CLEVELAND — The Indians paid what Chris Antonetti, their president of baseball operations, has called “a steep price” for Andrew Miller.

It’s been worth every penny.

Just not in the role most envisioned.

When the Yankees acquired four highly regarded prospects from the Indians on July 31 in exchange for Miller, the belief was that Cleveland finally had landed a consistent closer.

Manager Terry Francona, whose Indians take on his former club, the Red Sox, Thursday night in Game 1 of their American League Division Series, had other ideas. At the time of the trade, Francona engendered some snickers when he said Miller might be used anywhere from the sixth to the ninth inning. He might close some nights; others, he might not.

And indeed, Miller has been more of a jack of all roles in Cleveland after compiling nine saves and a 1.39 ERA in 44 outings with the Yankees. The lefthander closed during Aroldis Chapman’s 30-game suspension to start the season, then was used almost exclusively as the eighth-inning setup man.

And he’s been every bit as effective as he was in pinstripes. Miller posted a 1.55 ERA and 0.552 WHIP in 26 games with the Indians, earning three saves. He’s been part of a bullpen that, along with regulars such as Bryan Shaw, Dan Otero and Cody Allen, compiled a 1.84 ERA since Miller’s arrival.

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“It’s not just his numbers,” Francona said Wednesday before his AL Central champions worked out at Progressive Field. “It’s his willingness to pitch whenever you give him the ball. It’s allowed us to pitch Allen, Shaw and Otero in different spots, too, so it’s taken a little bit of a load off them. If you look, all of their numbers are probably better since Andrew has been here.”

The group has been a significant factor, and maybe the No. 1 factor, for the 94-67 Indians, whose once heralded rotation took major hits during the past month when Danny Salazar and Carlos Carrasco were lost to injuries.

Miller steered credit elsewhere Wednesday.

“As a bullpen, we think of ourselves as a unit and kind of feed off each other and try to hand the ball to the next guy in the best shape possible,” Miller said. “Tito (Francona) gives us good spots to go into the games, gives us good matchups, and I think we’ve picked up our end of the bargain pretty well.”

As for his willingness to pitch any inning, Miller pointed out he had to do that in Boston, Baltimore and even to an extent with the Yankees.

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“I don’t know why I get credit for that, I think most guys would do the same thing,” Miller said of publicly embracing whichever role, or nonspecific role, he’s given. “I think at the end of the day if everybody’s on the page that winning’s the most important thing, something like that doesn’t matter.”