Equestrian sports and shooting sports are the best. Women still have a physical disadvantage vs. men, but there is a mental aspect that puts them on a more even playing field. Especially equestrian sports (which are tough sports, the injuries can be catastrophic -- not for sissies). Women actually do better in those fields and compete with men. There's an extreme amount of body control and mental/emotional work that has to be learned, and women are very capable of competing against men because learning it is pretty much up to the individual. The trick is to not resort to trying to physically over-power, and women tend to have a better start as they don't need to unlearn that (although, in the last decade or so, I have seen problems with this: young women thinking they can ride very physically and aggressively...it ruins their talents and stunts their abilities). Yes, all my children shoot and ride; sometimes they do both at the same time! It's what we call "family fun time".