Memes of Production

So, the long-term effect of testosterone for athletic performance is that you can train harder, recover faster, and get more benefit even from the same amount of training. That's why bodybuilders on steroids often work out every day or even twice a day.

The short-term effects are to do with explosive performance, reduced fatigue, and just being more aggressive/competitive, which can be a good thing in certain scenarios. Coming from a family of athletes but not being athletic myself, while still having a fairly high level of testosterone (at least in my earlier years before I got overweight), I've been known to keep up with people in much better shape than myself purely because of competitive drive, achieving results I could never dream of without competition. Now, everyone has that, women too, but it's amplified by testosterone, at least according to some studies - and women get a larger boost to competitiveness from a testosterone supplement, according to at least one paper I found - this is likely because men are less sensitive to slight testosterone increases (we have higher baselines after all).

wouldn’t we expect cis-women athletes (and indeed, athletes of any gender-category) to also abuse it? That’s just the same old problem of doping

And they absolutely do! It's easier to check though, because you'd find compounds they're not supposed to have at all, since synthetic testosterone is chemically different from natural and you'd have specific metabolites in your blood. The remaining question, I guess, is can we test that trans women are getting the correct amount of testosterone blockers, and what the correct amount is. If that's testable easily enough, then this whole thing might be an easily solved problem.

and so I believe that’s up to the sports’ associations to sort out.

That goes without saying IMO. These rules should always be on the level of individual leagues and associations, not mandated by government. The latter option would be stupid as fuck because there are so many variables and there are even sports where men hold no advantage anyway.

I also want to push back on an impression that seems to be forming here, that testosterone is directly linked to success in sports - I don’t think that’s the case.

Then what is the advantage men hold over women, that they lose when they transition, to be allowed into women's leagues? Because men being inherently advantaged in most sports is not a made up piece of information, it's present both where you'd expect (100m sprint, weightlifting) and in some cases where you'd expect a smaller difference (marathon running - something where big muscles and a large frame actually work against you). It's the reason we have women's leagues in the first place, otherwise we could just have one league for everyone.

I agree that testosterone alone is not the whole answer to athletic performance, there are many, many other factors, but it definitely seems to help perform. It's one of those things where a population with higher testosterone would perform better on average, but on an individual level you can't really judge purely by that.