The part of the above statement after the dash is not quite the same as the part of the above statement before the dash.

Suppose that both the men and the women in a field form normal distributions, with peaks at the same points. So this meets the requirement of the part after the dash–a randomly chosen woman has a 50% chance of being better or worse than a randomly chosen man.

But if the SDs for the distribution of men is higher than that SD for women, we could still expect top ten lists (and bottom ten lists!) to be composed mostly of men. Etc. Like what Q. said re. outliers.

One thing I’m wondering about is whether the difference between a Top-X list and a random sample of X matters. (This is based on stuff I’ve seen/read about there being more male outliers than female ones in various areas.) Suppose that whatever kind of greatness you’re selecting for has something like a normal distribution (and that the shape of the distribution is the same for both* genders). If we take the “top” 10 individuals (from the high end of the bell curve) in a field consisting of 30% women and 70% men, are we more likely to end up with 10 men than we would have been if we had picked at random? (I think we might be, but I don’t actually know enough math to work it out for myself with any real confidence.)

On the other hand, once we try to bring into the picture whatever quality “Top-10” lists are trying to reflect, there are a lot of other potential complications that don’t lend themselves as easily to mathematical modelling. If a field is strongly skewed towards men, then perhaps a woman has to be very, very good to break into it at all—in which case the assumption that the distribution is the same between* genders is unwarranted. Perhaps, in fact, we should expect a much higher proportion of the underrepresented gender among the best exemplars of the field than we find in the field as a whole.

*I’m treating gender as binary for purposes of mathematical simplicity only.

For a Top-10 list:
50% of lists being all male = 93% men in industry
75% of lists being all male = 97% men in industry
90% of lists being all male = 99% men in industry
99% of lists being all male = 100% men in industry (actually, it’s 99.8995%)

It gets worse for a Top-25 list:
50% of lists = 97% men in industry
75% of lists = 99% of men in industry

I would be fascinated to see if anyone has a reasonable sample of Top-x lists to analyse (barring Top-10 Women in Business, which is an entirely different issue)

This math is very easy, by the way, and you can replicate it quickly for any Top-X list and any percentage of men. If m is the percentage of men written as a decimal, just raise m to the power of X. So to find the likelihood a Top-25 list is all-male if you suspect a field of being 3/4 male, you would do (.75)^25 (which incidentally equals .075% — in other words,

OY. Tell you what, pencil, I need them other woid thingies. But I THINK I caught the gist of what you are saying: somethin’s fishy in Denmark der. Something is askew. Math don’t lie. Probabilities and statistics are quantifiable and now kk is talking out her arse. I ain’t a math person, dang it. But I do remember reading something about the Edgar Awards this past year, and how the field for Best Novel was all men, not one woman in the bunch, and I thought, WAIT. Surely there were some great novels written by women who were up to snuff, right? Surely one or two, at least, deserved to be contenders. Which would have, by default, at least given them a shot.

Maybe it wasn’t the Edgars. Poo.

Regardless, as I said: math don’t lie. I don’t pretend to understand how you are showing what you are showing, nor even WHAT you are actually showing in your precise and amazing way, pencil. But my spidey senses are pricklin’ and a’cracklin’, and they are telling me, something doesn’t add up, and THAT’s the point.

Right, pencil?