Maybe something physically is preventing women from being able to perform at a Filler level. But it seems to me nothing physically is preventing them from being able to perform at a Siming or Kelly level. Or maybe less women playing pool just makes the probability of a male Filler emerging more of a once every 30 years occurrence and a woman at that level a once every 300 years occurrence and it's physically possible.
Keep in mind I will accept there may be physical brain elements to how interest, obsession, learning, and mastering occurs that can possibly make reaching the very highest heights of skill more accessible where population differences are actually explained by those physical differences. And maybe Kelly and Siming emerge despite physical disadvantages and not just because of population sizes and the richness and availability of talent-generating environments (training programs, facilities, local skilled competition, etc.). So the physical aspect is possible but I don't feel knowledgeable enough to expound any further on it given how high we've already witnessed what women are capable of. It's not going to be a focus of my attention.
But I think we'd be naive if we ignored the cultural influences of patriarchal societies. How many families might encourage their boys to competition disproportionate to encourage their girls? How many would be more inclined to disallow a daughter to hang out at pool halls vs. disallow their sons? How much grooming occurs to steer girls toward craft-oriented activities during those formative years vs. competition-oriented activities? How may boys have been given the green light to trash talk women out of competitive activities at the time women start showing interest? The number of times at a casual bar situation I've seen young men start sharking, talking trash, and being disruptive the second a young woman looks like she's about to win a single game of pool far outweighs the number of times I've seen the reverse.
And if I ask myself why does women's sports exist? In more physical sports it's obvious it's needed for them to even have a chance and for their safety. In pool, it's obviously acknowledging less women play and creating a space to stimulate their involvement. It's to give a place away from sexist behaviors where they can compete amongst themselves. Create an environment where they can explore their interest in the activity without active resistance of their participation. A place to grow their interest in the sport. And if physicality is not a factor, provide a springboard where they can ideally transition into open competition after having established their fundamentals and maybe a certain battle hardiness for the behaviors they'll likely still encounter in open competition.
The transgender situation is tough. It reminds me of the Bane quote from the movies: "Ah you think darkness is your ally? You merely adopted the dark. I was born in it, molded by it. I didn't see the light until I was already a man, by then it was nothing to me but blinding!" Take someone born biologically male. They may have lived in secret identifying as female. But were they culturally raised female? Did they face all the same obstacles and hurdles females faced? Did they enjoy any male privilege in regards to encouragement for competition and skill development? In which bell curve did they establish their skills and in which bell curve are they now competing?
I'm not really against trans athletes competing. I have a lot of sympathy for their journey. I'd like them to be able to live safely, freely, and with full self-actualization. But I do want to be mindful of why women's sports exist and what's fair. And if the talent distribution of trans women athletes doesn't align with the same talent distribution of natural women athletes then I can appreciate there is a fairness problem from a statistical perspective. If that problem exists, solving it might not be as simple as measuring hormone levels, legal gender recognition, eligibility requirements, sports policies, or health/safety considerations. I don't have a solution but I do think it would be naive to assume there isn't a problem (or the potential for a problem).
NOTE: Graphs created for illustrative purposes of a hypothesis and is not a sampling of real data.