Battle of the Sexes is almost by definition predictable — the outcome of its title tennis match is well known — but there was one scene that made my jaw drop.

It's the early 1970s, and Billie Jean King (Emma Stone) is listening as the head of tennis' governing body goes over a tournament's prize money — $12,000 for the men's winner, he says, $1,500 for the women's.

That disparity is monumental. But so too is the disparity between that 1973-era cash and the compensation tennis players receive today. The winner of the U.S. Open received $3.7 million — the prize money is now the same for men and women. And ratings, by the way, were higher for the women's final.

Those numbers are a happy postscript to the fight that Billie Jean King started more than 40 years ago, as depicted here. She believed that women's tennis could be as entertaining as men's tennis, that fans would be just as interested, that pay scales should reflect that. Tennis commissioner Jack Kramer (Bill Pullman) did not agree, so King, as we see here, spearheads a separate tour for women, with the indispensable sponsorship the help of Virginia Slims cigarettes, which the women do their best to pretend to smoke.

Battle of the Sexes shuffles along with this underdog sports movie narrative. King and her sister players barnstorm — making radio appearances, handing out fliers, selling tickets at intersections, conducting clinics. These scenes have a DIY appeal, the '70s fashions are fun, and Sarah Silverman gets laughs tossing off barbs as the ladies tour's brassy manager.

But the tour needs a boost, which it gets in the form of a self-described male chauvinist pig — aging former men's champ Bobby Riggs (Steve Carell), now 55 and a debt-ridden gambling addict, a hustler looking for a big score. He proposes a match with top-ranked King, with a winner-take-all pot of $100,000.

Battle of the Sexes is not sure what to make of Riggs. It's not really clear that he believes a word of what he says. Sexist or not, Riggs works tirelessly to promote (and brand and merchandise) the match, which ends up being a huge ratings success, and a symbolic confirmation of King's goals and ideals. Also a template for how the sports industrial complex operates on a massive scale today — one reason why the prize money has grown exponentially. You could say that "chauvinist" Riggs is one of the best friends women's tennis has ever had, also an accidental genius who foreshadowed the hucksterism of reality TV — ironies the movie leaves unexplored.

King's side of the story is marked by her sexual awakening. She's having her first lesbian relationship (with a hairdresser, played by Andrea Riseborough), creating deeply confusing feelings for her devoted husband (Austin Stowell), and putting her for the first time in the closet — she knows it's a make or break moment for the ladies tour, and senses her affair would destroy what she's trying to build.

She's under enormous pressure — the word Kramer keeps using to justify structural inequality. Women can't handle pressure, he insists — it's why they will never be paid equally, or hold top jobs in business and politics.

Did he really say that? And did he say it while swirling brandy in a snifter, and smirking?

The movie is often clumsily scripted, and given to caricature, which Carell and Stone manage to transcend. The best, most telling dialogue seems to be archival — snippets of Gollum-like broadcaster Howard Cosell, his arm around his female co-commentator, oafishly telling her how pretty she is. When King hits a winner and strides away, he says "now she's walking like a man."

You've come a long way, baby.