After looking at the rating gaps between ethnic groups, we will today turn our inquiring gaze towards the relative performance of women in chess. More than a decade ago, there was a paper that purported to explain the relative absence of female players at the very top by the low participation rate of women .
This never sounded particularly convincing to me, because if underrepresentation were the only reason, we would expect a women among the top twenty (at a 1:19 underrepresentation) and 5 women among the top 100. Instead there are 0 and 1 women in the top 20 and the top 100. I also knew that women average roughly 200 points lower in the German rating system. So a lower performance across the board based on differential ability or interest in the game seemed more likely.
Initially, my investigation supported this suspicion. For 150,000 men and 16,000 women among the active chess players in my database, the men have on average roughly a 200 Elo advantage (1679 vs 1474). A closer look at the distributions, however, made it unlikely that this gap is due to innate differences.
As we can see, the female curve is not even remotely gaussian. The true bell curve seems to be hidden under an avalanche of beginners. By restricting the dataset to those players born between 1960 and 1990, we eliminate most of the influence of age and almost all beginners.
Now, the avalanche of very weak players is almost completely purged and the bell curves become very similar. There is actually a female advantage between 2100 and 2400. Maybe this is the area where you are very good as a woman but nothing special as a man (the rating necessary for women titles fall into the space: 2100 for women fide master, 2200 for women international master and 2300 for women grandmaster).
After 2500 there is a distinct male advantage, which reproduces the observation that underrepresentation cannot explain the under representation at the very top. However, given that overall these bell curves are very similar and given that there was actually a women in the top ten only a decade ago, this doesn’t seem to point to innate ability differences.
Of course, underrepresentation can hide innate ability differences, if the female players are just sampled from a higher percentile of innate talent. But this is difficult to investigate and certainly beyond this blogpost.
 Why are the best women so good at chess?