As evidence that there's no correlation between natural T levels and athletic performance, Veronica Ivy (the athlete formerly known as Rachel "cis people should all die in a grease fire" McKinnon) said that 0.5% of male Olympians had extremely low [natural] testosterone [for males] when they competed at the Olympics, yet they nevertheless were able to compete against men with 80x higher T levels with "no competitive disadvantage."
This is totally beside the point. The fact that there's no clear correlation between the natural T levels of male athletes at or near the time they engage in sports competition and how well they do in that competition against other males doesn't justify males using gender identity claims and T reduction schemes to horn in on women's sports so they can compete against females. These are two entirely separate topics that have nothing to do with one another at all.
The reason that males have such huge advantages over females in most sports is not because they have high levels of natural T at or near the time of any given competition - it's because of the accumulated legacy effects of what happened to their bodies previously due to the high natural T levels they had during crucial stages of development in the past.
Males acquire a host of physical characteristics that make them much better suited to nearly all sports than females due to the massive amounts of natural T their male gonads, the testes, pump out over the course of three distinct formative stages in life - during gestation in utero starting from the 7-8th week when the testes first form and start producing natural T; during the male mini-puberty of infancy that occurs in the first year after birth, a 4-7 months-long period when baby boys' natural T levels are high as in male adolescence; and during the years-long transformation from boy to fully-grown man that begins when puberty of adolescence starts, usually around age 11-12, through the rest of the teen years.
It doesn't matter whether males have low natural T later on in life. Once they've acquired, or start acquiring, any of the many distinctly male physical features males obtain going through male puberty of infancy and adolescence, males will always have a big leg up over females in nearly all sports.
From age 12 on, the male physical advantage in sports becomes so huge as to be glaringly obvious and undeniable. But even long before 12, males have physical features - such as a hearts with a 6-8% larger and more powerful left ventricle than female hearts of the same size and age - that put nearly all male children at a distinct advantage over nearly all female children in the vast majority of sports.
One of the many reasons Ivy's blather about natural levels of T is so maddening is that the high levels of natural T which males have and benefit from during development are only a boon athletically to males. In girls and women, natural T elevated above the normal female range during any stage of life is sign of a serious endocrine disorder such as CAH or PCOS, a life-threatening tumor, or pregnancy - none of which are conditions that are associated with peak physical fitness and top-tier sports performance.