Conviction opens on a crime scene. It’s 1980 in Ayer, Massachusetts, and the camera passes through a house trailer, past blood stains on walls, the refrigerator, and the bed. A woman’s body lies on the floor, her limbs flailed, her face obscured.

It’s a gruesome image, even harrowing as long as it’s on screen. But this dead woman, stabbed 30 times, is not the movie’s focus. The next scene sets out what is, namely, the plight of Kenny Waters (Sam Rockwell), wrongly convicted of the murder in 1983, and, even more insistently, the heroism of his sister, Betty Anne (Hilary Swank), who went to law school in order to free him.

Their story is astounding, of course, a test of her commitment and his faith, a saga of the hardships endured by both. And Conviction italicizes all that’s astounding, not only about the siblings, but also about the repeated failures of the social, legal, and penal systems they defied and also, in her case especially, engaged. That engagement is evident in Betty Anne’s first scene: she’s in law school, in class in fact, answering a question that inelegantly establishes the film’s thematic focus. Asked to define “contract, ” she declares, “When it’s breached, the law provides a remedy.”

Or, as happens here, when the law does not provide a remedy, you’d better pray you have a sister who will pursue one—relentlessly. Here she does so against all imaginable odds, from underclass background to resentful husband (Rick [Loren Dean]) to confused sons. This is Betty Anne’s melodrama, earnest, affecting, and of a piece with the sorts of films Swank has been making lately (like, since Boys Don’t Cry), where she’s the hardworking, admirable, and ever sensitive underdog. Here, Betty Anne works so hard that she falls asleep on her desk, but still finds a way to listen to her son’s poem about peace in the world, and get him and his brother to school with homework done. She works so hard at so many things that she actually delivers her own paper, the one she fell asleep over, 30 seconds late, which makes clear (again) the insensitivity of all those systems, here represented by the inflexible instructor won’t take it.

It’s only 10 minutes into the film, and you know its narrative and thematic gist: Betty Anne is excellent, and she will persevere despite arcane rules, unsupportive peers, and unimaginative supervisors.

Surrounded as she is by detractors, the film submits, Betty Anne’s devotion to Kenny is understandable. So that you fully understand, Conviction provides flashbacks to their appalling childhood: essentially abandoned by their self-absorbed mother, the kids break into people’s houses to pretend to have one, eat candy, suffer beatings and emotional abuse. Through it all, they are defiant, devoted to one another, and plainly damaged. The siblings only have each other (even when they grow up and have spouses, briefly) and share a sense of dread, their world shaped by pain, danger, and tragedy.

The worst does happen when Kenny is picked up and accused of the murder, based on a case apparently contrived by Ayer police officer Nancy Taylor (Melissa Leo), the movie’s primary villain. Unpleasant and perpetually irritated, Nancy has no background here (in real life, she testified falsely that there were no usable fingerprints at the crime scene), only a vaguely sketched animus against Kenny.

You might say that Nancy’s generalized hostility parallels Kenny’s, both indignant about their underclass privations. But the film sets Nancy as Kenny and Betty Anne’s opposite: unlike the children’s reasonable acting out, hers is bad. To reinforce Betty Anne’s good, the film provides her with a friend (or more precisely in this film’s construction, a sidekick), a fellow law student named Abra (Minnie Driver), as well as, eventually, an ally in Barry Scheck (Peter Gallagher), from the Innocence Project. As it turns out, when Betty Anne graduates from law school, she has a revelation—one of those awful movie-style revelations where the music comes up and the camera zooms: technology has made DNA into evidence, 15 years after her brother’s incarceration, and as wondrous as that actual new possibility is, the film overkills it.

Overkilling is something of a pattern in Conviction, from Betty Anne’s fights with Rick and Abra to Kenny’s aging makeup to the surprisingly terrible moment when Betty Anne and Barry confront a witness in the original case, Roseanna Perry (Juliette Lewis), and she confesses all, in a spectacularly white-trashy way. Remembering just how much she was pressured to lie to the court, she wails, “Ah was railroad!”

However real the story on which Conviction is based, such scenes are debilitatingly unreal. It’s not only a question of too convenient plotting regarding Betty’s quest, but also a general disregard for Kenny’s experience in prison (reduced to glimpses of his depression when Betty Anne visits and insists he buck up, because, after all, she’s sacrificed everything for him). As Betty Anne’s story overwhelms his, the film relies on class and, somewhat less conspicuously, gender stereotypes, both to derogate the bad woman cop (and the bad woman witness) and to celebrate Betty Anne, who triumphs over her environment rather than succumb to it.