Over the last few weeks, I’ve been trying to answer a question. Fifty years ago, it was routine for teams to carry only four starters, and for those four starters to complete a good chunk of their games. Pitching on three days’ rest was common, and pitchers regularly posted pitch counts that would get a manager fired today if he let it happen once. What happened?

Well, we know that the dip in pitch counts has been slow and gradual but fairly consistent over time, and that managers have developed a quicker hook because a fresh reliever is better than a tiring starter. The four-man rotation began to disappear in the mid-1970s, and by the 1990s, pitching on three days had mostly been eradicated. (The evidence suggests that it was not actually necessary to do this, but that now that pitchers have been trained in the “every four days” ecosystem, when they try to go on three days’ rest, it’s a risk factor for injury.) At the end of the last article, I wondered whether there was another factor at work. Perhaps the reason that pitchers have been switched to four days of rest is that teams saw that pitchers who had particular skills needed more rest, but that these skills were valuable enough (and abundant enough) to warrant the tradeoff.

There have been two major trends in pitching over the past few decades that are worth noting. One is that strikeout rates have increased sharply in the past 20 years. In 1993, pitchers struck out 5.8 batters per nine innings. In 2013, that number was up to 7.6 per nine innings. The other trend in pitching, also peaking around the same time, is that pitchers are getting bigger. Here’s a graph of the body-mass index of starters (more than half of their appearances as starts) of all pitchers in MLB for each year. Body-mass index (BMI), for the uninitiated, is a ratio of weight to height—actually, height squared—that is a standard measure of whether someone carrying too much weight, medically. BMI is widely used in medical and public health research. Scores under 19 and over 25 (sometimes 26) are associated with an increased risk for health problems.

The average BMI for a starter (relievers had the same basic graph) went from the mid-24s from 1950 until the mid-1990s, and then rose sharply. This is a pattern that’s also been observed among position players. For what it’s worth, I’m using the players’ listed (which, um, could be a lie) height and weight in the Lahman database, meaning that the player maintains that listed height and weight for the entirety of his career. Having personally been both 24 and 34—let’s just say that’s not always the case. But I think the point comes across.

Oddly enough, the trends toward bigger pitchers and higher strikeout rates do not seem to be one and the same. We don’t have velocity data back into the 1950s, but bigger pitchers generally throw harder. However, BMI and strikeout rate for each pitcher-year from 2000 to 2012 were completely uncorrelated (r = .006). There were also small correlations between BMI and walk rate (r = .127) and HR rate (r = -.097). Bigger pitchers aren’t necessarily better pitchers. But perhaps bigger pitchers are slower to recover from pitching and need an extra day of rest?

Warning! Gory Mathematical Details Ahead!
Once again, I looked at the seven basic outcomes of a plate appearance (strikeout, walk, HBP, single, double/triple, HR, or out in play), and used the logged odds ratio method to generate an estimate of the chances that a given hitter/pitcher matchup would end up in each of those, using that as a control variable in all regressions. Only plate appearances in which a hitter with at least 250 PA in that season faced a pitcher with at least 250 PA in that season were considered, and the pitcher had to be that day’s starter.

I created a series of binary logistic equations predicting each of the seven outcomes using the following predictors: the logged odds ratio control from above, the pitcher’s BMI, the number of pitches he threw last time out (using the estimate formula I developed), and a binary indicator of whether this start was on three (or fewer) days of rest. I also included the interaction between the pitcher’s BMI and his pitch count from last time, and the interaction of BMI and the three days’ rest variable. These two interaction variables are the key. If they are significant, it means that BMI affects how good a pitcher is at bouncing back from a high pitch count or how good he is at going on three days’ rest.

The results? There were no significant interaction terms. I re-ran the same analyses, this time using only data from a couple of different decades (the ’60s and the ’00s) to check for any era effects, and got the same results. There are hangover effects from throwing a lot of pitches, but they do not vary based on BMI.

So maybe it’s not the size that counts, but how you use it. Maybe it’s high-strikeout pitchers who have the recovery magic. I re-ran the above analyses swapping out the pitcher’s seasonal strikeout rate for BMI. It turns out that there are effects for high-strikeout pitchers. Some of them are only marginally significant (p > .10), but high-strikeout pitchers are actually better able to bounce back on three days of rest, with desirable effects seen for strikeouts, walks, and outs in play. When I isolated this by decade, the significance levels varied some, but the arrow was always pointing in the direction of high-strikeout pitchers not suffering as much on three days’ rest. There were also some desirable effects for high-strikeout pitchers not being as affected by coming off of a high pitch count in the start before. At the very least, the new breed of high-strikeout pitcher shouldn’t be better or worse on three days’ rest than we would otherwise expect of him. (We know from previous work that results on three days’ rest are actually rather similar to those on four.) There is (tentative) evidence that he even has an advantage over a low-strikeout pitcher.

Okay, so maybe the move away from the four-man rotation wasn't due to concerns about bigger pitchers being able to hold their performance. Instead, maybe it was concern over injuries. To test that, I used methodology similar to last week's work, using a Cox regression to model when a starter would sustain his first injury. Similar to last week, I included the estimated number of pitches the starter had thrown to date that season, the number of times he had gone on three days’ rest, and the number of times he had thrown more than 120 pitches in a start. I included BMI in the model, and then the interaction of BMI and the other three variables. The model also included the number of pitches that the pitcher threw in the previous year. As with last week, I looked only at pitchers who had made at least 50 starts in MLB.

Once again, the key variables are the interaction terms. If bigger (or smaller) pitchers are more (or less) likely to sustain an injury because of one of these three issues, the interaction term will tell us. The results were that pitchers with a higher BMI were generally no more or less likely to be affected by these issues, and in some cases, having a high BMI was slightly protective. There's still injury risk from throwing high-pitch-count games, but it is slightly reduced for big guys. The same basic findings show up when I substitute strikeout rate for BMI.

What’s entirely clear is that the move toward bigger pitchers and higher-strikeout pitchers and the move from a four-man to a five-man rotation do not appear connected. If we learned nothing else, we learned that these bigger whiff-machines aren’t any worse off than thinner, pitch-to-contact guys, and may actually have an advantage over them in bouncing back on shorter rest. Teams have been trending toward the very pitchers who would do better in a four-man rotation, yet at the same time, moving away from a four-man rotation. What gives?

What Does Your Appendix Have to Do with It?
The five-man rotation exists. Right now, your favorite team’s front office is obsessing over finding five men who will stand on the mound, each taking his appointed turn on the merry-go-round. It’s not that this is a written rule of the game. It just developed that way. Over the past few weeks, I’ve looked for an empirical reason to justify why teams use a five-man rotation of starters, other than the fact that… well, we’ve always been at war with Eurasia (a billion points for your junior year English class for that reference).

There’s evidence to suggest that pitchers do not perform worse (or better) on three days’ rest than four. There’s evidence that back when pitching on three days’ rest was common, injuries were no more common among pitchers who commonly threw on three days’ rest. (However, this is no longer the case.) Here we see that the bigger, more strikeout-getting type of pitchers who have been preferred over the past 20 years are the types of pitchers who would actually fare best in a four-man system. Why do bad starters get 34 chances to take the mound each year when someone better is available?

In fairness, maybe there’s a hidden variable. There could be some biomechanical issue for which I’m not accounting, or maybe I’m just looking in the wrong place. I can appreciate that the entire baseball eco-system, including training regimens, roster structure, and even what pitchers expect to be doing has developed around the idea of a five-man rotation, and now, it might be that there’s no infrastructure to develop pitchers who can go every three days, stay healthy, and be effective. The thing is that it wasn’t always like this, and from what I can tell, there’s no reason—at least philosophically—that it couldn’t be that way again.

One theory I’ve seen (in the comments section of one of the previous articles) was that the change in pitcher workloads started in the 1970s, because of free agency. Because teams now faced the reality of having to pay players market salaries, they got more protective of their investments. Maybe they’ve gotten too protective, or at least they’ve been using the wrong techniques. Even in the heyday of three days’ rest (the 1970s), the majority of starts were actually made on more than three days of rest. Pitchers would have had experience with both three and four days of rest, and may have preferred getting a fourth day. At the time, quantitative analysis of these sorts of things was not very advanced. In the absence of proper evidence, it’s easy to imagine teams making the mistake that if a little bit of something is good, a lot of it must be better.

Everything that exists does so for some reason, but not everything exists for a good reason. If the answer is that teams went to a five-man rotation based on faulty reasoning and then it just kinda stuck around, then the five-man rotation is not tradition. It’s just really old faulty reasoning that an ecosystem has developed around. The human appendix exists for a similar reason. It once served a purpose, but no longer does. Yet, there’s been no move on the part of human evolution to get rid of it, so occasionally, Jason Heyward has to miss two weeks because his got infected and he had to have it taken out. So I leave you with a question. Is it time to do an appendectomy on the five-man rotation, or to simply leave it in, figuring that it would do more harm than good to take it out?