Topic: Explaining male predominance in chess

There is an active topic on the boards right now by that title. 

http://www.chess.com/forum/view/general/explaining-male-predominance-in-chess?lc=1#last_comment

The subject was met with derision, and outright hostility, by some of the guys, so I am going to put a few of my thoughts in my blog.  What I am going to do is discuss one of the key graphs from the article, and contrast it with some more representative, in my opinion, data on the distribution of ratings in chess, by sex.

So here is the key diagram from the topic:

This purports to compare male versus female chess ratings.  The figure clearly shows that men in this presentation are about 200 rating points, or one full class, stronger than women.  But the parameters used immediate should jump out to the discerning eye.  First, the rating scale only presents ratings from 2000 to 2900, and only for those who played more than 750 rated games!  So this is not a representaive subsample of the chess-playing population.  You are looking at a "tail," likely out 2  or 3 standard deviations from the mean ("68-95-99.7 Rule").

And the ratings are plotted against "Percentage of Players."  This attempts to normalize the data between the sexes, but contains an important flaw, failing to take into account that the sample  population are wildly different in size.  Though accounts vary, women make up fewer than 10% of all rated players, perhaps as low as 5%.

It is too easy to make a leap of faith jump and suppose the chess ratings distribution, above, mimics a common distribution of human height by sex:

These are apples and oranges comparisons.  Human males are morphologically bigger, taller, and stronger than females.  But does this physical difference extend to intellectual abilities?

Below I show a figure that put the frequency disparity into better focus:

The best fit curves for these two population show a slightly skewed normal distribution, but note the means are less than 100 rating points apart (2016 for men; 1920 for women).  Also, this graph adequately illustrates how many more male than female players there are.

The reason there are not more female players in the very high rating tails of the distribution is that there are many fewer women players, playing fewer games.

I submit that the 100-point difference in the means is reflective of a difference in rating opportunities rather than abilities.