Christopher Bird’s review published on Letterboxd :
BATTLE OF THE SEXES reminds me a lot of HIDDEN FIGURES in that it is an earnest, competently made historical drama/dramedy that doesn't really hit the mark of being a great film.
To be clear: SEXES is better than HIDDEN FIGURES was. The latter film was shot competently and told a story without really digging into the interior life of its focal characters; SEXES is shot competently with occasional flourishes of brilliance, and there's at least a solid attempt to try to dig into the deeper emotions running through Billie Jean King's closeted homosexuality. Bobby Riggs' storyline, about his dealing with his gambling addictions and his need to hustle all the time, isn't bad but is markedly less successful. The choice to depict his wife finally deciding to leave him and then just coming back at the end harms the film, even if that's what happened in real life; they needed to find a better way to tell that story, and the Riggs portions of the film drag down the movie as a whole even if they aren't bad in and of themselves; they end up feeling superfluous to the story as a whole. The story is about someone dealing with the double whammy of sexism and homophobia; giving Riggs' B-story too much weight unbalances the movie.
That having been said, it gets a lot of stuff right - Margaret Court is an asshole, Larry King is basically a good dude suffering in a terrible position, Ted Tinling's existence is actually addressed (dude had a fascinating life - he was a spy in WW2!), and the staggering sexism that pervaded and pervades every element of American life is omnipresent, like a blanket made of shit. And it has a roster of good performances: Emma Stone is excellent, Steve Carell very solid, Alan Cumming and Sarah Silverman endlessly fun, with good turns from Elizabeth Shue, Bill Pullman, Natalie Morales, Austin Stowell and Andrea Riseborough as well.