“I think it’s important to have that mix,” Colangelo said. “I think Coach K would tell you that having the N.B.A. guys is very important because dealing with N.B.A. players is not quite like coaching kids in college.”

For Krzyzewski, the differences are stark. Dealing with professional players means doing more to optimize their production, as opposed to figuring out the best way to teach. “In college, you’re trying to guide kids across bridges — here, these guys have already crossed them,” he said.

Boeheim said he and Krzyzewski spent much of their first few years with USA Basketball talking about which aspects of college coaching they could realistically incorporate; even now, he said, Krzyzewski will rely on Thibodeau and Williams to guide him on the rhythms of professional players.

In college, for example, teams rarely play games on consecutive days, but in the N.B.A. it is commonplace. So when the American team has a bunched schedule, Krzyzewski might look to Williams or Thibodeau for a read on how much the team should practice, if at all. He might even ask the players for their opinions.

“At Duke, he’s not doing that,” Boeheim said. “But here Mike is very good at that, at bringing people in.”

The mechanics of the staff are unusual, too. During the Americans’ semifinal victory against Lithuania, Boeheim sat in the first seat on the team’s bench closest to the scorer’s table. He is something akin to Krzyzewski’s consigliere, a big-picture observer who leans in with his opinions.

Krzyzewski does not always follow Boeheim’s advice, but Boeheim said he had long since made peace with that. At Syracuse, he is the final voice; here, he is one of several. “And that’s fine with me,” he said. “I know there are plenty of guys who would have problems with it — a lot of guys, probably — but I don’t. I have too much respect for Mike.”