Days before Wimbledon, the trailer for a tennis film came out: Battle of the Sexes. It is based on a true story, one you may already know. In 1973, 55-year-old Bobby Riggs, a former world No 1, took on Billie Jean King, who was 29 and the dominant female player of the time. Much of the contest was razzle-dazzle spectacle: Riggs entered the court in a rickshaw pulled by models; a coterie of topless men carried King on a gold throne. But the $100,000 match itself, watched by 30,000 in the Houston Astrodome stadium and 90 million on television, was a serious business – something shown by the fact that it is still being talked about 44 years later.

The film, to be released in October, looks great fun. Oscar-winner Emma Stone plays King, and Steve Carell seems a perfect fit for the hammy chauvinist Riggs. Like Austin Powers or Anchorman, Battle of the Sexes will be a snapshot of how far attitudes have changed. Riggs’s assertion that women belong in “the bedroom and the kitchen” will probably get a good laugh now. In 1973, King was fighting in part for women to receive equal pay to men in grand-slam tournaments. That has existed now across those four events for a decade.

But, scratch the surface, and Battle of the Sexes is still relevant to tennis. And Wimbledon 2017 has provided further evidence for those who believe we have not moved on so much from the days of King and Riggs.

The debate started, on the eve of the tournament, when John McEnroe made the claim that Serena Williams, who has won 23 grand-slam singles titles, would rank “like 700” on the men’s circuit. The BBC dutifully tracked down Dmitry Tursunov, the men’s No 701, and he said sure, he’d fancy his chances.

Bobby Riggs, 55, poses with Billy Jean King, 29, ahead of their 1973 showdown in Houston, which King won in straight sets. Photograph: Bettmann/Bettmann Archive

You could argue this was a silly hypothetical. Williams, and her sister Venus, have for a long time shown little appetite for this battle. At one point the current US president was the pitchman: in 2000, Donald Trump said he would offer $1m prize money for a match between McEnroe, then 41, and either of the Williams sisters. Venus responded at the time with exemplary courtesy: “I don’t think it’s fair to put a 20-year-old against a fortysomething person. So, I’ll let that pass.”

Serena was equally polite and unenthused on Twitter about the latest match-up. She’s pregnant, so not at Wimbledon, and these days she is less interested in discussing whether she would beat an average male player than she is in talking about equal opportunities off the court. She was recently made a board member of Survey Monkey, the tech company, having been put forward by Facebook chief operating officer Sheryl Sandberg.

“Silicon Valley is really, really, really not open yet to having a lot of women or anyone of colour, male or female,” Williams said at a SheKnows Media conference last month. “Those two barriers alone are really things we have to break down.”

Back at Wimbledon, there was a less conspicuous, but perhaps more damning snub to women’s tennis last Monday. Manic Monday is a Wimbledon tradition: all of the last 16 in the draw, both male and female, are in action on the same day. It is wildly popular with spectators: for a £25 ground pass, you can see the best players in the world in the intimate surrounds of the outside courts. The queues this year began to form on Saturday morning.

But Manic Monday is also a nightmare for the scheduling committee. They can only fit six matches on the Centre and No 1 courts, so a lot of world-class players are going to be sent out in the sticks. Jelena Jankovic, a former world No 1, once huffed that she “needed a helicopter” to get to Wimbledon’s furthest-flung courts.

This year, a disproportionate number of those athletes were women. On No 2 Court, the No 1 seed Angelique Kerber, a Wimbledon finalist in 2016, took on Garbiñe Muguruza, who reached the final in 2015 and again this year. On modest No 12 Court, Jelena Ostapenko, the new star of women’s tennis who is fresh from winning the French Open, played Elina Svitolina, the fourth seed. Manic Monday was so topsy-turvy that even Anna Wintour, the editor-in-chief of US Vogue, was spotted on No 3 Court.

Kerber, after losing a gripping three-set match against Muguruza, said that she might speak privately to the Wimbledon organisers about the court allocation. Ostapenko said, simply: “I think our match was a very interesting match for the people to watch. And they put us on Court 12.”

Wimbledon’s schedulers pleaded that they were “spoiled for choice” and they simply couldn’t justify, emotionally or financially, putting one of the Big Four men – Roger Federer, Rafa Nadal, Andy Murray or Novak Djokovic – on an outside court. “We know the demand for tickets, for hospitality, for debentures,” said Richard Lewis, Wimbledon’s chief executive. “There are so many metrics, and it’s not just slightly that way. It’s very strong, and that’s not a criticism of women’s tennis. It’s a reflection of the state we’re in with the golden era of men’s tennis.”

The statistics do show a bias: in 2015, 66% of matches on the two main show courts featured men; in 2016, it was 58%. Caroline Wozniacki, the No 5 seed, said last week: “I think the other grand slams are more equal.” Martina Navratilova added that gender-based favouritism had been “going on for decades”.

There was a further slight during Johanna Konta’s match against Caroline Garcia on Monday. Fans in the grounds watching the big screen from the famous grassed terrace – Henman Hill or Murray Mound renamed, variously, Konta Kop, Konta Contour, or most lamely, Konta Cliff – were not impressed when the pictures switched from that tense three-setter to images of Murray warming up. Murray himself is unlikely to have agreed with the call: he corrected “casual sexism” in a press conference after his defeat and made the eminently sensible suggestion that, if you want equal numbers of men and women on the show courts, you could just start matches earlier.

The sense that men receive preferential treatment at Wimbledon can be traced back to the arguments over equal pay. The US Open was the first major tournament to give the same rewards to both sexes back in 1973, the year of the King-Riggs showdown. It took Wimbledon until 2007, some feel begrudgingly, to fall in line.

This weekend, both the men’s and women’s champion will receive £2.2m, although over the course of the season the best female players will earn much less. Counting prize money, endorsements and appearance fees, Federer banked £52.4m between June 2015 and June 2016; Serena Williams made £22.3m in the same period.

Female tennis players are, of course, much better remunerated and have far higher exposure than women athletes in other sports. Serena Williams is in fact the only woman to figure on the Forbes annual list of the 100 best-paid athletes.

The coverage, too, of women’s sports is a fraction of what their male counterparts receive. The 2017 women’s cricket World Cup, which has been taking place across England for the past three weeks, is now down to the last four. But it has struggled to penetrate the mainstream, perhaps because of Wimbledon. Still, the tournament has been broadcast more extensively than ever before – with 14 matches on Sky Sports – and the final next Sunday at Lord’s is expected to be a sell-out.

From a distance of almost half a century, it is not straightforward to work out what impact the original King-Riggs Battle of the Sexes had. King felt it unthinkable that she lose and she didn’t: she ran Riggs ragged and won 6-4, 6-3, 6-3. But in recent times, King has expressed doubts that much has changed in women’s tennis. In 1973, the commentators fixated on her appearance, and there is similar scrutiny of female athletes today.

While it is hard to see another Battle of the Sexes in tennis right now, other athletes and sports might see the appeal of such a showdown. Lindsey Vonn, the US downhill skier, is hustling to organise an equivalent mixed race after next year’s Winter Olympics. It is a way, she believes, to keep ski racing in the news more than once every four years. “Everyone believes it’d be great for the sport,” she said. “There is no downside.”