Few players have much direct contact with the data analysts; their reports are often disseminated through the coaching staff. And those reports have an impact. Headley, the third baseman, has been moved further off the line defensively this season and has been encouraged to be more aggressive in certain counts.

“It’s a different dynamic being told by somebody who hadn’t played the game before where you need to stand,” said Headley, who recalled veteran pitchers like David Wells, Greg Maddux and Chris Young yelling at him if he strayed from the line.

Headley continued: “It’s like, ‘Hey, I’ve done this for 15 years,’ or somebody who’s done it for 25 years coaching. But I think the more you communicate, the more you talk, you realize we’re trying to accomplish the same thing and that there’s a nice balance. It’s a tool, not the tool belt.”

Earlier this year, Headley asked David Grabiner, the director of quantitative analysis for the Yankees, to bring him something that might be useful.

“It can be frustrating when you get information passed down to you without any communication,” Headley said. “More than anything, I’m trying to get that relationship going so that when he brings me something there’s that trust that this is something that might really help me, it’s not just some obscure number.”

Carlos Beltran, the Yankees’ best hitter this season, said that while he studied video, he considered himself an intuitive hitter, relying on his 19 years of big league experience to guide him. But Miller, the reliever, said he believed that would change with the next generation who will come up understanding metrics such as Z-scores or wOBA and use them to influence how they swing the bat or throw the ball.

That generation may soon be on its way.

A raft talent in the Yankees’ minor league system has inched its way closer to the majors. And no matter how the next iteration of Yankees look, they are certain to be shaped by Fishman’s increasingly visible hands.