the beginning of September (again, minimum 50 previous games started). Before you begin filling up the comments section with objections, let me make them all for you. We have no way of knowing that what happened was an injury. There are certain players who may have been doing just fine health-wise, but were demoted to the minors. There are some young players (Matt Harvey comes to mind) who suffered a major injury, but who would not appear in my sample. I am painfully aware that there are limitations of this method. If you don’t want to call them injuries, just call them “mysterious disappearances.”

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