Are there any "sports" (using the term loosely) in which women compete equally with men?
Surprisingly, there are! Ultrarunning, ultraswimming, and rifle shooting.
Ultra runs or swims are any race over the standard marathon distance. Women do about as well as men in these competitions, and it may be down to some specific physiological sex differences. One theory is that women, having lower body weight, require less oxygen to complete ultra-long distance runs at a slower pace than marathoners. Women may also have greater pain endurance, although this hypothesis is controversial.
Rifle shooting is holding a rifle steady and hitting a stationary target. Women may perform as well as men in this particular event because their lower center of gravity enables them to hold a rifle steady for longer periods of time.
Interestingly, women don't do as well as men do in the pistol or moving target events. The situational awareness requirement to analyze trajectory and shoot while in motion appears to favor men, which may explain why men make better police officers. This sex difference in aiming and firing while in motion likely has its evolutionary origin in the fact that pre-modern men did all of the big game hunting, which closely mimics pistol shooting at moving targets or while in motion.
