The day after their talk, Schlossnagle said, Carpenter was different. If someone ordered pizza for the team, he passed. He never touched soda. He lost 40 pounds, studied better and, as a fifth-year senior, nearly led T.C.U. to the College World Series.

Yet all of it was worth only $1,000 to the Cardinals, who drafted him in the 13th round in 2009. Carpenter eagerly took the small bonus. He had no other choice.

“I think after taxes it was like $500,” Carpenter said. “I just put it in the bank. Honestly, though, 500 bucks, when you’re in college and you have no money, it’s like, all right, cool, thanks.”

Ten years earlier, the Cardinals had found another gem in the 13th round: a stocky community college shortstop named Albert Pujols. With Pujols, picked 402nd over all, the standout tool was power. With Carpenter, it was uncanny plate discipline — and, like Pujols, he had a burning passion to improve.

By his second professional season, Carpenter was hitting .316 in Class AA. Invited to major league camp the next spring, he made an immediate impression.

“He was one of those guys showing up at 5 a.m. every day, just trying to soak up every minute of it — and he still does it today,” General Manager John Mozeliak said. “To envision him from Double-A to where he is today, I don’t think anybody could have told you that with a straight face. But when you think about how disciplined he is and how he prepares, I don’t think anybody in this organization would tell you they’re surprised.”