December 16, 2013

Baseball Therapy

What Happened to the Four-Man Rotation?

by Russell A. Carleton

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Lately, I’ve been wondering about the development of the modern pitching staff. I’ve looked at how we got to the point where no one completes a game anymore and why pitch counts have fallen over the years. Here’s another. What happened to the four-man starting rotation? It used to be that a team had four starters, each of whom pitched on three days’ rest…or so the story goes. There were always days off and travel days, and then there were doubleheaders, so there were swingmen who picked up the occasional start. While we can’t yet be sure what happened, we at least have an idea of when it happened. Here’s a chart showing the percentage of starts featuring a pitcher who was on three days of rest (or fewer) from 1950 to 2012.

We see that in the 1950s and ’60s, pitchers were going on what is now considered “short” rest more than 40 percent of the time. In 1975, the rates began a rather quick decline and have reached the point where it’s a news story when a pitcher is going on three days’ rest. A five-man rotation (occasionally six) is now the norm.

Not only that, but using the pitch estimator that I constructed a couple of weeks ago, I looked at the number of (estimated) pitches that the pitcher threw in the start before this one, based on whether the start took place with four calendar days’ rest (or more) vs. three calendar days’ rest (or less). While in recent years, pitchers—on the rare occasions that they do pitch on three days’ rest—are more likely to do so only after a short outing, that wasn’t always the case. Before 1975, the lines are essentially running parallel. It used to be that pitching on three days’ rest was just something you did. Now, it’s something that you do only when necessary.

We know what happened. We know when it started happening. Why did it happen?

Warning! Gory Mathematical Details Ahead!
One hypothesis is that teams discovered that three days of rest wasn’t enough, and that pitchers seemed to do better when they had an extra day of rest due to an off-day or a rainout. I took all starts from 1950 to 2012, and found how many days had elapsed since the last start. I recoded that into a simple yes/no of whether the pitcher had three (or two or one!) days of rest or whether he had four or more days of rest.

To test that, I constructed a series of longitudinal regressions predicting whether a plate appearance ended in one of several outcomes (strikeout, walk, HBP, single, double/triple, home run, or out on a ball in play). I used the log-odds method to control for the batter, pitcher, and league rates as I have done in previous work. Only plate appearances featuring a batter who had 250 PA or more that season facing off against a pitcher who was starting in that game and had faced 250 PA in that season were considered.

On top of the control variable, I entered whether the start was made on “short” rest (i.e., three days or fewer), the number of (estimated) pitches that the pitcher made in the game before, and the interaction of those two numbers. This will give us some idea of whether the mere fact of going on three days’ rest had an effect, or whether pitching on three days’ rest is harder (or easier) for a pitcher if he’s recovering from a higher pitch count outing rather than a shorter one.

The results were that rest had little effect on any of the outcomes. The performance of a pitcher on three days of rest was consistent with what we would have expected of him based on his overall season stats and those of the batter whom he faced. Now, we have a nice little natural experiment here as well. I split the data set by decades (50s, 60s, 70s, 80s, 90s, and 2000-12). In the earlier decades, three days’ rest was common. In the 1970s and 1980s, that began shifting. Now, it’s very rare. It’s very possible that in earlier years, pitchers trained differently or set up their regimens in ways that were more conducive to pitching on three days’ rest. (It would make sense that they did.)

Surprisingly, though, the results came out the same. There was no indication that pitchers did better or worse based on how many days of rest they got. What was significant was the number of pitches that the pitcher had thrown in his previous start. Longer outings made for slightly less effective pitchers (more walks, more hits, fewer outs in play). It’s something we’ve seen before. Using more modern data, I found that a pitcher who threw 140 pitches might expect to perform slightly worse than expected in his next start, and that the effect was gone by the second start.

However, this model is aware only of when the pitcher’s last appearance was. Maybe there’s a cumulative effect—you can get away with having a pitcher throw on three days’ rest once, but over time it slowly wears him down. For each start, I coded how many times during the current season the pitcher had appeared on three days’ rest or fewer. This way, if there’s an attrition rate over time, we’ll see it. I added that to the model above and let it run. It turns out that what effects were present were actually in the direction of pitchers getting better as the season goes on as they pick up more starts on short rest. Here we should probably note that this might actually be managers using their manager-y smarts to correctly identify pitchers who actually get stronger on short rest (or don’t get worse.)

The evidence suggests that pitching on three days of rest does not sap a pitcher of any of his abilities. Throwing a lot of pitches in his previous start does. The finding holds whether you’re looking at an era where three days’ rest was the rule or the exception. So, why have we added a fifth—presumably worse than the other four—starter when one isn’t needed?

Maybe it’s the fact that managers started noticing that swingmen did well enough when they made their starts. In that case, why not slot them into the rotation to keep the other guys fresh? To test that hypothesis, I looked at all pitchers in MLB from 1950-2012 (same time frame) for whom 50 percent or more of their appearances came as starters. I lined them all up by the number of starts that they made over the course of the season. For the year 2012, I took the 30 pitchers who made the most starts (because there were 30 teams) and grouped them as the no. 1 starter group. I took the next 30 pitchers, again by games started, and made them the no. 2 group, and on down to no. 5. Anyone past that, I grouped into a slush bin. I looked at ERA for each group over time. (I re-ran it with RA9 and got the same basic findings.)

Here’s a comparison, over time, of how the no. 1 group, the no. 4 group, and the no. 5 group have performed over time.

We see that fourth and fifth starters have grown to be fairly close to one another in their performances, which is nice, but the real story is the distance from the red line representing the no. 5 starter group and the blue line representing the no. 1 starter group. In general, it’s about a run apart per nine innings. One of the most common critiques of the fifth starter is that he steals innings that theoretically should have gone to the team’s actually good starters (and Rany Jazayerli was making it in 2002, so it’s not like we just figured it out). The graph shows that over 160 innings, 40 of which would have gone to the team’s ace, the fifth starter would bleed away four and a half runs of value. And that’s just the innings he takes away from the ace. There’s no evidence that over time, fifth starters have done anything noteworthy to justify their inclusion in the rotation. There’s no evidence that they make the other pitchers better by giving them more rest, and they probably delete a win or so of value over the course of a season because they just aren’t as good.

On the Fourth Day…
What is keeping pitchers from living the fourth? (A billion points for that reference!) Strictly from a performance point of view, there is little evidence that pitching on three days of rest ever made them pitch less effectively, and it may have even helped a bit. So, if your ace is good to go, why not let him pitch?

There is evidence that high pitch counts have a negative effect on a pitcher in his next time out. So, while pitchers might be okay to go every fourth day, we do still need to worry about pitch counts. It’s strange, because the two movements toward being more protective of pitchers—lower pitch counts and longer rest periods—appear to be yoked together. There’s an assumption that we need to do both for maximum performance. The data do not back that up. In fact, the Rockies’ recent experiment with a four-man, 75-pitch rotation might be the most empirically grounded approach to starting pitching that’s been tried of late.

We know that the fifth starter exists, but so far, it’s not entirely clear why. There is one other possibility that we will discuss next time. We do know that piling up a lot of pitches is a risk factor for injury. One nice effect of a fifth starter is that it keeps pitch counts for the other four artificially low. Perhaps the real reason that teams employ a fifth starter is fear of injury.

Russell A. Carleton is an author of Baseball Prospectus. Follow @pizzacutter4
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