Why are there so few female-led films compared with male-led films? The answer to this frequently asked question is regularly delivered with a roll of the eyes, a sweep of the hands and a flash of a Benjamin: because female-led films do not bring in as much money at the box office as those led by men. Over and above offering entertainment to the masses, film is a money-making business. There are no two ways about it.

But a new study, conducted by the Creative Artists Agency (CAA) and tech company Shift7, analysed the 350 top-grossing films released between 2014 and 2017 and found that cinema audiences (comprising 52 per cent women) are not as sexist as Hollywood would like us to think. On the contrary: The analysis revealed that films with female leads actually outperform their male counterparts at the box office.

The report also analysed these films to determine which of them passed the Bechdel test: the lowest bar that determines how films represent women. For reference, to pass the Bechdel test a film must have at least two women in it and they must have a conversation together about anything other than men. Applying this test to films often sees those aimed at female audiences – the likes of romcom’s – fall flat and exposes their lazy attempts at female representation. When compared with total box office results, the CAA’s study determined that the films that passed the Bechdel test outperformed those that didn’t.

Let’s pick that apart, though. Among the high grossing female-led films cited by the study were stories that told diverse female experiences, such as Lady Bird and I, Tonya, but the study also cites “Anna Kendrick-led” Trolls, Inside Out, “Megan Fox-led” Teenage Mutant Ninja Turtles, two animations and a film in which Fox plays opposite the real headline stars – four animated turtles … who are male. Should we really be claiming these as a win?

In 2017, the three highest-grossing movies in the world were celebrated for all being female-led, but they had their problems. Wonder Woman: a sexed-up objectified superhero who watches as a man actually saves the day; Beauty and the Beast: a young woman who is kidnapped by a male beast and then develops Stockholm syndrome; Star Wars: The Last Jedi: More about the return of Luke Skywalker than any sort of female narrative.

But there are also legitimate triumphs. The 2018 UK box office has been replete with a smorgasbord of female-led films: 3 Billboards, Mamma Mia: Here We Go Again, Lady Bird and The Shape of Water among them. It’s exciting, also, to see films like Mary Queen of Scots, The Favourite and Can You Ever Forgive Me coming out in 2019 that will no doubt be hits. We don’t need to include animations and faux Disney feminism to skew the figures. The box office has the cold hard cash to prove that female-led films guarantee revenue.

But that isn’t the end of the story. While 2017 boasted a top three that were female-led, it actually saw a drop in the percentage of female protagonists overall. And if we look behind the camera, it’s not surprising to see why. In 2017, women only comprised 8 per cent of directors, 10 per cent of writers and 2 per cent of cinematographers. The most prominent directors working in Hollywood are men and their misogynistic blindness means they rarely produce pictures with female protagonists. The one that has offered up the most female protagonists over his career is Woody Allen – hardly an advertisement for progressiveness, given the sexual assault allegations made against him.

It’s not like female-led films aren’t being written. Hollywood is littered with stories of filmmakers battling for female protagonists. Can you imagine Alien with anyone other than Sigourney Weaver in the lead? Or how about His Girl Friday without … the girl? More recently, when Sicario screenwriter, Taylor Sheridan, approached potential backers with his script, he was asked to replace his female protagonist with a man. Sheridan refused and Emily Blunt led the film to $85m.

This goes beyond entertainment. Film becomes an historical record of contemporary society. If we continue to disregard women from this narrative, we disregard their contributions and support an erasure of them from history. When we see women appear as only subsidiary characters we tell audiences that women had no leading roles on or off the silver screen.

Female-led films need to be written and directed by women, too. The female gaze celebrates the female condition through a female lens, not one tokenistically imagined by men. Their careers in the film industry are shorter and less well paid than men’s, their films see a budget glass-ceiling and their careers are less celebrated than those of male directors. The situation is even more dire for women of colour.

While the CAA analysis doesn’t perhaps paint the most accurate comparison of male versus female-led films or what we can define to be a truly “feminist” film, it is impossible to ignore the writing on the wall. Female protagonists bring in box office numbers and the tired adage that male protagonists simply make financial sense will no longer fly.