I'm not so sure about that choice. If, for instance, women are underrepresented in pool because girls are raised in a way that outcome, that mechanism wouldn't apply to transwomen, who weren't raised as girls.
It isn't like flipping a switch. The trans kid in my son's grade school wasn't at all a surprise when they transitioned. Adherence to gender norms (or lack thereof) is completely applicable to pre-transition trans girls as it is to cis girls.
There may be some subgroup of socio-cultural factors that would apply to both women and transwomen, but the general case seems to be that the factor would be either biological or one imposed on the individual by some societal factor that was based not on the individual's perception of their gender but on society's perception of their sex. Even masculine women face discrimination based on being women, for instance.
This is a bit of a tangent (except that I've brought it up before), but what you are talking about
here is the perception of their adherence to gender roles. It's the same thing. We very rarely directly observe a person's sex, and even then there are exceptions. More often, we come to a conclusion about someone's sex (gender, really) based on how closely they match our idea of what a particular gender is supposed to look like.
For example, this is an
X thread showing a picture of mayor of Nashville, TN, Freddie O'Connell and his family. Based on the comments (and there are many, many threads like this one), this is a picture of either: two gay men, two lesbians, two adult transgender people, two adult transgender people and one transgender kid, or an entirely cis heterosexual family of four. If you care to dig through those comments, and I don't recommend it, you will see that some think that Freddie is not masculine enough to be a man. Or that some think that his wife is too masculine looking to be a real woman. I'm not quite certain which child some people think are trans, but I think it's the little one.
Now, no one is directly viewing the sex of any of these people. No matter how hard you looks, you will not see anything between the range four penises to four vaginas. People are, instead, comparing them to
their idea of what a male gender or female gender is
supposed to look like, despite the fact that biologically male and female people have a very wide and overlapping proportions, shapes, and amounts of body hair.
I think this is actually a major difference in our epistemics. I look at evidence from a bayesian framework, which includes a deep background of knowledge and theory as determining our priors on any particular question.
That is a very polite way of saying cognitive bias and has no particular merit over anyone else's personal experience-based Bayesian framework. I will fully admit I don't have the evidence to prove beyond a shadow of a doubt that there is no biological sex-based advantage in playing pool, but I also know there isn't enough evidence to suggest that such an advantage, if it exists, is greater than any
other genetic advantage one might have.
What I do know is that, as of 6 years ago, the organization that calculates and tracks the ratings of professional pool players published a video that states that biologically female professional pool players are just as capable of top-level playing as biologically male professional pool players. Right now, that is the closest thing to objective evidence from an authoritative source on the matter that we have.
Obviously I'm much less confident about the specific theoretical reasons for thinking that men have an advantage in pool. The point here is that those reasons are evidence.
There are
reasons, in the "hypothesis" sense, to believe that there is a biological advantage to playing pool.
Evidence is something we're very much lacking, to determine if it is a valid reason or not. Social influence is definitely a possible reason why there could be more men higher placed in the pool ratings that women. Is that a valid reason that trans women should not be allowed to play in the women's league?
