Bob Williams, the chief executive of Burns Entertainment and Sports Marketing, said that if Mr. Avery really wants a career beyond hockey, in which he trades on his name, he needs to be careful. He is in danger of veering into Dennis Rodman territory, Mr. Williams said.

As the Rangers fight to get into the playoffs, they have been winning more often since Mr. Avery returned. When he arrived, one of the team leaders, goalie Henrik Lundqvist, pulled him aside. “I told him,” Mr. Lundqvist said, “ ‘You’re a great player, keep focused on the game.’ ”

On Monday, as Mr. Avery was autographing pucks and photographs at a memorabilia shop on the Upper West Side, he said that he now does breathing exercises whenever he gets upset.

He showed off a tattoo he had gotten after his time at the Canyon, a rehabilitation center in Malibu, Calif. It is on the inside of his right arm, a quotation from a Radiohead song: “You used to be alright, what happened?”

“The way I think about it is, I used to be all right and now I am trying to be better than all right to people and to my teammates and to myself,” Mr. Avery said.

Born in Pickering, Ontario, Mr. Avery broke into the N.H.L. at 20 with the Detroit Red Wings. Shorter than many players, he adopted a rough persona on the ice. Over time, it grew into a monster. “I don’t think I really realized where it had gone,” he said, “until everything happened with the suspension and the time off.”