This is even true in mental sports like chess. Even after accounting for attendance rates the difference in strength is humongous. It seems men are just better at competitive activities although it's very unpopular position to take.

It's in fact so unpopular that you can get papers claiming the opposite published despite very simple math errors in them, like this one: http://rspb.royalsocietypublishing.org/content/276/1659/1161

while arguing for opposite gets you shunned even if all you need to prove your point is high school level math and a rating list with attendance rates.

In MMA it's not even interesting as men are way stronger, have better hand-eye coordination and way less body fat. I doubt she would have a chance again a local amateur small town champion let alone anyone competitive.

Not disagreeing with you at all, but I just want to throw in the caveat that at least in the more mental games, we have no idea how the competitive landscape would look if we had a culture that encouraged as many girls to put as much into competition as we do boys.

Humans are cultural creatures, cultural thinkers and movers, and in everything from chess to MMA we benefit greatly from growing up in a culture that is tooled to support our specific strengths. Not everyone gets that chance, and not all groups equally.

>>Not disagreeing with you at all, but I just want to throw in the caveat that at least in the more mental games, we have no idea how the competitive landscape would look if we had a culture that encouraged as many girls to put as much into competition as we do boys.

Well, we don't but attendance rate are already taken into account. There might be other cultural problems though like being in a minority being difficult or more likely girls just doing worse in competitive social environments which are typical for sports.

One can even argue that girls already have advantage in selection: assuming equal talent distribution in boys and girls populations and assuming most talented children from both make it to the competitive chess, the girls should do better (because less of them are selected and therefore more talented ones on average).

If anything it's likely that once selected (that is starting to play competitively) the environment is less welcoming to girls. On the other hand girls get more opportunities than boys (dues to women only tournaments, titles, world championship).

While I think the hypothesis that environment is less welcoming and thus inhibit development of women players I have trouble seeing how this can be tested.

Well, actually, we do.

Aptitude testing shows[1] that while females tend to cluster more towards the average, male populations produce more outliers. There are both more male geniuses and male imbeciles than their female counterparts.

[1] for example http://www.aei.org/publication/chart-of-the-day-scottish-iq-...

This is the product of the different evolutionary strategy for males and females, the males being high risk/high reward, the females being conservative/average. I don't have a citation for that.

I don't know if chess is a very good example since in that case there was a woman who was very clearly an outlier (as is Rousey) but able to compete against men, and reached a top ten ranking (Judit Polgár).

I am saying women do way worse on average. Judith Polgar did well but was nowhere close to be say world championship contender and she received more training as a child than about any man in history at that time. Judith was also the only Polgar sister who reach world class strength. These days Hou Yifan is close to world class strength and it can be argued that her level of play suffered because of politics (it's important for China that she plays in women team and playing vs weak competition isn't the best for the development). Maybe she had top 10 potential as well.

It's definitely less disadvantage in chess than it is in MMA but it seems the effect is still there.

Some data on elite male and female tennis matches:

https://en.wikipedia.org/wiki/Battle_of_the_Sexes_(tennis)

Man ranked 203 beats both Williams sisters in informal sets:

http://observer.theguardian.com/osm/story/0,,543962,00.html

Yep, and when the US U16 men's team scrimmaged the 2015 World Cup Champion USWNT, they won 8-0.