CLEVELAND — The biggest revelation we got from LeBron James after what might have been the final game he ever plays for the Cleveland Cavaliers had nothing to do with his pending free agency. It was health-related.

It turns out that the nasty poke in the left eye that James incurred from Draymond Green in Game 1 of the N.B.A. finals was not the most severe injury he suffered that night.

From the postgame podium late Friday, after his Cavaliers were mercilessly broomed out of the finals by the Golden State Warriors, James had an admission to share: He hurt his right hand badly after that crushing Game 1 defeat in a “self-inflicted” fit of pique.

Responding to reports that he punched a whiteboard in frustration with Cleveland’s blown opportunity to steal the series opener on the Warriors’ floor, James said: “I let emotions get the best of me. Pretty much played the last three games with a broken hand.”