Tis the season for biographical movies that stuff and mount their famous subjects like objects in a museum display. In the case of The Young Victoria (coming at Christmas), this reverent approach makes for a gorgeous bore; we quickly learn that what Queen Victoria wore in her youth was more interesting than anything she did.

Clint Eastwood’s Invictus has more going for it. As a character study of presidential-era Nelson Mandela (played by Morgan Freeman), it offers little viewers won’t expect. (At one point, the film’s white protagonists actually visit the museum on Robben Island to educate themselves about their leader’s time in prison. Thanks for the lesson, Clint!) Still, Invictus tells the compelling tale of a turning point in the history of South Africa, one with which many Americans are unfamiliar. Given this rich and inspiring material, it’s a pity Eastwood didn’t manage to make the movie less boilerplate.

It starts with an ominous vignette set in 1990, when blacks in South Africa were celebrating Mandela’s release. “What’s happening?” a white teenage rugby player asks his coach. “Our country’s going to the dogs,” the adult replies.

When he takes office as president in 1994, Mandela needs to demonstrate to his people — all of them — that a “Rainbow Nation” is actually stronger than a society under apartheid. Canny politician that he is, he understands that sports can help cement that sense of national unity. Whites and blacks may not feel they share many interests, but they do share a sucky rugby team.

So Mandela sets out to turn the Springboks, weakened by years of being banned from international competition, into the winners of the 1995 World Cup. First he has to defeat the skepticism of black South Africans, who know the team is beloved by Afrikaaners and hence cheer for whoever is whupping it.

Mandela also has to win over the team’s coach and members, depicted here as a bunch of upstanding young fellows — especially strapping captain François Pienaar (Matt Damon, bulked up with an accent). Soon the players are coaching township kids to build good will. On the field, they’re practicing as hard as they can to prove the truth of Mandela’s favorite Victorian poem, William Ernest Henley’s “Invictus”: “I am the master of my fate:/ I am the captain of my soul.”

Even for those unfamiliar with the facts, the outcome of this story is never in doubt. But did it have to be told in such a blandly uplifting way? Anthony Peckham’s screenplay never met a soundbite it didn’t like. The only character who seems even capable of complexity is Freeman’s dignified, gently witty Mandela: Everyone else in the movie exists either to resist him or (more often) to fall in love with him. Despite getting top billing, Damon has nothing much to do beyond gritting his teeth as he assures his teammates that winning is “our destiny.” Does Pienaar have private hopes and fears? We never find out.

Maybe that’s the problem with basing a film on recent history: A writer can’t take liberties with people who are still alive. Still, it’s tantalizing to imagine what David (“The Wire”) Simon might have done with this saga of behind-the-scenes politicking in a hotbed of racial and economic tensions. He certainly wouldn’t have poured syrupy music over the movie, the way Eastwood does. He would have shown more of the intriguing interplay between Mandela’s long-time entourage and the Afrikaaner bodyguards he inherited from former president F.W. de Klerk. And Simon might have reminded us that even the most admirable leader sometimes has to play dirty to win.