Everybody loves a conversion project, as long as "conversion project" means "turning a reliever into a starter." Why not take a closer like Neftali Feliz and, as long as he possesses the arsenal to handle the move, assign him a position that allows the team to squeeze significantly more innings from his arm? Closers come from the Rule 5 draft, from the independent leagues, and from every other possible route into the big leagues. Competent starters, though, are rare and wondrous beasts. If you have a Feliz, someone who had success as a starter in the minors, it would be folly not to at least consider the possibility of pushing him into the rotation.

For the same reasons, everybody hates "wasting" a starter in the bullpen. If Aroldis Chapman was supposed to be a starter from the day he arrived on these shores, why on earth does Dusty Baker think losing Ryan Madson to injury means that Chapman should move back into relief? Do the Astros really need Brett Myers to close when Houston might not take 25 savable leads into the ninth inning all season? We complain about this on a smaller scale, too: when Alfredo Aceves was named Boston's closer in the absence of Andrew Bailey, the thought that Aceves's multi-inning arm would be wasted in a one-frame role bugged a lot of us.

More than shouting epithets at team management, though, I'm interested in the insights these moves can give us into how teams view their pitchers and the value of the roles in which they're placed. I think such a move can teach us lessons about a player's perceived quality as well as, most intriguingly, the way organizations value high-leverage, late-game innings compared to the blank frames at the start of a game.

An organization's decision about whether to use a particular player as a starter or reliever has, as I see it, three intrinsic variables: quantity, performance, and leverage. (This puts to one side questions of allocation of resources on a team, personality considerations, and other issues not purely related to the question of whether a single given pitcher provides more value as a starter or a reliever.)

The most visible variable is also the one that many times begins and ends an argument about a role change: quantity of innings pitched. Said quantity is, of course, significantly related to the role itself, as a full workload for a starter can be well above 200 innings. By contrast, 2011's leader in relief innings pitched was Aceves, with a mere 93.

The inherent reduction in innings for a pitcher moving to the bullpen is not the only way that such a change can impact playing time, however. A team making a role decision will presumably take into account the possibility of injury. A pitcher who is more likely to lose his mechanics as he tires might be at greater risk of hurting himself in the starting role. Similarly, a pitcher who has trouble warming up quickly might find himself called on to pitch at max effort without being ready.

It is not entirely clear which way the injury question cuts on average, if "on average" is even a meaningful phrase to discuss when dealing with the randomness and biomechanical mysteries of pitcher injuries. Getting back to where we started, then: relievers pitch less often than starters do, with a stroll through our Depth Charts showing that even comparing top relievers with middle-rank starters has the starters more than doubling the relievers in expected innings pitched.

The second variable, performance, boils down to how many runs a pitcher is going to allow, but it is controlled by a variety of inputs. These include the quality of the player's pitches (including both "pure stuff" and command), pitch-variety, stamina, mental and emotional toughness, intelligence, and probably other aspects of pitching I'm leaving out. Many (perhaps all) of these inputs come into play in different ways depending on the chosen role: poor stamina can be hidden in the bullpen and a pitcher can get away with fewer pitches in the arsenal, but late-game relievers need to be able to deal with tight situations and close games that a starter does not always face.

Pegging the difference in performance that you would expect from a role change is not trivial and likely depends on the individual pitcher in question. Eric Seidman has studied swingmen in these pages and found that, depending on the type of pitcher, you see between half and three-quarters of a run improvement out of the bullpen as compared to starting. Mitchel Lichtman mentioned in his ProGUESTus piece last November that a reliever forced into starting would be expected to give up about a run per nine innings more.

Relievers, in other words, pitch better than starters on a per-inning basis, but it's far from clear how much better.

The final variable is that "high-leverage relievers" pitch in, as you might expect, higher leverage than starters. They're called on only to clean up messes or to keep the other team off the board in close games. As Colin Wyers has pointed out, however, existing measures of leverage miss crucial information, so we cannot just plug in, for instance, an average leverage index for closers for a starter-to-relief conversion to figure out whether the move is a good one.

A team, then, has a whole passel of unknowns to deal with when it decides whether to push its stud reliever into a starting role, or vice versa. Fortunately, we can fairly set one constant: innings. In what ensues below, we'll use an expectation of 170 IP for starters and 70 for relievers. These are admittedly somewhat arbitrary, especially the figure for starters, but I'm much more comfortable picking somewhat arbitrary innings counts than I am messing around with expected performance for a role-switcher. You can switch the innings counts to whatever you're happiest with.

Beginning with the basic idea that a pitcher's value is essentially their rate of run prevention above replacement times the number of innings they pitch times the leverage of those innings, taking a starter's leverage to be the baseline (i.e. setting it equal to one), and plugging in the innings totals we're using above, we see that:

RAR_SP * 170 = value_SP  
RAR_RP * 70 * leverage = value_RP

"RAR" above is a sort of fictionalized rate stat representing the pitcher's ability to prevent runs better than a replacement pitcher.

Since the point of this exercise is to see how teams determine that a pitcher is more valuable in one role than another, we need to find the point at which the values are equal. Thus

RAR_SP * 170 = RAR_RP * 70 * leverage

Rearranging so it looks like a simple function:

leverage = (RAR_SP / RAR_RP) * (170 / 70)

(I make no judgments about which variable is dependent and which independent. You can swap them if you like.)

You can graph this, but I think it's more enlightening to step through some values in a table.

Runs ratio leverage
1.00 2.43
0.95 2.31
0.90 2.19
0.85 2.06
0.80 1.94
0.75 1.82
0.70 1.70
0.65 1.58
0.60 1.46
0.55 1.34
0.50 1.21

Taking Aroldis Chapman, the way to understand this is that if you think that Chapman's run-prevention value over replacement will be equal no matter what his role (or, perhaps more importantly, if you think that the Reds think this), then his innings in the bullpen must be at least 2.43 times as important as his innings as a starter in order to provide equal value. If you think he can be twice as good in the bullpen, then those innings need only be 1.21 times as important.

Noting that the different run-prevention skill figures are being compared to different replacement levels (your replacement-level reliever being expected to pitch better per-inning than your replacement-level starter), we'd probably expect most starter-to-reliever "conversions" to end up on the high end of this chart, implying that their organizations value late-inning relief to a significant (possibly too significant) degree. This tentative conclusion will surprise nobody who watches the free-agent closer market every winter.

Thank you for reading

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