What gives rise to the most salient, contested and misunderstood of sex differences… differences that see men persistently walk off with the top positions and prizes, whether influence or income, whether heads of state or CEOs… differences that infuriate feminists, preoccupy policy-makers, galvanize legislators and spawn 'diversity' committees and degrees in gender studies?

I used to think that these patterns of sex differences resulted mainly from average differences between men and women in innate talents, tastes and temperaments. After all, in talents men are on average more mathematical, more technically minded, women more verbal; in tastes, men are more interested in things, women in people; in temperaments, men are more competitive, risk-taking, single-minded, status-conscious, women far less so. And therefore, even where such differences are modest, the distribution of these 3 Ts among males will necessarily be different from that among females — and so will give rise to notable differences between the two groups. Add to this some bias and barriers — a sexist attitude here, a lack of child-care there. And the sex differences are explained. Or so I thought.

But I have now changed my mind. Talents, tastes and temperaments play fundamental roles. But they alone don't fully explain the differences. It is a fourth T that most decisively shapes the distinctive structure of male — female differences. That T is Tails — the tails of these statistical distributions. Females are much of a muchness, clustering round the mean. But, among males, the variance — the difference between the most and the least, the best and the worst — can be vast. So males are almost bound to be over-represented both at the bottom and at the top. I think of this as 'more dumbbells but more Nobels'.

Consider the mathematics sections in the USA's National Academy of Sciences: 95% male. Which contributes most to this predominance — higher means or larger variance? One calculation yields the following answer. If the sex difference between the means was obliterated but the variance was left intact, male membership would drop modestly to 91%. But if the means were left intact but the difference in the variance was obliterated, male membership would plummet to 64%. The overwhelming male predominance stems largely from greater variance.

Similarly, consider the most intellectually gifted of the USA population, an elite 1%. The difference between their bottom and top quartiles is so wide that it encompasses one-third of the entire ability range in the American population, from IQs above 137 to IQs beyond 200. And who's overwhelmingly in the top quartile? Males. Look, for instance, at the boy:girl ratios among adolescents for scores in mathematical-reasoning tests: scores of at least 500, 2:1; scores of at least 600, 4:1; scores of at least 700, 13.1.

Admittedly, those examples are writ large — exceptionally high aptitude and a talent that strongly favours males and with a notably long right-hand tail. Nevertheless, the same combined causes — the forces of natural selection and the facts of statistical distribution — ensure that this is the default template for male-female differences.

Let's look at those causes. The legacy of natural selection is twofold: mean differences in the 3 Ts and males generally being more variable; these two features hold for most sex differences in our species and, as Darwin noted, greater male variance is ubiquitous across the entire animal kingdom. As to the facts of statistical distribution, they are three-fold … and watch what happens at the end of the right tail: first, for overlapping bell-curves, even with only a small difference in the means, the ratios become more inflated as one goes further out along the tail; second, where there's greater variance, there's likely to be a dumbbells-and-Nobels effect; and third, when one group has both greater mean and greater variance, that group becomes even more over-represented at the far end of the right tail.

The upshot? When we're dealing with evolved sex differences, we should expect that the further out we go along the right curve, the more we will find men predominating. So there we are: whether or not there are more male dumbbells, there will certainly be — both figuratively and actually — more male Nobels.

Unfortunately, however, this is not the prevailing perspective in current debates, particularly where policy is concerned. On the contrary, discussions standardly zoom in on the means and blithely ignore the tails. So sex differences are judged to be small. And thus it seems that there's a gaping discrepancy: if women are as good on average as men, why are men overwhelmingly at the top? The answer must be systematic unfairness — bias and barriers. Therefore, so the argument runs, it is to bias and barriers that policy should be directed. And so the results of straightforward facts of statistical distribution get treated as political problems — as 'evidence' of bias and barriers that keep women back and sweep men to the top. (Though how this explains the men at the bottom is an unacknowledged mystery.)

But science has given us biological insights, statistical rules and empirical findings … surely sufficient reason to change one's mind about men at the top.