I can’t answer that question but I did want to mention that what distinguishes unusually talented math students (meaning students who gain entry into the likes of Princeton based on their math abilities) is achievement in national math competitions; high schools, even very strong ones, generally do not have the needed resources. This is not my children’s’ specialty, but I believe online resources like Art of Problem Solving and Russian Math are intended to help develop such kids.
My kids are more in the humanities. While their private schools had good quality instruction, I believe it was the national recognition they received that made the difference.