Yankees reliever Dellin Betances should be one of the least likely players to get out of his chair when a reporter requests a one-on-one conversation in the clubhouse. For starters, the energy Betances must burn to hoist his huge frame from a sitting position seems almost environmentally unfriendly. More important, it would be easier for both parties if he remained hunkered down. When Betances sits, his head is at the perfect height for a reporter’s casually held recorder; when he stands, it forces a man of average stature to raise his recording arm in an uncomfortable, supplicatory pose. Betances is tall, is the point.

Of course, once at rest, few players of any size stand up to speak to a writer. We’re the ones intruding in one of the few places at the park where a player can relax, half-clothed and comfortable. And yet when I approached Betances after a recent win against the Royals and uttered the traditional haveaminutetotalk? he got up immediately, like an oversize grade-school student called on to recite a piece of poetry. Taller even than 6-foot-7 teammates CC Sabathia and Michael Pineda, Betances is intimidating because of his bulk, but he’s so soft-spoken that I had to inch closer to hear him, inclining my arm at an steeper angle to compensate. He’s not exactly a gentle giant, but he’s quiet, courteous, and articulate, and to the extent that a 6-foot-8, 260-pound person can, he keeps his size to himself.

Betances, a 26-year-old New York native who grew up rooting for the Yankees during the dynasty years, brings the same deceptive stillness to the mound. The fear he inspires stems from his size, his statistics, and his stuff more so than his manner. He eschews the usual accoutrements of intimidation: no goggles, no beard (banned in the Bronx), no chest-pounding or glove-cursing. He doesn’t have a strikeout ritual. If he did, we’d be seeing it in our sleep by now, because Betances has whiffed 40 percent of the batters he’s faced, the fourth-highest K rate among relievers. With 10 games to go, the rookie right-hander, who leads the majors with 88 relief innings pitched and boasts a 1.33 ERA, has struck out 132 hitters, breaking Mariano Rivera’s previous Yankees reliever record of 130, set in 1996, Rivera’s age-26 season.

I watched all of Betances’s inning-ending strikeouts with runners in scoring position — the scenario most likely to produce a fist-pump or a point to the sky — and he came close to celebrating on only two occasions, once (with the bases loaded, late in a tie game against a division rival) stopping himself just before some glee could escape …

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… and once giving himself a few glove pounds (but only because he’d finished a game).

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Betances usually does an adorable tiny hop and spins to face center field after a strikeout, ensuring that if he were to let slip a hint of emotion, no one would misconstrue it as a sign of disrespect. At times, he’ll even hang his head as if ashamed of making the batter look bad — which he does, often, even when it’s the reigning MVP at the plate.

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Then, incongruously for someone so large, Betances hustles back to the dugout as earnestly as David Eckstein sprinting to first after ball four.

Someday, when Betances is the guy getting saves and making millions instead of setting up someone else, he might be more demonstrative. For now, though, whatever elation he feels stays on the inside.

Given the special season he’s having, he’s certainly entitled to feel some joy. Speaking softly and carrying a big breaking ball, Betances is having one of the best campaigns by a reliever in recent years. In the process, he’s become a microcosm of the sport’s ever-evolving attitudes about bullpen usage, supplying two contradictory answers to a question that has divided fans, field staffs, and front offices for decades: What’s the best way to deploy one of baseball’s biggest bullpen weapons?

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Before we explore that question, let’s take a closer look at Betances’s historic campaign. It’s hard to say where his season ranks among the best ever by a reliever, because baseball is still conducting its decadeslong Entmoot to decide what to do with pitchers who aren’t suited to start. Over time, relievers have taken on heavier workloads collectively and lighter workloads individually, with a corresponding boost in inning-per-inning effectiveness, which makes cross-era comparisons more difficult. To simplify the task of putting Betances’s campaign into context, we can exclude seasons prior to 1988, when Athletics manager Tony La Russa turned Dennis Eckersley into a modern late-inning reliever and inspired imitators across the league. There’s still the matter of sample size, though: If we compare Betances only to past relievers who’ve thrown at least 80 innings, we exclude a substantial percentage of the pitcher pool. Half the fun of comparing relievers comes from marveling at the Lilliputian ERAs and Brobdingnagian strikeout rates they post in small samples, but Betances’s extra innings add value. It’s harder to sustain eye-popping peripherals over 80-plus innings, as he has, than it is to do the same over 60.

It takes a few new-age statistics to provide an accurate picture of Betances’s season. The first is Fielding Independent Pitching. Among 80-inning relievers since 1988, Betances’s 1.67 FIP ranks fifth, behind Eric Gagne’s Cy Young, zero-blown-save 2003 season; Rob Dibble’s 1990-91 Nasty Boy years; and Francisco Rodriguez’s second full season, 2004. However, FIP is a rate stat that doesn’t take playing time into account, aside from the innings minimum we set. We need something that incorporates workload.

One option is Win Probability Added, which attributes changes in a team’s win expectancy (how likely it is to win a given game) to the players who helped or hurt the club’s odds. For example, in a September 12 game against the Orioles, Betances relieved starter Brandon McCarthy with no outs in the eighth and a runner on second. According to FanGraphs’ WPA model, which is based on how often teams have historically gone on to win after finding themselves in certain inning, score, and base-out scenarios, the Yankees had a 25.9 percent chance of victory before Betances threw his first pitch. Betances got out of the inning without allowing the go-ahead run, which raised the Yankees’ odds of victory to an even 50 percent. WPA credits him with the difference: 24 percent of a win. Add up those changes in win expectancy from every outing and you have Betances’s WPA for the full season.

The problem with WPA, for our purposes, is that it’s context-sensitive. The biggest swings in WPA occur at the end of games, in “high-leverage” situations when the game can be decided quickly. As a result, closers — who pitch at the end of the game and thus have high Leverage Indexes — tend to have higher WPAs than equally effective setup men, solely because they pitch in the ninth instead of the seventh or eighth. One could make the case that the added pressure makes those ninth-inning outings more valuable, but we don’t want to ding Betances just because the post-Rivera closer role went to David Robertson, an elite reliever in his own right who’s been trusted with the Yankees’ highest-leverage outings, according to Baseball Prospectus’s Bullpen (Mis)management tool.

Despite being a setup man with only one save on the season, Betances has been lights-out enough to lead the majors in WPA — the first time a setup man has done so since Tyler Clippard in 2011. On the post-’88 leaderboard, though, the closers rise to the top, and Betances has to settle for a spot just inside the top 60.

The Goldilocks stat we’re seeking — a counting stat that doesn’t discriminate based on leverage — is Run Expectancy Wins, or REW. Using a framework similar to WPA’s, REW calculates the difference between the number of runs a team is expected to score in the inning at the start and the end of each play, credits/debits the batter/pitcher accordingly, and then compiles the differences to arrive at a full-season total of wins added or subtracted. But because it’s not sensitive to inning or score — a two-out, bases-loaded strikeout counts the same in the seventh inning of a six-run game as it does in a ninth-inning tie — it’s closer to context-neutral than WPA, allowing us to pit Betances against guys who got the chance to finish more games. And when we level the leverage field, Betances climbs close to the top of the leaderboard:

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Betances won’t catch Rivera, whose combination of elite performance and a workload that no reliever would be asked (or allowed) to take on today produced an REW that might never be bested. Barring a blowup between now and the end of the month, though, Betances’s 2014 will have a strong case for inclusion among the top 10 (if not top five) seasons since bullpens began to resemble those we see today.

So how did he get here? Just as in Rivera’s case, it took a conversion from the starting rotation and a tweak to an existing pitch to turn Betances into a beast. His formula for success is as simple as it is seemingly impossible to solve. Betances is a two-pitch pitcher, relying on a four-seam fastball when he’s behind in the count and a curveball when he’s ahead. Leveraging his long limbs to generate tremendous torque, he throws both offerings extremely hard, boasting the ninth-fastest four-seamer (97.6 mph) among relievers who’ve thrown 200 fastballs and the eighth-fastest curve (83.8) among relievers who’ve thrown 100 curves, according to the PITCHf/x Leaderboards at Baseball Prospectus. Only Brett Cecil, Vic Black, and Craig Kimbrel have higher curveball whiff-per-swing rates than Betances’s 53.1 percent.

Like Kimbrel, Betances used to throw a “spike curve,” a variation in grip that tends to yield both higher velocities and release points that are less differentiated from those of the fastball, without any sacrifice in spin. It’s no longer clearly a spike curve (and it could just as easily be labeled a slider or slurve), but despite its speed, Betances’s curveball has the 11th-most horizontal movement among relievers who’ve thrown at least 100 curves this season, and his fastball and breaking ball have almost identical release points, camouflaging which is coming. Aware of its effectiveness, Betances leans heavily on the hammer. The righty’s 47 percent breaking ball usage rate on the season (up from 41 percent in April) is the sixth-highest among relievers with at least 500 pitches thrown and no more than three pitch types.

“Obviously, hitters adapt to what you’re doing,” Betances says. “In the beginning, nobody really knew who I was, and I think now they have a better idea, so that just means I’ve got to adapt to them as well.”

Whatever hitters have learned about Betances hasn’t helped them hit him. In the second half, he has thrown more curves, inducing a higher percentage of out-of-zone swings. He’s actually lowered his ERA since the All-Star break, and an increased strikeout-to-walk ratio supports that improvement.

So now we know how good Betances has been. What can we learn about how manager Joe Girardi’s use of his big bullpen weapon has evolved? And what can that trend tell us about the way most managers assign relief roles?

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Check out the following fancy infographic, featuring cutting-edge numerals and spaces. The numbers represent the innings in which Betances entered each of his games before the All-Star break.

Betances, first half: 7 8 8 9 7 8 6 8 5 6 5 8 7 6 6 5 6 5 5 9 8 6 6 7 7 8 6 7 7 8 8 7 6 6 8 8 7 8 8 8

Before the break, Betances entered in the fifth inning five times and in the sixth inning 10 times, getting outs whenever Girardi wanted one. He looked like the relief ace that sabermetricians have been pining for since they went out of style: “stoppers” or “firemen” who came in whenever they were needed, not just “closers” who appeared whenever they could pick up a save. Why waste your best bullet with a three-run lead the statistics say even an average reliever could preserve virtually every time? Instead, break the glass whenever the emergency arises. Case in point: a scoreless game against the Mets on May 15, when Betances relieved starter Chase Whitley with two outs in the fifth and runners on second and third. The big righty got a groundout to escape the inning unscathed, then stayed in to strike out all six of his opponents in the sixth and seventh innings. Robertson got the save in what would be a 1-0 Yankees win, but Betances provided more value.

Contrast Betances’s first-half usage with the Royals’ deployment of Wade Davis, the setup man with a 0.94 ERA (albeit in 20 fewer innings) who’s second behind Betances in the 2014 REW rankings.

Davis, both halves: 8 9 8 8 8 8 8 9 8 8 8 8 8 9 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 9 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 9 8 8 9 8 8 9 9 9 9 7 8

Now that’s an eighth-inning guy, the push-button, one-inning pitcher that Goose Gossage complains about whenever he comes close to a microphone. From May 11 through July 7, Davis ran up a streak of 21 straight eighth-inning entrances. Until Royals skipper Ned Yost summoned him in the seventh on Tuesday night, Davis hadn’t entered a game all season in any inning but the eighth or ninth. Davis’s pitching has helped Kansas City despite that unimaginative managing, but it might have made an even more substantial impact if his innings had been distributed differently, because the eighth wasn’t always the inning when the Royals most needed an almost-automatic out.

Now take a look at how Girardi has used Betances since it became clear the rookie’s early success was no fluke:

Betances, second half: 7 7 8 8 8 7 7 7 8 8 9 6 8 8 8 7 7 9 8 7 8 8 8 7 8 8 8 7

Notice anything different? After the break, Betances has barely had a presence in the middle innings, pitching only once in the sixth and being banished from the fifth. He’s been as brilliant as ever, but the timing of his entrances has become much more predictable. He’s almost on the Davis plan.

“I feel like as of late I’ve kind of had a better idea of when I’m coming in, so that’s helped,” Betances says. “But at the beginning, I hadn’t established myself. It wasn’t like I was going to get handed the setup-man or eighth-inning role. I had to work my way in there.”

We can quantify this change in usage in a way that might be more compelling than a sequence of numbers arranged in a row. It’s possible to distinguish between the relievers with flexible roles and those with rigid roles using the standard deviation — a measure of how closely a set of numbers clusters around its mean — of the number of cumulative outs already recorded when they entered the game. (A reliever who enters a game to start the seventh inning does so after his team’s staff has already recorded 18 outs; with one out in the seventh, 19 outs, and so on.) A reliever who always enters games to start the same inning — Yost’s dream version of Davis — would have an entrance-outs standard deviation of zero. A reliever who bounces around, like first-half Betances, would have one much higher. The lower the standard deviation, the more rigid the role.

Here’s what this looks like graphically, as represented by Betances, Davis, and struggling Red Sox reliever Craig Breslow, whose role has gotten less rigid as he’s pitched his way out of high-leverage work. The numbers on the y-axis represent the standard deviation in team outs recorded before the three relievers entered their games.

Betances has seen one of baseball’s biggest increases in role rigidity; Breslow one of its biggest declines. Davis, meanwhile, has been Mr. Eighth Inning all year long.

Yost’s dogged adherence to bullpen roles earns him more than the usual amount of first- and second-guessing. On Sunday, he chose pitch-to-contact Aaron Crow over Davis, Kelvin Herrera, or a number of other seemingly superior strikeout options in a crucial situation, which backfired when Crow allowed a grand slam. Yost justified the move with an appeal to his own bullpen presets, saying it wasn’t the predetermined point in the game when he wants to use his best pitchers.

He gave me a similar answer when I asked him recently whether he thinks there are times when flexibility might benefit a bullpen. “We like our bullpen, and I think the bullpen is better served when guys know their roles,” Yost said. “When this game starts, [Davis] knows to prepare for the eighth inning, Herrera knows to prepare for the seventh inning, everyone else knows to prepare for the sixth inning and then, depending on the score, the seventh, eighth, and ninth inning, so I think if you can define your roles it makes it easier for them and they can be more successful.”

Yost’s assertion is difficult to disprove. It’s possible that relievers really do pitch better when they have a clear sense of which inning to psych up for. It’s conceivable, though, that with the proper preparation, relievers would adjust to less regimented roles. Although Betances seems to have a slight preference for his increasingly predictable pitching pattern, he acknowledges the value of a pen with movable parts. “I feel like we have a great group of guys in the bullpen where we can mix and match [Adam] Warren and Shawn [Kelley] and David, myself, we could go in early or we could go in late,” Betances says. “I think that gives the manager a lot of options, and that’s good for all of us.”

Davis is agnostic on the issue of defined relief roles. “Maybe it helps, maybe it doesn’t,” he says. “I don’t know.” He’s does tell me, though, that he’s confident coming in mid-inning instead of starting clean. “I’ve built my own jams enough to get out of them this year, so I think that helps along the way,” he says. “So if people get into them and if they need you to help them get out, then you’ve already done it.”

Yost put those words to the test on Tuesday with that Davis sighting in the seventh, which was a sign of either the apocalypse or intense pennant race pressure. In an attempt to preserve Kansas City’s weak grasp on a playoff spot, Yost wisely went to Davis up by one run with two on and Jose Abreu due up, but Davis walked Abreu and gave up a bases-clearing, game-losing triple to Conor Gillaspie. It was the right move, from a statistical perspective, but the wrong outcome. And it’s probably the last time Yost will try departing from his bullpen blueprint — which likely means more #Yosted ahead.

Of course, it could be that Yost’s bullpen usage isn’t all that unusual, especially in light of the trajectory Betances has taken. Fans of almost every team believe their clubs struggle against rookie starters (even though it’s the rookie starters who struggle on the whole), or that they could trade for Giancarlo Stanton or David Price. Writers assigned to almost every team insist the club they cover has good chemistry. We could almost certainly perform the same exercise for bullpens: What fan base doesn’t believe its manager regularly signals for the wrong reliever or shows too slavish a devotion to the _th-inning-guy structure?

With an assist from Dan Brooks, we can put both Yost and the Yankees into context with a team-level version of the stat we introduced above for Betances, Breslow, and Davis — the Reliever Role Rigidity Index. Much like the Managerial Meddling Index, these ratings reflect not only manager tendencies, but also roster strengths and weaknesses: A team with a deep bullpen might not need to be as flexible as one with a bigger gap between its top-tier and second-tier arms. Still, this can give us a good idea of which teams’ relievers have strayed the least from their regular assignments, whether out of manager preference or circumstances beyond the skipper’s control. (Note that the y-axis starts at a standard deviation of 1.5 outs, to make the differences clearer.)

The Triple-R index, which includes relievers with a minimum of 30 appearances, suggests Yost is true to his words: He’s baseball’s strictest observer of the reliever hierarchy. The recently resigned Ron Washington’s Rangers and Ron Roenicke’s Brewers, two teams that have drawn bullpen-management complaints over the past few years, are less rigid than the Royals. Some teams known as sabermetric early adopters appear on the extreme flexible end. Perhaps that’s significant, though there’s no clear correlation between reliever role rigidity and bullpen performance, so this metric is more descriptive than prescriptive.

Which brings us back to Betances, who has seen both his leverage index and his role rigidity rise as Girardi has realized what he has and begun to handle Betances in the way modern bullpen dogma dictates. The relationship between leverage index and role rigidity is an extremely strong one, leaguewide:

In part, that’s because it’s hard to have a high leverage index if you’re getting lots of work in early innings, when LI is lower. However, it’s also because it’s rare for a reliever to diversify after he’s locked into a traditional setup role. Betances hasn’t produced an outing of more than four outs in September, which could be a change intended to keep him fresh but could also augur shorter appearances in seasons to come. I asked him how Girardi has helped him stay healthy while pitching at (by 2014 standards) a furious pace.

“We’ve definitely communicated a bunch,” Betances says. “He’s called me into his office to try to explain to me what days I’ll have off, just workload stuff … so I think that’s helped me stay healthy to this point.”

But how long can the hard work continue, particularly for a pitcher with a history of shoulder and elbow issues?

“I feel like for myself, I can continue that, as long as I stay healthy and continue doing certain stuff that helps me feel healthy,” he says. “I think that it gives Joe Girardi options for when to use me.”

At the end of his age-26 season, Rivera had several hundred saves ahead of him — but he never again came close to 100 innings or to recording the REW he did in 1996. We might see Betances shutting down hitters and racking up saves for seasons to come, but judging by recent events, he’ll be another inflexible, late-inning brick in the bullpen wall, not the wild card he was early on. For better or worse, his fifth-inning flamethrowing is over. And for now, at least, the flexible fireman dream is still dead.

Charts reflect data through Wednesday’s games. Dan Brooks, Andrew Koo, Rob McQuown, and Harry Pavlidis of Baseball Prospectus provided research assistance for this article.