Gay men sleep around much more than straight men. That's true, isn't it? Even gay people would admit that, right? The infection rates of STIs from gonorrhoea to HIV tell that story. It is unequivocal. Or so you might think.

Last week one of the world's largest dating websites, OkCupid, collated and published the results of their user "match" questions, which are designed to find out as much as they can about their 4 million members in order to help them find dates. The statistics are startling.

There is only a one percentage point difference between heterosexuals and homosexuals in their promiscuity: 98% of gay people have had 20 or fewer sexual partners; 99% of straight people have had the same number. Tellingly, OkCupid found that it is just 2% of gay people that are having 23% of the total reported gay sex.

Of course, as with all statistics, there are flaws. This sample is largely North Americans who use the internet to find dates. How, therefore, can it be representative of the general population? But are those people – gay or straight – who go online looking for love and sex really going to be less promiscuous than those that don't? I doubt it.

For the first time we have a statistical glimpse into an unreported truth: that your average gay person's sex life is every bit as dreary and unremarkable as a heterosexual's. But that a tiny proportion of them are freakishly promiscuous. Sex, it would seem, is distributed as unevenly as money.

And yet, that is not the narrative we have been fed. The idea of the rampaging predatory homosexual is so ingrained in the western psyche as to inform not only fear, hatred and abuse but also policy and laws. Part of the justification of Bill Clinton's risible "don't ask, don't tell" policy, preventing gay people in the military from coming out, was fuelled by the belief that in doing so their straight colleagues would either feel at risk or actually be at risk of unwanted sexual advances.

And here is where these online statistics get even more interesting. Gay people, apparently, don't even want sex with straight people. Just 0.6% of gay men on the site, for example, have ever searched for straight "matches". And just 0.1% of lesbians have. The theoretical idea of the heterosexual male might be appealing for gay men – a tryst with Brad Pitt or George Clooney, perhaps – but in practice we are making no efforts to turn the theory into a reality. There wasn't even one single gay user of the website who predominantly searched for straight users. Not one. Straight men of the world, you are safe.

Other parts of the data were so expected as to reinforce rather than invert stereotypes: that gay men like Lady Gaga, The Devil Wears Prada and Six Feet Under, and that lesbians are obsessed with the L Word and Buffy the Vampire Slayer. But this reveals a universal truth about human nature: people, of all races, orientations, genders and classes, crave depictions of their lives in the arts. We need narratives we can relate to.

This is why Stonewall was right to condemn the BBC in July for failing to tell our stories, pointing out that only 1.7% of the public service broadcaster's most popular programmes depicted gay people. By contrast, ITV, which is much less obliged to portray minorities, came out at 6.5%. The gay equality charity also found in its report that the 49% of all the BBC's portrayals of gay people were stereotypical, routinely depicting gay people as "figures of fun, predatory or promiscuous".

You might think that this is unimportant, that it's just TV, and a few harmless stereotypes. But any gay person will tell you that when they were growing up, the lives they saw on screen informed them precisely about the kind of life they had to look forward to. When I was 10, in 1987, I watched the first gay kiss on a British soap: EastEnders. It was fleeting but tender. I knew I was different and in that moment I knew there was hope – not least because my sisters cooed at the scene.

With the recent spate of teenage gay suicides in the US, our media needs urgently to tell a new story: that of the happy, everyday gay person, who is largely accepted for who they are, who leads a life of dignity, value and meaning but whose love life may not always be very exciting.