“It’s the latest freak show out there,” explains Frankie Dunn (Clint Eastwood), for why he refuses to train a female boxer and why she shouldn’t have any trouble finding someone else who will.

The fact that he believes the 31-year-old Maggie Fitzgerald (Hilary Swank) is too old for the sport doesn’t help matters. But the moonlighting waitress won’t take no for an answer.

Repeatedly working into the wee hours at Frankie’s Hit Pit Gym gains Maggie an ally: Eddie “Scrap-Iron” Dupris (Morgan Freeman), a former contender who now manages the place. Under Eddie’s prodding, Frankie caves and decides to help sculpt this new fighter into a champion.

And so goes a setup that could lapse into what studio suits might pitch as “like ‘Rocky’ … with a girl!”

Yet “Million Dollar Baby” turns into a movie fully removed from the trite trappings of the sports genre. This film is a dramatic powerhouse, thanks to a jarring third act that explores themes far darker than “overcoming adversity” or “going the distance.”

The project scored seven Academy Award nominations on Tuesday, making it a co-frontrunner along with Martin Scorsese’s “The Aviator.” While “Million Dollar Baby” seems somewhat “small” by comparison, it’s the most emotionally resonant of the Best Picture nominees (which also include “Sideways,” “Finding Neverland” and “Ray”).

Four-time Oscar nominee Eastwood gives one of his finest performances. The 74-year-old legend (who also directs) is more craggy voiced and confrontational than ever. Some of his choicest moments are the smaller ones, whether he’s engaging in antagonistic conversations about religion with his long-suffering priest (Brian O’Byrne) or scolding the hazy-eyed Eddie about the holes in his socks.

Fellow Oscar veteran Swank is restrained in a role that could be played as flashy. She renders Maggie as a person who is — outside of boxing — fairly unexceptional. Her very averageness grants the heroine credibility. Moreover, the actress really looks comfortable (and formidable), whether pummeling a heavy bag or decking an opponent.

Hilary Swank plays 31-year-old Maggie Fitzgerald, a female boxer begrudgingly trained by Frankie Dunn (Clint Eastwood), in the Oscar-nominated Million

No body doubles needed here.

As with Eastwood’s been-through-it-all-before character, there’s a lived-in feel to the movie. Every locale has a slightly dilapidated quality, and the picture’s somber colors conjure the gritty feel of ’70s indie cinema. But Eastwood also revels in light and dark extremes. There are enough shots of people half-obscured in shadows to fill a film noir from the ’40s.

“Million Dollar Baby” isn’t a perfect movie. Eastwood has always proved susceptible to coddling extraneous plotlines. Witness last year’s overpraised “Mystic River” and the ludicrous character played by Kevin Bacon’s estranged wife, who phones him at random and listens in silence.

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Similarly, a lot of footage is spent at the gym on Danger (Jay Baruchel), a scrawny, white, wannabe boxer who is all mouth. This individual would be right at home providing comic relief in a teenage sex comedy, not an Oscar-bound drama. Fortunately, Danger’s role has more of a payoff than the spectral wife in “Mystic River” because it at least sets up a crowd-pleasing moment with Freeman.

Also handled rather clunkily is Maggie’s family. Hailing from southwestern Missouri, no less, the Fitzgeralds represent everything a native Californian like Eastwood fears about the Midwest. It’s an ugly depiction of them as overweight, tattooed, welfare-grubbing, anti-intellectual trash who don’t have a single redemptive trait.

Clint Eastwood, left, and Morgan Freeman study a fighter from ringside in the drama Million

These are secondary distractions, though, in a film that nails all the primary elements: acting, emotion, realism, mood, unpredictability and a thematically pure ending.

In the early narration, Freeman intones, “Boxing is an unnatural sport. Everything about it is backward. Sometimes the best way to deliver a punch is to step back.”

That certainly applies to the subtle “Million Dollar Baby.” Sometimes the best way to deliver a cinematic punch is to step back.