Debates are raging again over who should be allowed to compete in women’s sport. Take two recent examples that inflamed the internet. First the Sunday Times reported that the International Association of Athletics Federations (IAAF) intended to classify women with higher natural testosterone as “biological males”– just as 800m runner Caster Semenya was headed to court to challenge IAAF regulations that would exclude her and others from competing owing to higher than typical testosterone levels. Then tennis great Martina Navratilova asserted that trans women “biologically, are still men”, and shouldn’t be allowed to compete in women’s events.

The IAAF and Navratilova quickly backed away from these claims, but the damage was done. Many journalists intent on covering a mind-bogglingly complicated subject with authority have asked me the same question recently: “Are women with high T [testosterone] ‘biological males’?” The answer is that there is no simple definition of what a biological male is.

For decades, sports governing bodies have sought a single biological criterion by which to exclude some women from the female category; yet the idea of a true sex is mistaken, and tries to make something incredibly complex seem simple and binary. The latest effort claims gonads – and the testosterone they have a role in producing – as the key factor in what constitutes a “biological male”. But to reduce sex to a single trait is to profoundly mischaracterise decades of research into sex biology. The science is clear: there is no single physiological or biological marker that allows for the simple categorisation of people as male or female. Gonads were once thought to define one’s sex. In the 1800s. By the 1950s scientists had identified at least six markers of sex: chromosomes, gonads, hormones, secondary sex characteristics, external genitalia and internal genitalia. While these markers may align along a female-typical or male-typical path, that’s not always the case.

What’s more, each of these markers comes in more than two versions. For example, people are often assumed to have either XX or XY chromosomes, but some individuals are born with an extra X chromosome and others have a mosaic where each cell has one karyotype or the other.

So while sex is commonly thought to be straightforward, consisting of two clear categories of male and female, the breadth of human physical variance is more complex than the categories suggest. The upshot: there are many biological markers of sex but none is decisive. Claiming that one factor is does not reflect the science of sex biology, and certainly can’t be used to determine who can and cannot compete.

There is another outdated idea circulating that testosterone is “the male sex hormone” and that its presence in women is a problem. But this, too, is wrong. This idea was cemented long before the hormone was even isolated in 1935 and has persisted despite decades of science showing otherwise. Early scientists assumed “sex hormones” would be exclusive to one sex or the other, that their physiological roles would be restricted to sexual development and functions, and that they would be antagonistic. That is, if T caused the cock’s comb to swell, oestrogen would make it shrivel.

As early as 1920, though, scientists had reported data that they described as “surprising”, “paradoxical” and “disquieting”. Much to their surprise, the hormones were not sex-exclusive. Both men and women had them. And findings that contradicted the dualistic paradigm were easy to find: the showy feathers of the rooster were not restored by testicular implants or injecting T; instead, it seemed that “female hormones” were responsible for their masculine appearance. They also learned that the hormone was critical for bone development, heart function, and liver metabolism – functions that have nothing to do with sex difference.

Yet the idea that testosterone is the “male sex hormone” and oestrogen is the “female sex hormone” is a paradigm which persists and is being drawn on now.

And what of testosterone and athleticism? This relationship is also far from simple. Renowned testosterone researcher Shalendar Bhasin, director of the research program in men’s health at Brigham and Women’s Hospital in Boston, has been trying for years to get people to understand the important distinction between the particular effects of T and broad statements about “athletic performance”. In a New York Times article in which one scientist proposed that T could “take [an athlete] to the next level”, Bhasin threw cold water on the notion, saying: “The explanations of cause and effect between athletic performance and testosterone are very weak.” He addressed the apparent paradox that giving people T can increase muscle mass and power as well as what’s called maximal voluntary strength – as do things other than T, by the way – but doesn’t seem to “build a better athlete”.

Of all the physiological factors relevant to athletic performance, the two for which there are the most abundant and convincing links to T are skeletal muscle mass (also sometimes called “lean body mass”), and physical strength – something those who oppose trans women competing have deployed. But studies of T levels among athletes fail to show consistent relationships between T and performance. As one example, some studies show a correlation between higher baseline (endogenous) T levels and either speed or “explosive” power, but many other studies show either weak or no links. Quite a few studies even find that higher baseline T is associated with worse performance.

Some of the data the IAAF is using to fight Semenya’s case show this. Other studies have found that T relates to performance only in specific subgroups of athletes, such as those who play certain positions in soccer or rugby, or players who are stronger to begin with.

This hormone doesn’t dictate better athletic performance. T is involved in processes that underlie athletic performance for most people, but it’s neither a sufficient nor even necessary ingredient. Take, for example, women with complete androgen insensitivity syndrome, who appear to be overrepresented among elite women athletes and for whom their tissues have no ability to respond to T at the cellular level. Just as T isn’t simple, neither is athleticism.

Think of Usain Bolt, the fastest human in the world. Yet he isn’t the fastest at every race. When asked why he never runs the 800m, he responded: “I’ve tried it and trained and my PR (personal record) is like 2:07, and that’s really slow, like, a woman could beat me.” The interviewer laughed him off, saying: “You’re going to get in trouble for that!” But Bolt was serious: “It’s true, though – they could!”

This is because sport encompasses an enormous array of activities requiring vastly differing combinations of skills and physical capacities. When is power more important? When is finesse? How crucial is endurance? What about flexibility, hand-eye coordination, communication with teammates, strategy? When you hear “athleticism”, do you think of sprinting, where success is all about explosive speed? Or do you think of something like luge, where the ability to isolate body parts and make subtle adjustments, and to remain flexible and relaxed while going unprotected down a track at 90 miles an hour, are just as important as power? There is no one answer to these questions.

What is clear is that testosterone is not the unique essential ingredient for success across every conceivable sport. Labelling women “biological males” draws a dubious connection between sex, testosterone, and athleticism that relies on long-discarded ideas that men and women can have a “true sex”, that testosterone is a “male sex hormone”, and that testosterone is the key to superior athleticism. None of these are true, and it’s long overdue that people stop saying they are.

• Katrina Karkazis is a senior research visiting fellow in the Global Health Justice Partnership at Yale University and the author of Fixing Sex: Intersex, Medical Authority, and Lived Experience. She is co-author of the forthcoming Testosterone: An Unauthorized Biography