“There’s no question that he wants to win, and his I.Q. for the game is actually very good,” George Karl told me in a conversation about Anthony during the 2013-14 season, when the Knicks faltered and missed the playoffs, leading to the hiring of Phil Jackson as the team president. “He always wants to think like a coach, but he always doesn’t want to sign the contract with the coach.”

Asked what he meant by that, Karl, who coached Anthony in Denver, said: “I don’t think Melo understands that coming to work with the best attitude every single day is a precious commodity when you’re the best player. That’s not the same thing as playing hard. That’s bringing the total package, 100 percent focused on all the little things. Those are rare breeds.”

To his credit, Anthony was typically a willing passer out of double teams, especially during a 54-win season for the Knicks in 2012-13 that elevated him into most valuable player contention. But against single coverage, he held the ball, stunted the offense and too often jab-stepped the shot clock to oblivion.

Though he quickly became a polarizing figure with the Knicks’ fan base and the news media, I never considered him a player who was selfish by nature, but more a victim of his stylistic limitations.

In my interview with Karl, he agreed with my assertion that Anthony was the prototypical A.A.U. showcase player, his body alive and his feet moving in earnest when he had the ball. Battling his way under the rim to rebound teammates’ missed shots, fighting through screens on defense, rotating to the ball? Not so much.

You can argue that he didn’t deserve the shabby treatment he received from Jackson last season (he didn’t) or that he set himself up for misery in 2014 when he opted to take more money from the Knicks, along with a no-trade clause, than he could have made escaping from New York as a free agent.

For all the talk of how professional he was during Jackson’s psychological warfare to pressure him into waiving the no-trade clause (and erase Jackson’s negotiating error), Anthony has, season after season, seemed to revel in attention related to his possible departures and potential destinations.