Why do women need less ELO to obtain FIDE titles? As well as FIDE norms, you need a certain ELO to obtain a certain title. Women need a lower ELO to obtain the same title as men:


Grandmaster (GM) 2500+
International master (IM) 2400+
FIDE master (FM) 2300+
Candidate master (CM) 2200+



Woman grandmaster (WGM) 2300+
Woman international master (WIM) 2200+
Woman FIDE master (WFM) 2100+
Woman candidate master (WCM) 2000+


I have read many times the reason why women don't reach the super GM level is social and not cognitive. For example in this interview to WFM Rodrigo she is asked:

XL. Why are there still no women in the elite?
M.R. For various reasons, but basically for two. For a statistical
question (we are less players) and for a cultural factor.
Evolutionarily, women are more used to collaborating and men to
compete. It is an imprint that comes to us from the hunter-gatherer
tribes. In addition, the male brain processes visual information
faster, which favors the recognition of patterns on the board, while
women have more developed memory. But in ten years we will see girls
fighting for the world title.

So why is FIDE giving titles to women with less chess knowledge than the equivalent title for men? I know there are fewer women players than men, but women can play in men's tournaments.
I think WFM Rodrigo is correct when she says that the reasons are statistical and that having fewer female players means having far fewer players at the top.
If you assume that males and females have the same mean and standard deviation (we shall see soon that this assumption is false) and you draw the two normal curves you see that the curve with fewer members (females make up only 15% of FIDE registered players) tails off to zero long before the one with more members.
However WFM Rodrigo also mentions &quot;cultural&quot; reasons. Translated into mathematical terms I think she is suggesting that females have a lower mean (average) FIDE rating than males. This we can check by loading the latest FIDE rating data into a database and doing some SQL queries.
Doing that gives us:
Female
Mean = 1505, standard deviation = 339
Male
Mean = 1675, standard deviation = 346
We see that there is little difference between male and female standard deviation but the mean female ELO is 170 points lower than the mean male ELO. This is half a standard deviation which is a lot. It looks to me that WFM Rodrigo is right about this too.
Comparing these figures with the rating differences between the open (there are no male only titles) titles and the female only titles it looks like FIDE are being generous to the females by a margin of 30 points. Perhaps they rounded the difference up to the nearest hundred?