Over the decades, the sport’s larger-than-life history, outsized personalities, and damning contradictions have proven ripe for storytelling, be it fiction or nonfiction. The conventions of the boxing film are familiar enough to be nearly ritualistic: glove leather and ring-rope, men in crouched defensive positions in televisual black and white, the squalling at the ringside of punters and red-lipped lovers and newspapermen. In spite of—or maybe because of—the genre’s familiar tropes, it’s a topic that’s excellent at being about something else. Boxing can provide the occasion for “safe” racial reprisal against the white powers-that-be; it can make literal the fight to the top of the American high life in a dog-eat-dog world. So you can see where director Walter Hill was coming from when he remarked about his 2002 film Undisputed: “This film is actually about boxing and not a metaphor.”

At the more uncomplicatedly triumphalist end of the spectrum, there are the midcentury biopics. Their heroes are almost invariably white. Robert Wise’s atypically optimistic story of rough-and-tumble Rocky Graziano, Somebody Up There Likes Me (1956), ends before Graziano has time to lose again. Raoul Walsh’s adventuresome, old-school Gentleman Jim follows Errol Flynn as Gentleman Jim Corbett, a name Bob Dylan fans may recognize from his song “Hurricane.” (The film also holds the dubious honor of being Mike Tyson’s proclaimed favorite.) These are movies that examine the manly virtue of their protagonists, seeing an optimistic path of upward mobility in the boxer’s rise from the slums to the role of modern gladiator.

And yet, there are complications and physical dangers that go unacknowledged in these romanticized stories. Filmmakers have just as often turned away from the glory of victory, treating the ring as a miniature theater for some of capitalism’s most violent inequities. Therein lies the crux of so many of the period’s more noir-inflected boxing movies: the sport provided avenues to the cash-strapped, the immigrant, and the working-class, while just as often exploiting their bodies and treating them as disposable. In Mark Robson’s Champion (1949), penned by HUAC-blacklisted Carl Foreman, a champ who will do anything to get to the top, played by a cruel, shovel-faced Kirk Douglas, dies in the ring. In The Harder They Fall (1956, also directed by Robson), based closely on the true story of the luckless Primo Carnera, a clueless oaf has the mob fix every one of his fights, only to leave him broke, beaten, and without even the dignity of having won anything for real. And in The Set-Up (1949), the rackets’ control over the sport makes it impossible for a worker to maintain his dignity and his living. These films grasped what Joyce Carol Oates would later note in her 1992 essay “The Cruelest Sport”: that fighters are “poorly paid, nonunionized workers with no benefits in a monopolistic business without antitrust control.”

Kopple holds these two truths side by side without attempting to influence matters, including often-contradictory input from Tyson’s former trainers and friends, as well as from his victim, Desiree Washington. At times, some of the documentary’s subjects even resemble Hollywood fiction: the shady promoter in the form of the unscrupulous Don King, the femme fatale in the form of Robin Givens, Tyson’s ex-wife. For all of Fallen Champ’s psychological complexity, Kopple is ultimately less interested in having the final word on Tyson’s character than in exploring how his actions ripple out into American society, from the white public’s schadenfreude over his downfall to the Black women’s support group discussing the way their voices have been minimized in the conversation.

Martin Scorsese, a master of rendering macho antiheroes with unseen depths, claimed to know nothing about boxing when he began making Raging Bull (1980), only agreeing to tell Jake La Motta’s story after being pestered by Robert De Niro. Though La Motta was a middleweight world champion, victory is ultimately hollow in Raging Bull: it is as much a film about masculine ego, domestic abuse, and the broken bonds of brotherhood as it is about any sport. Its inspiration, in part, can be found in Luchino Visconti’s Rocco and His Brothers (1960), another boxing epic of brotherhood and betrayal.

La Motta’s violence is more destructive outside of the ring than within it, particularly when he uses it to purge his animalistic rage. (“He ain’t pretty no more,” someone spits from ringside after he brutalizes an opponent his wife dared call handsome.) His sexual jealousy over his wife, Vickie (Cathy Moriarity), seems to be the locus of this feral impulse, and his treatment of her is openly abusive. Scorsese draws potent visual parallels between La Motta’s psychosexual anguish and the organized violence of the sport. See how an ice cube melting in the hollow under Jake’s belly button as he lies in bed with Vickie is recalled by the washed-off blood streaking past his waistband in the ring. His embrace of a woman and his visiting violence upon a competitor are linked implicitly. And in a disturbing fictional echo of Ring of Fire’s real story, homophobic slurs are constant: Jake tells his brother Joey that he “throws a punch like he takes it up the ass.” There’s a needling sense that all is not well in the world of Raging Bull’s gender relations, and it articulates hetero-masculine anxieties around sex and sexuality in a fashion that points toward something deeply rotten in the machismo of its men.

For as long as the fight game endures, its screen depiction carries weight because of its ability to put our notions, fears, and fascinations into gladiatorial physical form, all in the microcosm of the ring. The stories it can hold between those ropes are tragic, triumphant, disturbing, and manifold. Or could their appeal really be something more primal? As former Tyson trainer Teddy Atlas once remarked, “People are full of shit. They want to see something dark.” Perhaps that is why, long after it is forever flung into the bad old days, its screen stories remain impossible to shake from memory.