An important fact-based story is turned into an unabashed star vehicle in “Concussion,” in which Will Smith does for Nigerian-born forensic pathologist Bennet Omalu, who first raised questions about the long-term physical dangers to players posed by football head injuries, much the same thing that Cuba Gooding, Jr., did for Ben Carson in the TV-movie “Gifted Hands”—turn him into something of a saint. That’s not to say that Omalu isn’t a good guy, or that Smith—who showed his facility at mimicry in Michael Mann’s “Ali”—doesn’t capture his vocal inflections and courtly manner. But writer-director Peter Landesman’s account of the physician’s battle with the NFL devolves into an earnest, well-meaning combination of character study, medical procedural and corporate thriller that rarely rises above the standard of conventional TV docudrama, despite the presence of an outstanding supporting cast.

Omalu is introduced as a highly educated, talented pathologist working in the Pittsburgh morgue, where he soothingly talks to the corpses whose cause of death he’s assigned to investigate and occasionally appears in court to explain why some poor soul had been erroneously convicted. One case particularly piques his interest, that of former Steelers star center Mike Webster (David Morse), who suffered a catastrophic mental breakdown and died homeless in his car at age fifty. Paying for elaborate tests himself, Omalu concludes that Webster’s brain showed severe neurological deterioration that led to Alzheimer’s-like dementia, and begins an investigation of whether other players have exhibited a similar condition. On the basis of his admittedly limited research, he publishes an account of his findings on the effects of the repeated head trauma suffered by football players in a medical journal, calling the disorder C.T.E, or chronic traumatic encephalopathy.

The NFL immediately ratchets up its considerable muscle in response to the article, and Omalu’s supportive boss Cyril Wecht (Albert Brooks) advises him to be cautious, reminding him, in the movie’s single best line of dialogue, that he’s up against a virtual religion in the form of “a corporation that owns a day of the week—the same day the church used to own.” Still Omalu soldiers on, finding an ally in Julian Bailes (Alec Baldwin), a former Steelers team doctor who’s witnessed the effects that the pathologist is studying in former players he’d treated and is privy to evidence that the NFL establishment had known of the game’s physical effects for years but had failed to act on it.

Meanwhile Omalu becomes romantically involved with Prema (Gugu Mbatha-Raw), a recent Nigerian immigrant whom the physician is asked by his church to host in his spare room until she can find a job and a place of her own. After an appropriate courtship, they marry and plan to move into a suburban house with the child they’re expecting, but the controversy over his work on C.T.E will undermine their personal dreams. It’s only after years of refusal to admit the validity of Omalu’s findings that the NFL leadership, now headed by Roger Goodell (Luke Wilson), and prodded by increasing numbers of cases (including some involving the corporation’s own executives, former players themselves like Dave Duerson, played by Adewale Akinnuoye-Agbaje), accepts his research, begins to negotiate proper compensation for players, and takes steps to alleviate the dangers the game poses.

Using Jeanne Marie Laskas’ Gentlemen’s Quarterly article “Game Brain” as a basis, Landesman, a former journalist himself, manages to fit the various plot strands into a workable if somewhat lumpy narrative, but he resorts to some narrative turns that are simply manipulative and lead nowhere. At one point, for example, Prema thinks she’s being trailed by another car while driving home; she loses the supposed tail, but it’s never made clear whether her fear was justified or not. Similarly, Dr. Wecht gets a visit from the FBI that threatens his position and could lead to prison time. The implication is that the NFL is behind the investigation, but there’s no evidence presented for that, and we’re simply informed that the charges against him (actually for public corruption) were subsequently dropped, though in fact he was tried, but not convicted. Controversy had also erupted over the film’s characterization of Duerson as a corporate shill who berated Omalu and cruelly brushed off a former teammate suffering from C.T.E. His family has bitterly complained about his being turned into a villain without any corroboration.

On the other hand, while his direction doesn’t have the nimbleness that a different hand brought to his previous fact-based script (Michael Cuesta on “Kill the Messenger”), Landesman, as in his only previous helming effort “Parkland,” about the Kennedy assassination, does show skill in dealing with a large ensemble cast. He puts the spotlight on Smith, of course, sometimes too much: we might have well done without the sequence in which Omalu, his funds running out, vandalizes the dream house he’s been building for himself and his family, which has become a familiar cliché even since Orson Welles used a similar moment in “Citizen Kane.” But the lovely Mbatha-Raw has her moments as Prema, and Baldwin is especially effective as Bailes, even if his accent sometimes slips. Even more impressive are Morse, who creates a fearlessly honest portrait of a man on the edge of disaster, and Brooks, who, simply by bringing his patented low-key charm to Wecht, effortlessly steals every scene he’s in. Vets like Arliss Howard, Eddie Marsan and Paul Reiser make brief but vivid impressions as doctors, but it was surely a mistake to cast Wilson as Goodell; not only isn’t he a good fit for the part, but his on-screen moments are so few that so identifiable an actor is more a distraction than a help.

“Concussion” is well-made, from a technical standpoint, but again the craft contributions (Salvatore Totino’s cinematography, David Crank’s production design) are more conventional than imaginative. And perhaps a lack of cooperation from the NFL explains the relative paucity of on-field footage to convey the brutality of the hits that players take. Further demerits for James Newton Howard’s score, which doesn’t so much incline to brassiness as embody it.

Landesman’s film is based on an important—and still very topical—story, but could have used a better game plan to tell it.