Here is a Netflix documentary with a real story to tell: the giant friendship and frenmity (or frivalry) between Chris Evert and Martina Navratilova, the two titans who throughout the late 70s and 80s dominated international women’s tennis and did so much to boost the sport whose existence, incidentally, helped to silence certain sexist reactionaries who doubted the feasibility of women’s football. The film shows us their intense relationship now, supporting each other as they both go through the challenge of cancer.

It’s a highly watchable film, which makes the strong and valid point that even in the cutthroat world of professional sport there is, in fact, room for real friendship and “sportsmanship”. But it leaves open the suspicion that the friendship between Evert and Navratilova, though perfectly genuine, may be a little more complicated than it looks here. And the dual storyline tilts the balance, just a little, away from the side of the story which for me is more compelling: the extraordinary drama of Navratilova’s courageous defection in 1975, when she was just 18, from communist Czechoslovakia to the US. She knew that she might never see her mother or sister again, and for a while faced the real threat of abduction by Soviet or Czech security forces. (Nureyev was 23 when he defected, chess star Victor Korchnoi 45.)

So what does an 18-year-old do, without family, in a strange land? The answer appears to be: find an alternative, supportive, sisterly family in the world of women’s tennis, a world that Evert and Navratilova perhaps experienced differently, being respectively straight and gay.

The movie takes us through the ups and downs of the Chris and Martina relationship: the early, uncomplicated friendship and doubles partnership, the tough break when Chris focused more on her career, a period of icy estrangement, and then their growing reconciliation as they embraced joint international treasure status. We hear from other stars, including Pam Shriver and Zina Garrison who were shut out by the Evert/Navratilova duopoly – and, of course, from John McEnroe.

As ever with American documentaries about tennis, I smile at the British pop-culture legends who pop up, presumably without American viewers noticing; we hear the voice of BBC commentator Dan Maskell calling Navratilova “the best lady player we’ve ever seen” and keep seeing the beamingly ethereal and enigmatic Duchess of Kent handing over the Wimbledon trophy.