# 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 "cultural" 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?

It's not the same title. Women Grandmaster (WGM) for example is clearly less prestigious than GM because the requirements are lower. FIDE isn't giving out the same title to women who have less knowledge than men, they are giving out exclusive titles for women. In the same way there are female players who have achieved the actual GM title (e.g. Hou Yifan is a WGM and a GM).

As for why they would do that - why not? Chess is heavily male dominated, and a WGM title makes the game more inclusive. Can you think of a good reason not to have the titles?