And, as I have already answered, it depends. It depends on the nature of activity/sport/competition. It depends on when in their life the person transitioned. It depends how they transitioned. Hell, it probably depends on the person was like pre-transition.
There is no one single answer to that question without context.
I'm having a hard time parsing this as a response to Zig's question. His comments which precede the question were specifically in the context of pool, so your first point doesn't make sense in this context. When we're talking about pool, sure, the nature of the sport matters, but we already know what sport we're talking about. "How many calories in a 100 gram apple?" "It depends on what kind of fruit it is." isn't a meaningful response.
But here's his quote again:
We're talking about a competition, in this case pool. You're saying transwomen have no advantage over women, so they should compete against women. But as Joe alluded to, you aren't saying that men should compete against women, that there should be zero segregation at all. So I have inferred that you think men have an advantage over women (the only reason to segregate the competition), but transwomen do not. And that logically requires that men have an advantage over transwomen.
So what is that advantage?
You list a number of things "it depends" on. Is "it" the advantage that Zig has asked for? I think it's worth pointing out that this question is being asked in the context of segregation into men's and women's divisions. A similar question could be asked about that segregation "what is the advantage that males have over women?"
You
could reply to that question similarly to how you replied to Zig's. "It depends on the nature of the sport, it depends on their diet as a child, it depends on what country they grew up on, it depends on what sports they played as a child, it depends on the DNA of their parents, hell it probably depends on their
personality as a child".
But you accept this segregation, so you don't consider any of those things to be a reason not to have it.
One reason to ignore all of those "it depends" claims is that they're irrelevant because they're looking at the issue on the wrong level. The question is about the general
classes of men and women, not the specific case of any particular individual.
But the same objection applies to your response to Zig's question in the trans case. The question isn't whether
a particular trans woman has an advantage over females, but whether or not transwomen
in general have such an advantage. Or, at least, if that's
not the question then you need to explain why it
is the question in the men's/women's division case.