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Consider Brandon Gray of Box Office Mojo unimpressed by “The Undefeated’s” opening weekend.

“Maybe it did very well at a few theaters. It’s nothing to write home about. Even among political documentaries, it’s still not in the top tier,” Mr. Gray says. “Maybe they didn’t spend money on publicity, but they didn’t need to there were a lot of articles and news stories about this leading up to its release.”

Karie Bible, an analyst with L.A.-based Exhibitor Relations, says the film’s social media marketing approach meshed with the film’s content.

“You get one person who’s a Sarah Palin fan, and they can reach all kinds of people,” Ms. Bible says. “It’s a very inexpensive, highly effective way to get the word out.”

But social media can’t replace traditional ad buys, the kind that bring awareness across audience demographics. If “The Undefeated” preaches to the choir, so does Facebook.

The film’s true test may come this weekend as it rolls out into additional AMC Theaters in Tucson, West Palm Beach, Fla., Milwaukee, Charlotte and Ontario, Calif. while playing in more movie houses in Atlanta and Phoenix.
By Monday, movie analysts may have a better feel of just how “Undefeated” Mrs. Palin’s documentary truly is.

• Additional reporting for this story by Valerie Richardson.