According to an 18 month review by Equality in Sport which is made up of representatives from Sport England, Sport Scotland, Sport Wales:
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Many sports will favour faster, bigger, stronger people in a physically competitive event. The Equality Act recognises this through the ‘gender-affected’ nature of many sports, and this can be further understood through an analysis of the physical and performance differences between the sexes.
Adult male athletes have on average a 10-12% performance advantage over female competitors in swimming and running events, around 20% advantage in jumping events, and 35% greater performance in strength-based sports (e.g. weightlifting) for similar-sized athletes. When average-sized males are compared with average-sized females, the difference is such that the males are half as strong again as females.
According to data from the NHS, 50% of males are taller than more than 95% of females, with longer, straighter limbs, and bigger hands and feet. Males have greater muscle mass (concentrated in the upper body), bigger hearts and lungs, and greater stamina through higher hemoglobin (oxygen carrying capacity) than females.
The difference in performance, even at the lower range of 10-12%, is not small in terms of competitive outcomes; and would result in Adam Peaty being beaten by half the pool length in a short-course 100m breaststroke competition, Dina Asher Smith by more than 20m in the 200m track sprint, and Sir Mo Farah being lapped twice in the 10,000m track race.
The reality that males and females do not often play competitive sport against each other makes it difficult to appreciate the difference in physical capacity in most cases, particularly in team sports. However, an understanding of the gap between the two sexes can be recognised by results of practice matches between national senior women’s football teams against under-age boys’ teams in recent years: the national teams from Australia, USA and Brazil were beaten comprehensively (7-0, 5-2, 6-0 respectively) by club teams of 14 and 15-year-old boys.
Research on children indicate that there is a significant difference in strength, stamina, and physique at all ages, and this has been recorded from six years until maturation in comprehensive data sets. While the difference between the sexes increases after puberty, there is a brief period around the age of 10-11 in which females attain parity in height due to their naturally occurring earlier onset of the growth spurt of maturation.
Current scientific evidence indicates that the difference between the strength, stamina, and physique between the sexes is largely due to the higher testosterone levels of males during their lifetime. While this is not universally accepted, it is the basis for limitation of testosterone levels as required by the IOC for those transgender women wishing to compete at the Olympics. Such regulations have been adopted by most international governing bodies of sport, and by many NGBs in the UK.
The expectation has been that the suppression of hormone levels will create the guarantee of fairness as outlined by the IOC, as well as restitution of disadvantage within gender-affected sports as per the provisions in the Equality Act 2010 in relation to gender reassignment.
However, at this time, emerging evidence does not support the view that testosterone suppression for 12 months will achieve parity of strength, stamina and physique for transgender women compared with females; and hence cannot guarantee fairness. Rather, there appears to be a retention of physical capacity in transgender people who suppress testosterone from male levels. Research has only been collected for less than two decades and does not include longitudinal objective measurements of high-level transgender athletes. There is, however, considerable evidence which collectively demonstrates modest reduction in muscle mass and strength following testosterone suppression when compared with the average difference between the sexes, and this reduction may be further minimised with physical training. Testosterone suppression beyond 12 months may result in further strength reduction, but this does not reach parity with female levels up to the three years of current study length. Physique factors such as skeletal height, as well as lung size and bone density, also remain largely unchanged by testosterone suppression. However, stamina is likely to be affected as haemoglobin levels (which impacts oxygen carrying capacity in blood) decrease to those of females within 12 months of therapy; but the evidence for comparative performance loss is equivocal.'
TLDR: The science is clear!!