Augustus
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Are you assuming "biologically male" a "trans woman" are equivalent?
Under current rules, in order to compete, trans women have to bring their testosterone levels into the typical female range. Once that's done, it's unclear whether there's any advantage at all; some studies suggest that trans athletes are at a decided disadvantage in some sports:
On Transgender athletes and performance advantages | The Science of Sport
The article basically says there isn't enough evidence as it's not been thoroughly studied.
We also know that the benefits of PEDs remain long after people stop taking them, so simply lowering T doesn't = no advantage.
Studies on elite athletic performance are very difficult due to small sample size, the difficulty of isolating variables, the wide variability in individual responses to the same thing, differences between athletic disciplines, the fact that elite athletes generally have more pressing things to do than take part in a study, etc.
A few years ago, the following nonsense was published.
Lance Armstrong's drug of choice, EPO, 'doesn't work', scientists claim
In the first study of its kind, scientists challenged a group of 48 cyclists to tackle a series of challenges, including the infamous Mont Ventoux ascent, which often forms part of the Tour.
Half had been given eight weekly injections of EPO, a drug that promotes red blood cell production with the aim of increasing delivery of oxygen to the muscles, while the other half took a dummy.
But after the gruelling 21.5km climb - which was preceded by a 110km cycle for good measure - the average results of the two groups showed no difference whatsoever.
The scientists behind the trial, which is published in the Lancet, say athletes are “naive” about the benefits of illicit substances such as EPO, but that myths about their effectiveness go unchallenged in the murky world of doping.
Lance Armstrong's drug of choice, EPO, 'doesn't work', scientists claim
Study:
https://www.thelancet.com/journals/lanhae/article/PIIS2352-3026(17)30105-9/fulltext
If a study fails to find a performance advantage from something that so obviously improves performance as EPO then we have a problem [see times decrease based on EPO availability, and increase when the first doping test comes in, also numerous elite cyclists who took it while closely monitoring their performance and understood it was impossible to win without taking it]
PEDs give a useful analogy as to what can be assumed where there is an absence of scientific evidence.
Lance Armstrong was very obviously doping, not with the benefit of hindsight, but at the time because he underwent a magical mid-career transformation. Magical mid-career transformations that are too good to be true are (almost) always doping.
We already have examples of non-elite athletes winning women's elite competitions post-transition, and We know that the benefits of PEDs remain long after people stop taking them so can't say 'lower T = no advantage So we have to choose what is more likely:
a) She suddenly turned into an elite athlete
b) She was doping
c) She was gaining a relative performance advantage from being born with male anatomy
It's almost certainly b or c (or both).
If you flip a coin 49 times and it comes up heads, what are the odds the next one is heads? Some might say 50/50, but it's close to 100%. You have no evidence the game is rigged, but the results make it almost certain.
A non-elite athlete suddenly beating elite athletes (or a lower/mid-tier elite athlete suddenly consistently beating top-tier elite athletes) is always going to be far less plausible than the alternatives.
For example, people talk about a 'new era' for cycling in the light of doping scandals, biological passports, etc. Some people will say 'no evidence of cheating', but, just as it was with Armstrong, et al., it is perfectly obvious from results that the sport is still rife with doping (magical transformations, speeds as fast as during the EPO era, etc).
I elite sport, the proof is usually in the pudding regardless of whether or not it has been proved in a lab.