It is 2019 and cheerleaders are still a thing in the National Basketball Association. The Chicago Luvabulls. The Memphis Grizz Girls. The Charlotte Honey Bees. And this is the N.B.A., the most progressive league in professional sports, with the most enlightened commissioner. The good news is that the best broadcaster in the game is Doris Burke. This has been the case now for years. There is no one remotely close.

As a basketball analyst for ESPN and ABC, Burke is the smartest, best prepared, most original on-air voice that the game possesses. She is as insightful about the stratagems taking shape on the court as she is about the emotional currents in the locker room. The question, then, is: Why is Burke relegated to being a role player, doing hurried sideline and post-buzzer interviews during the Finals while the announcers Mike Breen, Mark Jackson, and Jeff Van Gundy are left to dominate the airwaves at courtside?

You can be sure that when Game 6 of the Finals begins, Burke will know more than anyone about the murkiest subplot so far in the series between the Toronto Raptors and the Golden State Warriors: What’s the story with Kevin Durant? Why did he play hurt in Game 5, and who, if anyone, should take the blame for his ruptured Achilles, an injury that could put him on the sidelines for a year and cost him untold millions of dollars as a free agent?

Van Gundy has called Burke “the LeBron James of sportscasters.” A former high-school and college point guard, Burke, who is fifty-three, has been studying the intricacies and evolution of basketball for decades. It was once said of Ginger Rogers that she did everything Fred Astaire did, only backward and in high heels. Ditto for Doris Burke. My favorite video clip of her shows her walking along a waxed N.B.A. court in high heels, carrying papers and a notebook in her left hand while dribbling a basketball with her right. Suddenly, she swings the ball around her back and picks up the dribble with the same right hand. Steph Curry could not have done it much better—and let him try it in heels.

James, Durant, Curry—everyone in the league seems to respect Burke and to await her inquiries about the game or the state of their spirits (elated or crushed) with genuine esteem. Real fans do, too. Burke’s interviews are passed around online as treasured memes. In 2016, at a game in Toronto, Drake, a crazed courtside Raptors supporter, wore a T-shirt emblazoned with Burke’s picture and the phrase “WOMAN CRUSH EVERYDAY.” Deadspin has pronounced Burke “the best damn basketball broadcaster there is.”

Burke’s style is hardly flamboyant. She doesn’t have a memorable or eccentric voice like Johnny Most or Marv Albert, and she doesn’t do shtick. Burke is earnest, prepped, serious. She goes at the work the way that Elizabeth Warren has been going at the Democratic primary campaign. She is determined to succeed on the basis of substance, agree with her or not.

There are many (depending on your definition of “many”) women working now as play-by-play and color commentators in the N.C.A.A., N.B.A., N.F.L., and M.L.B., but it has not been even remotely easy for women in the business to get past the old prejudices. Bill Simmons, a gifted basketball writer and sports podcaster, and hardly a dinosaur of the Dick Young era, wrote about Burke on ESPN.com, in 2008, with a condescension he’d grow to regret: “She’s doing a fine job, but does it make me a sexist that I can’t listen to Doris Burke analyze NBA playoff games without thinking, ‘Woman talking woman talking woman talking woman talking . . . ’ the entire time?” A decade later, Simmons answered his own question, saying that Burke was, in fact, a “fantastic analyst” and that it was “embarrassing” that she was working the sidelines during the playoffs.

There is a long history to all of this. For half of forever, women had a nearly impossible time breaking into sportswriting and broadcasting, suffering endless indignities and worse. In 1978, Melissa Ludtke, of Sports Illustrated, brought a lawsuit against the M.L.B., which was resisting her right to report the baseball beat with equal access to locker rooms, clubhouses, and other malodorous sacred places.

Leigh Montville, a sports columnist for the Boston Globe, interrogated Ludtke’s right to be in baseball clubhouses. “I have only a few questions for the lady,” Montville wrote. “I don’t care about all the wink and leer jokes about a grown woman going into a room where grown men are undressing. I just want to know if the lady is doing this job because she really wants to do this job…. Is she for real? Is she serious?” And then came a long litany of qualifying questions: “Did she ever spit in a baseball glove? Was her life absolutely dominated by sports when she was a kid?” And on and on he went.

Ludtke said at the time that most people understood her case as “girls wanting to go into a locker room and see men naked” rather than one of equal access. She won in court. But even after that decision, Jerome Holtzman, of the Chicago Sun-Times, who was one of the best-known baseball writers of his era, was resistant to the change. “I suppose the fact that this was an all-male world was what made it so exciting to me at first,” he told Roger Angell, of The New Yorker, for a piece from 1979 called “Sharing the Beat.” “And now that it’s being invaded and eroded it’s much less attractive. Maybe I’m a chauvinist—I don’t know. The press box used to be a male preserve—that was its charm. I’d rather not have a woman as a seatmate at a World Series game. It wouldn’t be as much fun. I’ve never met a woman who knew as much baseball as a man.”

But things changed all the same. Not long after, in the mid-eighties, I was a rookie on the sports staff of the Washington Post, a department run by George Solomon and featuring Tony Kornheiser, Tom Boswell, Michael Wilbon, and Dave Kindred—and Jane Leavy, Christine Brennan, and Sally Jenkins.

Jenkins, a rigorous reporter and a witty writer who still does a regular column for the Post, told me that as recently as last year the beat writers for all four of the pro sports teams in D.C. were women. “The thing is that in sportswriting the breakthroughs came at least twenty years ago and more,” Jenkins said. “But television sports has far more trip wires than sports journalism. Sports TV is still Wall Street. And there is no real change unless there is mandate from a guy on high. All the breakthroughs—and here you can name whatever women behind microphones—are decisions made by a single man at the top who wants to be Branch Rickey.”

On sports television, the early breakthroughs included Mary Carillo, Lesley Visser, and Robin Roberts. But women are all too often still judged by their looks. “Are they attractive enough? But if they’re too attractive, then maybe you’re a Twinkie,” Jenkins said. And their voices, too. Are they “shrill” or “squeaky” or do they sound like “your first wife in divorce court”? Which sounds awfully familiar to anyone who followed the Clinton campaigns, in 2008 and 2016, or those of the many women running now.