In the last week of July, the teams on top of baseball’s Central divisions tore two late-inning relievers from the Yankees’ seemingly decomposing carcass. The Cubs acquired Aroldis Chapman, who’d handled New York’s ninth-inning duties; the Indians added Andrew Miller, who’d been the Yankees’ backup closer and had pitched primarily in the eighth after Chapman’s return from a season-starting suspension. Since moving to the Midwest, both pitchers have been as brilliant as their new employers envisioned: In August, each allowed two earned runs while whiffing more than 40 percent of the batters he faced.

Those similar stats disguised one significant difference, though: The elite lefties’ usage with their new teams looked nothing alike. The table below lists each outing Chapman and Miller made last month, with three data points per appearance: inning entered, number of outs recorded, and whether it was a save situation.

Chapman didn’t enter a game before the ninth inning or stay in any game for more than three outs. Miller, meanwhile, saw action as early as the sixth. He jogged in as often in the eighth as the ninth, and he entered in the seventh most often of all. He also turned in longer outings, throwing more innings than Chapman despite appearing in three fewer games. Chapman pitched in save situations all but three times; Miller pitched in non-save situations all but three times. He’s a closer-quality pitcher abnormally unbound by saves, which frees Indians manager Terry Francona to deploy him as a more flexible stopper.

Francona, who managed Miller in Boston in 2011, says the Indians would have wanted Miller even if he insisted on being a no-show before the ninth, but knowing he “wasn’t tied into any inning” was a plus. “I’ve always liked the idea of having a guy that you can kind of leverage,” Francona says. “When we got Miller, that was one of the most enticing things about it, is not only are you getting a really good pitcher, but you’re getting a guy that is willing to pitch any inning, which in my opinion makes him more valuable.”

The stats support Francona’s statement. Thanks to his near-flawless work in tight games, Miller ranked fourth among relievers with a 1.21 Win Probability Added in August. Chapman, despite carrying virtually the same surface stats, fell all the way to 93rd, with a WPA of only 0.15. That’s partly because Chapman’s worst outing was particularly ill-timed: His WPA suffered a huge hit on August 19, when he entered a one-run game that the Cubs were 75 percent likely to win and coughed up two runs to take a blown-save loss. (Miller’s few mistakes didn’t cost Cleveland a victory.) But it’s also because Chapman generally enjoyed more comfortable leads. Of Chapman’s 11 converted saves last month, only one was a one-run game when he faced his first batter; the Cubs’ average margin of victory in those games was 2.36 runs. That doesn’t mean that Chapman’s contributions were worthless, but it does discount them somewhat from a win-probability perspective. Virtually any major league reliever can reliably throw an inning (even, in most cases, the ninth) without surrendering three runs.

Chapman’s slant toward save situations hasn’t cost the Cubs anything: With a 15-game cushion in the division, they haven’t had to go to any extraordinary lengths to preserve leads, and they’ve had larger leads to begin with because they’ve outscored their opponents at such an extreme rate. Chapman hasn’t been misused; he’s just been used the same way as every other high-profile reliever. Miller is the outlier. “He can impact the game more this way, and I think he understands that,” Francona says.

Francona cites some examples of previous pitchers he’s managed who’ve filled a Miller-like role — Jonathan Papelbon (when he was a setup man) and Daniel Bard in Boston, and the Indians’ current closer, Cody Allen, before he started getting saves. “But what happens is, those guys evolve into being closers,” Francona says. And once they’re closers, their usage grows rigid.

In 2014, statistician Dan Brooks and I developed a metric to measure the rigidity of a reliever’s role, which with great imagination we dubbed “Reliever Role Rigidity.” The stat assesses the variation in the number of team outs recorded before each of a given pitcher’s appearances began. For example, a pitcher who starts the eighth enters after his team has recorded 21 outs; a pitcher who starts the ninth enters after his team has recorded 24 outs; and so on. RRR calculates the standard deviation, or spread, of each of those out totals: The lower the standard deviation (and the less spread out the entrance times), the more rigid the role. Among pitchers with at least 30 appearances this season, the 10 lowest RRR values (excluding extra-inning games) through Tuesday belonged exclusively to pitchers with more than 20 saves on the season.

In general, better pitchers get locked into more restricted roles. The chart below plots Deserved Run Average against Reliever Role Rigidity for each 2016 reliever with at least 30 appearances through Tuesday. There’s a moderate (r=.44) correlation between the two; the lower (and better) the DRA, the more rigid the reliever’s role tends to be. The blue dot at the bottom stands for Miller’s stint with the Yankees; the red dot represents his work for Cleveland so far.

Clearly, DRA thinks Miller has been baseball’s best pitcher on a per-batter basis. But based on how effective he’s been, we would expect his usage to be far more regimented than it has been in Cleveland thus far. If we run a regression to predict role rigidity based on DRA, the only reliever whose usage has been less rigid than Miller’s in Cleveland, relative to expectations, is Mariners phenom Edwin Díaz. Díaz is a rookie in his first year of full-time relief work, without a single minor league save before this season; unlike the more established Miller, he’s just the sort of pitcher one would expect to see used in an experimental way. Yet even he’s been co-opted by the closer system: In August, 11 of his 13 appearances fit the familiar three-out, ninth-inning mold.

“Younger relievers, they want to pitch at the end because they’ve got a chance to make money,” Francona says. “I get it. But it’s not always your best way to win.” Miller, who signed a four-year, $36 million deal in December 2014, has already made money: He’s living proof that some teams will pay for free-agent relievers with almost no saves to their name. Miller did have a chance to catch closer fever last season, when he worked in the ninth and recorded 36 saves. Yet in a David Puddy–esque, possibly precedent-setting act only slightly less selfless than George Washington’s refusal to run for a third term, he’s risked the cachet that his hard-earned closer status conferred.

As MLB.com columnist Anthony Castrovince noted last month, it’s slightly more common for a team’s best hitters to come up in the sixth, seventh, and eighth than the ninth. But aligning your best reliever with your opponent’s best batters doesn’t matter that much. The bigger benefit of Miller’s mind-set is the ability to bring him in whenever trouble arises instead of acceding to the tyranny of the save situation. And the lefty’s success against both left- and right-handed hitters removes the last limitation that might otherwise stay his manager’s signal. “I hate waiting for the ninth inning,” Francona says. “I never did understand that. You know, you wait around, wait around, and you lose a game in the eighth. Well, wait a minute, that might’ve been the most important inning of the game.”

Miller is a trump card most managers don’t have in their deck. But playing that card can be complicated. “The one thing you don’t want to do is surprise the guys in the bullpen when the phone rings,” Francona says. “If you communicate, things work; when you don’t communicate, they have a chance to get fouled up.” Continuity in other bullpen personnel — Allen, Bryan Shaw, and Zach McAllister have all been in Cleveland for four years or more — makes that communication clearer.

Even so, Francona knows the Miller model may backfire at times. Although analysts can come up with theoretical models for flawless bullpen management, Francona has to take into account the need to have the right pitcher ready in time to come in, and the competing desire not to have the same pitcher prep multiple times. “Even the way we use Andrew, there’s going to be a game where we have him warmed up in the sixth and something goes awry, and we’re going to have arguably our best pitcher coming in in a situation where we’re down a run,” Francona says. “And people are going to be like, ‘What are you doing?’ That’s the fallout that can happen, and I know it’ll happen at some point, but … in my opinion, it’s worth having him ready to impact the game the most amount you can.” It helps that Francona has a rich résumé and the support of an analytically inclined front office, but ultimately, he goes with his gut. Fortunately for the Indians, his gut says something different from most managers’. “I think you open yourself up to be second-guessed by bringing somebody in early, but I’m OK with that because I know down deep it’s putting us in the best position to win,” he says.

In Cleveland, Miller has looked like the closer Kwisatz Haderach, capable of being in many places at once and tapping into the genetic memory of the fireman lineage that’s all but lost in modern bullpens. “Guys like Andrew Miller don’t come around very often,” Francona says. “If everybody could have a guy like this, they would, but there’s not too many around in the game.”

Miller himself has alluded to a “changing landscape” of bullpen management, but there’s little evidence that the deeply ingrained post-Eckersley conception of the relief ace’s ideal role is eroding around the rest of the league. However, Miller might bring that change into being if he has a huge moment on the postseason stage. As Theo Epstein said last October, “Whatever team wins the World Series, their particular style of play will be completely en vogue and trumpeted from the rooftops … as the way to win.” Instead of celebrating the Royals’ strategy of stacking an overpowering but paint-by-numbers pen with short-fuse flamethrowers, this October’s most memorable narrative might be about Miller erasing an early rally, proving that the ninth isn’t the only inning worth worrying about.

“I hope he does,” Francona says. “I would think that that would help managers a ton.”

Thanks to Rob McQuown of Baseball Prospectus and Dan Brooks of Brooks Baseball for research assistance.