The Costs and Benefits of Six-Man RotationsBen Clemenson January 13, 2021 at 3:50 pm

Planning a starting rotation for 2021 carries innumerable pitfalls. Nearly every pitcher in the league saw a reduced workload last year, and they did it in strange circumstances to boot. It’s not merely that the short season set everyone’s innings back — though that’s a huge component. A large number of cancelations and postponements also meant more doubleheaders and more cobbled-together games, another way to throw pitchers off their rhythm.

Put it all together, and protecting arms sounds like an appealing plan for 2021. The Mariners announced that they’ll use a six-man rotation next year, a continuation of the plan they leaned on for all of 2020. The Red Sox are talking workload management. Is an embiggened rotation the solution to this universal problem? Let’s do the math.

It depends, first of all, on what you give up. The innings tradeoff of a six-man rotation is straightforward. Giving your pitchers an extra day off limits their workloads, naturally enough. The math on that is straightforward if you assume it doesn’t affect their in-game workload. Take a pitcher who averages six innings per start. In a five-man rotation, that’s 192 innings of work. Adding a sixth pitcher to the rotation cuts that down to 162 innings.

How much do those 30 innings of work matter when it comes to health? I’ll level with you — I’m not sure. We simply don’t have the data to say with any amount of certainty, because the number of comparable situations is so small. Pitchers have light workloads all the time, but in most cases it’s due to age or injury. Looking at what a 21-year-old pitcher did in first building up stamina probably can’t tell us much about how many innings Jake Odorizzi, to pick a random example, should throw in 2021. Likewise, a pitcher’s workload in his first year back from Tommy John surgery can’t tell us how many innings Trevor Bauer can be effective for.

We do have a few points that we could look at for a natural experiment. The ‘94 strike depressed every pitcher’s workload, injured or not. The problem, here, is that due to the length of the pre-strike season, no healthy pitchers added innings in the way we expect to see this year. Heck, Greg Maddux threw 202 innings in 1994. He threw 209.2 the next year. Lance Lynn led baseball with 84 innings pitched last year, and we project him for 191 in 2021. The increase in workload isn’t comparable.

The same problem exists for the 1981 season. To make matters worse, pitcher workloads barely resembled today. In 1982, 50 pitchers threw 200 or more innings. In 2019, only 15 hit that threshold. Speculating on what will happen to modern pitchers based on what happened to Charlie Hough in the 80s hardly seems like a productive approach.

Fine, then: we won’t assume any benefit, at least from a performance perspective, from adding an extra pitcher to the mix. That doesn’t mean there’s no benefit at all, however. An extra day of rest gives pitchers more time to recover between starts. Assuming no benefit from that rest doesn’t make much sense to me.

To approximate this effect, I looked at the number of days of rest between each start made in baseball this year. I threw out starts made on three days’ rest (there were only 14) and starts made on seven or more days of rest — those aren’t rotation- or schedule-based. That left me with 1,291 starts to look at.

You might think that the right thing to do is simply look at league ERA on four, five, and six days’ rest. You’d be wrong, though, due to population effects. Pitching on standard rest — or getting an extra day to recover — isn’t a decision that teams make at random. They have motives, and those motives depend on the identity of the pitcher. Getting an ace an extra turn makes sense. Using a bad pitcher as infrequently as possible makes sense. If you ignore this distributional effect, you’re liable to end up with a confusing answer.

Instead, I focused on how each pitcher fared relative to their seasonal line. I focused on xFIP, since we’re looking at noisy individual game lines, and compared starts on each relevant amount of rest to a pitcher’s overall seasonal line. In other words, if a pitcher had a 4.50 xFIP overall, a 4.60 xFIP on regular rest, and a 4.40 xFIP on five days’ rest, we’d say that four days’ rest increases his xFIP by 0.1 while five days’ rest decreases it by 0.1, an overall difference of 0.2 runs.

The numbers don’t need to be exactly symmetrical like that example, of course. Pitchers don’t make an equal number of starts with each type of rest, and they also don’t pitch an equal number of innings per start in each case. The overall point, however, is that extra days of rest seem to have a small but beneficial effect on pitchers’ results. For each extra day of rest, their xFIP improves, relative to their seasonal average, by roughly 0.06.

I won’t claim that this effect is obvious and incontrovertible. It’s tiny, below the threshold of statistical significance. Break it down into strikeouts and walks, and it’s even smaller; an extra day of rest is associated with a 0.3 percentage point increase in strikeout rate but also a 0.15 percentage point increase in walk rate.

In other words, the extra day of rest doesn’t appear to be worth that much. If you take my math at face value and assume that all previous starts were on regular rest — a poor and lazy assumption that I’m absolutely going to make for the sake of time — that works out to something like 6.5 runs over the entire season. Though I’m tired of saying it, I still will — I have very little confidence in this number. As a ballpark guess, however — and pun very much intended, I have a reputation to uphold — I think it gets the job done.

Okay, so teams can get an indeterminate injury benefit and also maybe save 6.5 runs by going to a six-man rotation. Let’s talk cost. The cost is clear: your top five starters all throw roughly 30 fewer innings, and those innings get replaced by your sixth-best starter. Sorry, Max Scherzer, but it’s Austin Voth’s turn to shine, and so on.

The cost of this downgrade varies by team. It depends on two things: the average quality of your existing rotation and the quality of your sixth starter. To approximate this cost, I took Depth Charts projections for every team in baseball and then calculated the existing rotation’s average projected ERA and the sixth-best starter’s projected ERA. The difference between those two numbers, over the 150 innings we’re granting our sixth starter in this scenario, will be each team’s cost of going to six starters.

Take the Royals, for example. Their best five starters — Brady Singer, Mike Minor, Kris Bubic, Brad Keller, and Danny Duffy — project for an average 4.70 ERA. Their prospective sixth starter, Jakob Junis, projects for a 4.87 ERA. That difference, expressed over 150 innings, is worth roughly three runs. Per my admittedly hazy math, the Royals might be better off with a six-man rotation even before considering the injury benefits.

With the caveat that all of this is ridiculous fantasy-land math that I did on the back of a not-particularly-large envelope, here’s how many more runs each team should expect to allow if they go to a six-man rotation next year:

You might notice that the Rockies don’t appear on this list. That’s because if you asked me to project their sixth starter, I’d mutter “Hey what’s that behind you?” then run away when you turned to look. They obviously have someone detailed for that job, but I don’t find assigning it to any specific player particularly meaningful.

Do you want a solid takeaway from this article? Tough luck. Some of these teams could easily shift to using a sixth starter. Some would need to give up a little more. In no case is it a massive effect, depending on how you define the word “massive” — even the top-heavy Padres would only cost themselves 15 runs (roughly 1.5 wins) by adding a sixth starter, and that’s if there’s no benefit from an extra day of rest.

Will more teams shift to six-man rotations? I think so. It’s prudent — pitcher health is tenuous in the best of times, and while I’m certainly no biomechanical expert, extra rest meaning extra health hardly seems farfetched. It might help, performance-wise — teams probably have better data on this than I do. It’s cheap, runs-wise — thinning out the rotation is a matter of single-digit runs over an entire season for most teams. Weigh those three factors, and I don’t think Seattle will be the only team using this plan.
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