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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. 
Click here to see Russell's other articles. You can contact Russell by clicking here

Related Content:  Four-man Rotation,  Pitching

28 comments have been left for this article. (Click to hide comments)

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1) Playoffs. For a good team, the value of Ace innings during the year diminished relative to Aces being healthy at year-end.

2) Advanced training and re-structuring of minor leagues. During the early 1980s, teams began developing super teams at AA by not advancing their best prospects to AAA leading to the structure we now see: best prospects jump from AA to MLB while AAA is show-ready depth. Thus a switch away from swing-men to full-time SPs available with just a short flight. More SPs became available and using a 5th starter did not impact the bullpen.

Dec 16, 2013 09:53 AM
rating: 0

Re: Playoffs: Let's say that Russell's hypothesis is true and teams are leaving a couple wins on the table by choosing a 5-man rotation. You'd have to balance the odds of making the playoffs against your odds of success in the playoffs (assuming the 4-man negatively impacts October health).

The economics of baseball dictate that small-market teams have to gamble to win. It's possible that the 4-man rotation is both superior to (better average result) and more risky than (higher variance due to injury) the 5-man rotation. The underdog should embrace that role.

Dec 16, 2013 13:01 PM
rating: 1

When the trend to a five-man rotation began, Bill James gave a good analysis -- you are taking eight starts from your best starter, eight from your second-best, eight from your third and eight from your fourth and giving them to your fifth-best starter. Your payoff better be obvious if you are doing that and I don't think it is.

The Dodgers in 1966 had a four-man rotation (Koufax, Drysdale, Osteen and Sutton) that started 154 of 162 games, with reliever Joe Moeller picking up the other eight -- mostly during or around doubleheaders.

Dec 16, 2013 10:08 AM
rating: 0

Starters should LT4 just as we pledged at Kairos. Five starters is an abomination that is born of fear plain and simple. Some day a smart team run by men free of fear will develop starters in the minors who pitch on three days rest. Then they will promote those starters to the big leagues and run roughshod over their competitors who are paralyzed by the fear of going against the accepted practice.

Dec 16, 2013 10:47 AM
rating: 4
BP staff member Russell A. Carleton
BP staff

One billion points!

Dec 16, 2013 13:11 PM

Another advantage to the four man rotation is that if the starters leave earlier, you have more relievers and relief options. The worst relievers in the bullpen are less of a problem than a 5th starter because the relievers can be relegated to low leverage situations allowing the better relievers to pitch with higher leverage.

Dec 16, 2013 11:43 AM
rating: 2
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it's only the sanctified union and the horrendous quality-diminishing expansion that created the "need" for expanded starting staffs; the stuff you see "explaining" the changes is comical, needed only by statheads trying to justify what they see as expertise

Dec 16, 2013 11:45 AM
rating: -8

MLBPA requires "short rest" for pitchers? Did they say something to Colorado?

Dec 16, 2013 12:06 PM
rating: 2

While we're at it, expansion means there are nearly double the number of major league players as pre-1960. Not only has the US population nearly doubled, but major league players are being drawn from far more of the world - the major Latin American nations supplying players and Japan mean the actual pool of talent is three or four times larger than in 1960 (depending on exactly how you count it). None of this accounts, either, for racial integration - started a decade before expansion but both leagues as a whole only because integrated after 1960. Overall, simple odds of making a major league roster (number of players over population drawn from) are much lower now than pre-expansion.

Dec 16, 2013 16:24 PM
rating: 7

You mean the odds are much lower for white guys, right?

Dec 16, 2013 22:00 PM
rating: 1

I mean that, based simply on the statistical odds, you have to be a better player now than pre-expansion, to make the major leagues. That's what I said. If this calls into question whether they were in fact the "major leagues" when only white guys played in them, good, I'm for that.

Dec 17, 2013 13:35 PM
rating: 0

I know this is not statistical but what about interviewing managers GMs and pitching coaches from the late 70s early 80s to ask them why? Some are still aroynd.

Dec 16, 2013 12:17 PM
rating: 3

Old Hoss Radbourn is still clamoring for the one-man rotation.

Dec 16, 2013 12:29 PM
rating: 6

Aside from the (more important) quality issue:
Would a four-man rotation yield a cost savings? On one hand, "#5 starters" command more money than a swingman would. On the other, signing guys as your #1-#4 will probably cost you more because of (real or perceived) increased risk of injury.

Dec 16, 2013 12:53 PM
rating: 1

As a Rockies fan who thoroughly supported the ideas behind the 4 man rotation (just not the haphazard implementation and terrible pitching candidates), I'm glad to see some data to support this conclusion.

Nice work, Russell! Thank you for your work!

Dec 16, 2013 14:38 PM
rating: 2

The Rockies management was uniformly excoriated for trying the 4-man rotation and tandem starter approach. The staff was in shambles, the team was in last place going nowhere in June when the Rox announced this experiment. Paper, local TV, ESPN, and MLB Network pundits all declared it insanity.

What was true insanity was continuing doing what they were doing and expecting better results. Finally management caved to the pressure.

I gave them props for trying something, ANYTHING, so as to try to learn how to cope with the unique aspects of pitching in Coors Field.

I still think it would work, particularly for a mid-market, cost-constrained team like Colorado, especially if they committed to it down through the minors.

Dec 16, 2013 15:18 PM
rating: 1

Not to nitpick, I just want to make sure I understand the first graph:

"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."

It looks to me as if it fluctuated from a little over 20 percent of the time to a little under 40 at the highest. Is that wrong?

Dec 16, 2013 17:19 PM
rating: 3

This is what I think as well. The number of teams that had four quality starters was very low. The caveat being that they tended to win, maybe where 'pitching wins pennants' comes from. Spend a little time looking at team stats from t945-60 or the 30's and you see that the scarcity of quality pitching is about the same as today if not worse.

If anything, I think that the evolution of bullpen usage looks downright efficient considering the numbers. I would say that there are a lot of factors at work here: pitchers throw harder, strikeouts are valued more, fielding is far more efficient, 3 true outcomes are the focus on both sides of the ball, better athletes in general.

But to support the argument for a four man rotation, we now uniformly have the bullpen depth to support it. Plus it would/could return a position player to the bench. Another thing to consider is that most teams run a de facto 4 man rotation as you discuss the first 6 - 7 weeks of the season.

Thanks for the thinking points Russell!

Dec 16, 2013 20:55 PM
rating: 0
BP staff member Russell A. Carleton
BP staff

You're right... I started writing one sentence and then finished another. It's high 20s early on, peaking around 40% in the 70s, and then falls from there.

Dec 17, 2013 13:52 PM

So you'd still need to give away 15 starts or so to other guys to stay at 50's/60's frequency with today's schedule. (I think). Which is sort of a 4.5 man rotation.

Dec 17, 2013 15:13 PM
rating: 0
Lloyd Cole

Wonderful work.

Dec 16, 2013 19:28 PM
rating: 0

Back further in history teams had "Sunday" starters. Why not now? I'm old enough to remember 4 man rotations. Saved a lot of crappy starts thats for sure.

Dec 16, 2013 19:52 PM
rating: 1

What's the possibility that the Sunday starter is the equivalent of a designated driver? He allowed all the other boys to be boys Saturday night wherever they were. I believe Mike Marshall proved pretty well relieving for the Dodgers that more work does not equate to poorer results. I think more starts for the four best would be more efficient than using a sub-standard fifth.

Dec 16, 2013 21:55 PM
rating: 0

To be fair citing one outstanding rleiever or 1 group of 4 starters doesn't prove much. It's tantamount to aksing why everyone isn't Nolan Ryan.

That said I don't see why this couldn't work more often than not.

Also makes me wonder - though I'd say this is likely impossible - if average starter velocity could be plotted besides the average starts graph that kicked off here. Data isn't available back then but i'd guess some serious inverse proportionality that might be a variable.

Dec 17, 2013 16:37 PM
rating: 0

How different was the schedule back before the shift? If 4-man rotations were the norm, then why does the percentage of short-rest starts drift between 20 and 40 in the 50s-early 70s? I mean, there's still a clear transition in how often teams start a guy on short rest, but I'd expect to see percentages closer to 70 or 80 if a team stuck to a 4-man rotation today. Or does the data include so many pitchers who made only a few spot starts? I wonder what it would look like if you restricted it to pitchers who made at least 10 starts in a season.

Also, the injury/fatigue point of view seems like an important one. If the consensus favored the idea that a pitcher who threw more than 200 innings (or whatever number) in a year was more likely to get hurt that year or the next, then that would be a good reason to sacrifice a win to keep your ace healthy. Same with fatigue - the stats on how pitchers did on 3 days rest based on how many previous starts with 3 days rest they'd had that season are interesting, but I have two questions:

1) How did you calculate pitcher success based on # of three-day-rest starts? I assume that it was relative to the pitcher's own baselines for the year in a similar way to the overall analysis (in other words it isn't simply an effect of better pitchers getting more starts). If so, it seems pretty meaningful that there would be enough pitchers who did better on short rest to create that trend.
2) What does it look like if you do the same analysis, but using # of total starts? In other words, do pitchers wear down after a certain point and thus it is actually worthwhile to "keep them fresh" for the post-season?

Dec 17, 2013 07:57 AM
rating: 2

Interesting point about the schedule, I was wondering about that myself. Looking at a sample size of one schedule (namely the Yankees in 2013), a strict 4-man rotation would have led to 60% of the games being pitched on short rest. Below your estimate, but way higher than the '50s-'70s rate.

To get that number down to that 20%-40% range (and save your pitchers from going on 2 days' rest after double-headers) you'd need to give at least 12 starts or so to someone else. There are already teams that don't have five pitchers make that many starts.

Obviously that's all in a fantasy world in which you can make it through the season without an injury. Still, it makes it look a little murkier. The difference between having a four-man rotation which you supplement with an occasional spot starter and a five-man rotation which you strengthen by skipping the fifth guy every now and then isn't all that clear cut.

Either way, you could lean on your top four harder than they do now, but you couldn't really rely on just four starters without sending them out on short rest way more often than has been done in the past.

Dec 17, 2013 15:09 PM
rating: 0

3) Free agency, long term contracts and Sandy Kofax. Pre 1975, the end of a pitcher's career was the pitcher's worry. The timing can't be totally coincidental: Messersmith/McNally was before the 1976 season. Much of the drop in 1967 had to be Kofax directly, and indirectly new team worries after the Dodgers lost such an asset. Just a few years later the trend kicks in for good (but see below). Teams became worried about long-term losses to their pitchers.

4) Evolution of pitch selection. Post Kofax, pitchers began using pitches that are much harder on the arm, sliders, high torque hard curves, the splitter.

I wonder how much of the mid-1970s peak is Wilbur Wood. His knuckle-balling 45+ starts per year at least partially hides what would otherwise be a decline in 3-day rests that began when Kofax announced his retirement.

Major changes in both the economics of the game and the mechanics of pitching came at the same time as the changes in rotations. I don't think you'll find the answer in a short-term manager's viewpoint, it is more in the longer-term GM's veiwpoint.

Dec 17, 2013 23:06 PM
rating: 2

excellent article. Interesting that pitching every third day doesn't seem to stress the pitcher the same way that high pitch counts on the day he does pitch. This makes sense, as pitchers suffering from fatigue are more likely to make mechanical errors that result in walks, hard-hit pitches, and in the rare extreme, injury. I remember the Braves in the late nineties/early double-oughts, bucked the trend and only used the fifth starter when double headers or lack of off days made it "necessary". Perhaps that fifth starter should be kept on a starter regimen and brought in on in the fifth or sixth inning of the fourth starters start to finish the game. Each pitcher would only pitch 4-5 innings so they wouldn't need to face batters a third and fourth time (when they do the worst damage). You would get the best out of your two fringe starters, get a better pitcher on the mound for later innings than your middlemen, and provide a rest for the bullpen that "the Ace" used to give you but doesn't anymore thanks to the death of the complete game.

Dec 18, 2013 06:55 AM
rating: 0
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