The 1973 tennis match between Billie Jean King and Bobby Riggs, portrayed at the time as a clash between the blossoming feminist movement and resistant male chauvinist piggery, is the culmination of this period comedy-drama by directors Valerie Faris and Jonathan Dayton. But though Steve Carell gets a substantial amount of screen time as Riggs, “Battle of the Sexes” is actually a love letter to King—the tale of her emergence not only as a great player but as a person at ease with who she is. Only the second film that Faris and Dayton have made in more than a decade since “Little Miss Sunshine” in 2006 (the other was the underrated “Ruby Sparks” in 2012)—they seem to work with Kubrickian deliberation—it’s a solid lob, but not the grand slam one might have hoped for.

As played by Emma Stone, fresh from her Oscar-winning triumph in “La La Land,” King begins and ends the film. She starts by protesting the decision of US Lawn Tennis Association head Jack Kramer (Bill Pullman, excellent), an unquestionable troglodyte when it comes to female equality, to offer vastly different purses to male and female victors in an upcoming tournament. When he refuses to reconsider, she and her manager Gladys Heldman (Sarah Silverman, really getting into the spirit of things as a hard-nosed Roz Russell type), decide to create a women’s league that will host their own event, and convince the other top players to join them. When Heldman secures the sponsorship of the cigarette company, it becomes the Virginia Slims tour. In all this King has the unstinting support of her handsome hubby Larry (Austin Stowell).

But just as the Women’s Tennis Association is taking shape, Billie encounters pleasant blonde hairdresser Marilyn Barnett (Andrea Riseborough) and is immediately smitten, bringing her attraction to women to the fore. The two begin a hesitant but torrid relationship in Larry’s absence, which upsets King’s concentration and leads to her loss of the top female ranking to her rival, Australian Margaret Court (Jessica McNamee), who coolly deciphers the women’s mutual interest and takes advantage of it. (She’s also the only player whose husband and infant accompany her on the circuit.)

Meanwhile Riggs, stuck in what he considers a stifling marriage to wealthy Priscilla (Elisabeth Shue, underused), who demands that he curb his gambling, and a boring desk job in his father-in-law’s firm, has come up with the notion of challenging the women’s champion to a match to prove—as he sees it—male superiority in tennis, and everything else. (Of course, the fact that it will also bring in a ton of money is an added inducement.) King had already turned the 55-year old, a former tennis great now struggling on the senior circuit, down, but Court falls for his line and wilts under the match pressure. With Riggs now crowing about male superiority, King feels that she must take up the cause herself, and the famous battle is on, even as King’s personal life grows increasingly complicated and Riggs’s marriage unravels.

Stone anchors the picture with a performance that’s far more than a physical impersonation, though it’s quite good in that respect. She captures the uncertain emotions that King must have experienced during this tumultuous period when she faced, for the first time, what her real sexual inclinations were and inched toward liberation off the court as well as on it. (The observations of Alan Cumming, the gay fashion designer for the WTA, are a bit on-the-nose, but the actor’s presence is always welcome.) Riseborough and Stowell add solid contributions as the two people with whom she feels a profound connection, though in different ways.

Carell, meanwhile, provides the laughs that give contrast to Stone’s most serious story. He eagerly seizes on Riggs’s gleeful con-man persona, though he also manages to add a touch of poignancy to Riggs’ fraught relationship with his wife and his rebuilding of one with his grown son (Lewis Pullman), who serves as one of his trainers. At times one actually feels sorry for the guy, who exudes false confidence as he consumes pep pills provided by a shady promoter (Fred Armisen) and tries to enlist Kramer as an on-camera TV commentator on the match in an effort to rattle King. It doesn’t work, of course.

Faris, Dayton and editor Pamela Martin insert bits and pieces of archival footage into the mix (including excerpts from commentary by Howard Cosell, no less—who at one point even has been visually manipulated to make him appear to drape his arm around actress Natalie Morales, as player/commentator Rosie Casals) to boost the authentic look, and along with production designer Judy Becker and costumer Mary Zophres the directors work to achieve a convincing period feel without over-exaggerating it. (Those early seventies fashions could be really ugly.) The background score by Nicholas Britell, but with pop tune appearances, contributes to the atmosphere as well. Cinematographer Linus Sandgren’s camerawork is generally unostentatious and straightforward, but he comes into his own in the match sequences, where the efforts of CGI artists obviously play a role as well.

“Battle of the Sexes” will be a pleasant nostalgia trip for viewers of a certain age, affording them an opportunity to revisit the silly hullabaloo of an event from a time that was simpler, if not necessarily more innocent. It also serves as a not always subtle reminder, at this time in American history, that the issues of female equality and sexual orientation that a mere tennis match raised nearly half a century ago are still with us.