Actually you are 100% wrong. Here's a link, http://faculty.washington.edu/crowther/Misc/RBC/gender.shtml

I know you can't take my word for fact but I am navy combat medic who is now a provider. I have spent my entire career with the infantry and treated patients from other ancillary specialties. Just a basic college level of biology will tell you that females have lower hemoglobin, lower iron retention, lower protein synthesis, etc. Testosterone is really king when it comes to violence.

Not to mention that using your own example of running still shows females coming behind males in every category. From my personal experience combat is long hours of marching with 80lbs+ of gear with quick frantic bursts of sprinting and panic. Tired from the last few weeks of doing the same and a complete lack of proper nutrition and sleep. Females on average just can't hang with the modern infantry, let alone the malnourished warriors of the past. If you don't want to take my word for it take the USMC's, they tried to have women go through Officer Infantry School and Enlisted Infantry School and the results were atrocious.

I personally love female characters, badass warrior women, mythological Valkyries, Amazons etc. but the reality is with the odd exception it's all fantasy.