[aaron425]

To be fair for your second point, speaking as someone attended an Ivy but is from a low income household and terrible at sports, many of the people who manipulated spherical objects adeptly also had brilliant minds.

I was always impressed with my friends who had the mental fortitude to wake up at 6 every day, practice for 3-4 hours, go to class, practice after class, and still take the courses/do the research necessary for elite graduate schools. Meanwhile, I woke up at 11 AM on a good day and only started going to the gym regularly my senior year. I honestly can't say the proportion of "regular" athletes to "smart" athletes was any different from that of students in the general population.