Well, I'm glad someone's actually using numbers instead of their "theories". I don't really "like" the idea men would be inherently better, but I can't really back it up. Some possible explanations for the curve:
1. Women are represented way more at the scholastic level, before they hit puberty. So some of those ratings could be of inactive players who never came near their potential.
Counter-argument: How many scholastic players have FIDE ratings?
2. Is a rating really accurate enough? I've heard 50 is the margin of error, which really isn't all that accurate.
Counter-argument: 100 points is quite a lot.
Everyone knows that the best male players are rated higher than their female counterparts. As of today, the top female player is Judit Polgar (53rd in world ranking) with a rating of 2686, over 100 points lower than the world leader Magnus Carlsen with 2814. Polgar's best rating was 2735 in the middle of the year 2005; the highest male rating achieved was around 2850 by Garry Kasparov. So there appears to be a difference of just over 100 rating points between the sexes.
According to the gender-neutral outlook, this difference is attributed to there being an order of magnitude less female players. Consider separate Gaussian distributions of male and female players: if their peaks are located at the same rating (i.e. men and women have equal skills on average), then the larger amount of male players results in the top of their distribution being located higher than the female distribution. Intuitively, this is like placing a large cup over a smaller cup - the larger cup extends farther in all directions from the center, even though the cups are centered in the same exact location.
Thinking about this last night, it struck me as odd that (to my knowledge) nobody had ever presented any data to back this up. So I spent some time this morning trying to find out the truth behind the matter. I downloaded the entire list of FIDE-registered chess players (273886 players as of today, some of whom are not rated) and wrote a program to process the data into two sets, one for each gender, comprising the distribution of registered ratings. I then made a Gaussian fit to both sets of data, and was surprised by the result.
The male distribution (blue) shows a peak at around 2016 points, while the female distribution (red) shows a peak at around 1920 points. A hasty conclusion would be that men are indeed about 100 points "better" on average than women.
Anyone with a trained eye will see that the data is far from perfect. Up until recently, FIDE did not issue ratings below 2000, which is visible as a glitch in both data sets at around that value. The peaks are "supposed" to be located at around 1200; this does not happen here because average everyday players do not register for a FIDE rating. From a statistical viewpoint, it must be assumed that "2000 is the new 1200", and that the set of players to be analyzed consists only of those players who are good enough for a FIDE rating. Thus, the gender-neutral outlook may assume a new explanation for the inter-gender difference: the (skillwise) threshold for registering with FIDE is actually lower for women than it is for men.
Caveats aside, it is tempting to play with the numbers. If Judit Polgar had a handicap of 100 points in her favor, she would now be about even with Vladimir Kramnik battling for fourth position in the overall list of players; at the apex of her career, she would have been on a par with Garry Kasparov. Since she's the best female player of all time, it all makes a fascinating kind of sense.
Questions? Comments?