A boxer named Rocky sounds like a hero: likable, steadfast, iconic. A boxer named Chuck, on the other hand, sounds like an ordinary guy — albeit one who “can take a punch,” to quote the title character of the boxing movie “Chuck.” Based on the true story of Chuck Wepner — the New Jersey heavyweight whose moment in the spotlight inspired Sylvester Stallone’s “Rocky,” the drama proves that real life isn’t quite like the movies. And “Chuck” isn’t exactly “Rocky.”

Early in the film we see Chuck (Liev Schreiber) fighting an unusual opponent: a bear. The cheap spectacle suggests a man less hungry for victory than one desperate for attention.

The real-life Wepner — nicknamed the “Bayonne Bleeder” for his tendency to get cut during fights — had a day job selling liquor. A subject of local admiration and ridicule, Wepner was a screw-up: By his own admission, his best trait in the ring was the ability to simply keep standing. As the film notes, outside the ring, he also struggled, with his wandering eye putting a strain on his marriage to Phyllis (Elisabeth Moss), who finally leaves him after one affair too many, taking their daughter with her.

As “Chuck” gets underway, the 35-year-old boxer sees himself as a has-been who never was, much like the character of Louis “Mountain” Rivera in the 1962 film “Requiem for a Heavyweight,” from which Chuck likes to quote. But Chuck’s career gets an unexpected boost in 1975 when he’s invited by promoter Don King to fight the heavyweight champion of the world, Muhammad Ali. Their matchup is the film’s only major fight, and it comes at the end of the movie’s first act. The real struggle for Chuck is yet to come, and concerns what he does with the ensuing fame.

Boxing movies, from 1949’s “The Set-Up” to 2015’s “Creed,” are usually emotionally pummeling affairs, with their broken protagonists often undergoing bodily punishment that parallels — and reveals — a less physical vulnerability. Although the central match in “Chuck” is effective, and hits all the right beats, unlike the best of the “Rocky” movies, the drama outside the ring is less potent than drama inside. This, despite strong performances by Schreiber and — especially — Moss, a grounding presence who summons a toughness not usually seen in her work.

Arguably, the story of a habitual loser should resonate as much as — if not more than — that of a winner. But the film keeps us at arm’s length emotionally, filtering its antihero’s troubles through a layer of 1970s nostalgia. The screenplay (by Jeff Feuerzeig, Jerry Stahl, Michael Cristofer and Schreiber) charts a familiar arc of failure and redemption, but director Philippe Falardeau (“Monsieur Lazhar”) doesn’t have Stallone’s eye for delineating the contours — both the highs and the lows — of the American Dream.

“Chuck” is, finally, the story of an unhappy man chasing after fame, while failing to notice that the people in his life already love him for who he is. Chuck isn’t larger than life, and neither is “Chuck.” Its charms are, like its hero, imperfect.

R. At Landmark’s E Street Cinema. Contains coarse language throughout, drug use, sexuality, brief nudity and some bloody fight scenes. 98 minutes.