There have been numerous articles in media over transgender women competing in women sports, and debating if this is fair with women whose birth sex was female.
I know there are some studies, like Race Times for Transgender Athletes, that show that after lower levels of testosterone follows a loss of muscle mass and bone density, and thus their athletic capacity is diminished.
I'm not sure if this loss of muscle mass and bone density is enough, or if there are other factors that could still provide an advantage. Perhaps the possible advantages vary for each sport.
So, is there evidence about the possible advantages of transgender women athletes over cisgender ones? Lets limit the question to sports where men have clear measurable advantages over women on average.
We should also specify how far into transition we are talking about, as pointed out in the comments. The International Olympic Committee (IOC) current rules are probably the best reference for how far in transition they must be to be allowed to compete in the women's category:
Those who transition from male to female are eligible to compete in the female category under the following conditions:
The athlete has declared that her gender identity is female. The declaration cannot be changed, for sporting purposes, for a minimum of four years.
The athlete must demonstrate that her total testosterone level in serum has been below 10 nmol/L for at least 12 months prior to her first competition (with the requirement for any longer period to be based on a confidential case-by-case evaluation, considering whether or not 12 months is a sufficient length of time to minimize any advantage in women’s competition).
The athlete's total testosterone level in serum must remain below 10 nmol/L throughout the period of desired eligibility to compete in the female category.
Compliance with these conditions may be monitored by testing. In the event of non-compliance, the athlete’s eligibility for female competition will be suspended for 12 months.