Carlos Martínez Epitomizes Contextual Value, and Other Business School Buzzwords

In recent years, moving a middling starter to relief and discovering a stud has become something of a baseball trope. Spare Andrew Miller or Drew Pomeranz on your hands? Chuck them in the bullpen and they’ll improve. Wade Davis doesn’t thrill you as a starter? Let him relieve and he’ll add velo and win you a World Series.

Of course, this doesn’t mean that we should simply make every starter a reliever. The gains you would get from making Max Scherzer a reliever (An even higher strikeout rate! Even more velo! Even more grunts!) don’t come close to the losses in innings pitched. When you have a great pitcher, it’s key to give them as much playing time as possible, even at the cost of efficiency. Reliever Scherzer might be untouchable, but then you get 60 innings of him and 150 innings of starts from Joe Triple-A.

This logic brings us, unerringly, to Carlos Martínez. Martínez is an excellent test case for the boundaries of starter-to-reliever conversions. As a reliever, he’s been spectacular — he had a 3.17 ERA, 2.86 FIP, and sparkling strikeout and walk numbers out of the bullpen in 2019, and was similarly good there in 2018. At the same time, he’s an above average starter. He boasts a career 3.36 ERA (and 3.61 FIP) in the rotation.

So where should the Cardinals use him? There’s some chance the decision is made for them — in 2019, he started the season on the Injured List and the team prioritized getting him back to the majors over getting him stretched out for starting. But in 2020, it will come down to a philosophical question: would you prefer an effective starter or a phenomenal reliever?

The reason our brains know without hesitation that borderline starters make good conversion candidates while moving Scherzer makes no sense is an intuitive application of marginal value. The value of a bullpen conversion comes down to two things: how much run prevention the pitcher provides relative to the next available pitcher in each role, and how many innings they can pitch in that role.

Consider a team where the fourth-, fifth-, and sixth-best starters are nearly equivalent in skill. There’s little marginal value to be gained by swapping those starts around; you could get roughly the same production by starting the three in any combination. Now assume that one of them is best suited for a relief conversion:

This decision is a no-brainer; move Pitcher A to relief. We can look at the math of it to confirm, but the outcome is intuitive:

I made it so that Pitchers B and C are also replacement level as relievers, but even if they weren’t, Pitcher A provides the most surplus there.

So what stops us from converting every player like Pitcher A, who is phenomenally better in relief? Let’s look at a slightly different scenario. Pitcher A and B are now both better, 4.50 ERA pitchers in expectation. A is still better in relief:

But now the replacement level calculations start to move. The bullpen replacement level is still the same; after all, we know that Pitcher C can provide replacement level innings in either role. Assuming 150 innings as a starter or 60 as a reliever, now what we do with Pitcher A gets tricky:

The same talent differential is still there — A gets much better as a reliever, while B and C don’t get the same boost. But there’s a new effect. It’s more important to maximize the innings from your best players, and now A saves 8.3 runs relative to the next man up in either role.

Make A and B better still, and the math flips:

Despite the same improvement from starting to relieving, the decision is now clear. It’s more important to max out playing time from Pitcher A, even if that means using him in his less “optimal” role.

If you want to flip the math back, we need only reach the playoffs, where replacement level changes. There are no fifth starters in the playoffs, no back end of the bullpen. Pitcher A’s replacement in the rotation would now be Pitcher B:

I used 30 IP for a starter and 14 IP for a reliever over the course of the playoffs assuming a World Series run, and you’re welcome to vary the assumptions. But interestingly, it can make sense to put someone in the bullpen even if they’re a better starter than their replacement:

Let’s swing the discussion from theory back to El Gallo. Martínez certainly looks the part of someone who would be better suited in relief. He runs a huge platoon split; lefties have accrued a 23% higher wOBA than righties against him over the course of his career. He’s 2019 Hyun-Jin Ryu against righties, 2019 Danny Duffy against lefties. It’s a giant gap, and the sample size isn’t negligible; even after regressing that rate appropriately, it’s still an 18.3% gap in wOBA allowed.

In fact, he has the sixth-worst regressed platoon split among all active right-handers. Why does that matter for the question of starting against relieving? Because teams can scheme their relievers into facing same-handed batters more often. There’s no issue of the other team cramming the lineup with platoon bats, and managers can pick spots where several righties in a row appear.

In 2019, right-handed starters faced righties in 51.5% of plate appearances. Relievers, by comparison, faced a juicy 57.8% righties. Why is Martínez considered a good bullpen candidate? Because he’s one of the pitchers in baseball for whom a platoon advantage is most important, and relieving is the easiest way to get those matchups.

But the top of the regressed platoon split list shows the perils of thinking only in this way. Number one in baseball? None other than Scherzer, who has allowed a 24.6% higher wOBA to lefties than to righties over his career in a massive sample (22.2% after regression).

Forget Ryu and Duffy; for his career, Scherzer has pitched like 2019 Gerrit Cole’s overall line to righties and like 2019 Matt Albers to lefties. No one’s suggesting he should switch to relief, because we intuitively understand what I showed above; the further a pitcher gets from replacement level, the less it makes sense to move them to the bullpen, even if they’d get a huge boost there.

The Cardinals haven’t shown their hand when it comes to plans for Martínez in 2020. They’re in roughly the position of the theoretical team above; Martínez has a game that may be best suited for relief, but he has a talent level best suited for starting.

In my mind, the decision isn’t that close. If he’s healthy enough to start, he should start. The team has a mess of interchangeable starters who are meaningfully worse than Martínez; Daniel Ponce de Leon, Adam Wainwright, Austin Gomber, and even Dakota Hudson are all in his rear-view mirror as a starter.

So let’s take our framework from earlier, only with real players replacing hypotheticals this time:

These are conservative assumptions. Martínez hasn’t had an ERA above 4.00 since 2014. He’s better as a reliever — 0.8 runs better than his replacement, against only 0.5 runs better than replacement as a starter. Still, he should start. The value of bulk innings is simply too high.

Decisions are never this simple. Some pitchers don’t have the stamina to start, even if the math says they should. Innings caps tilt players towards relief; if you’re working with a set amount of playing time, the playing time multiplier for starters stops mattering. Personalities matter, too; when the decision is close, only a few runs a year, it’s more important to keep players happy than to squeeze out every last drop of optimization juice.

But this is the decision tree that teams should use to make role decisions. When Kenta Maeda makes his yearly migration to the bullpen, it’s not exclusively because the Dodgers are playing games with Maeda’s incentive-laden contract (though that doesn’t help). It’s also because he’s their version of Martínez — huge platoon splits, meaningfully better than a regular-season replacement-level starter, and more valuable in the playoffs as a reliever.

More teams should do this, I think. The tradeoff between starting and relieving isn’t static, and it’s not exclusively about how well suited a particular player is to a particular role. It’s contextual, and the context can change over time. We baseball fans have always understood the rough logic of the decision, but putting numbers to it can illuminate the right path in situations, like that of the Cardinals and Martínez, where it’s not an open-and-shut case.

This article has been updated to correct a typo in Max Scherzer’s regressed platoon splits (by 1%).