I read an article somewhere about how Harvard fill its 1600 or so spots each year. At the end, you only have about 300 - 500 students get in per their merits only.
Out of 3 MM or so HS graduates plus thousands international applicants, I will think many have the exact set of hook or light spot or whatever.
A girl from our D's HS has been accepted to H this year. She is an Olympic level swimmer and has a 4.0 UW GPA. It might as well as that difficult to get in.