I feel bad that no one is responding to your question. The reason is probably that nobody knows.
Something like 15,000 apply to USNA, and something like 1500 are offered appointments. Of those, about 1250 enter. Another 275-ish attend NAPS -- but how many attend isn't the same as how many are accepted. Who knows how many are accepted but turn it down?
Of the 275-ish, about 85% finish and graduate, and of those, about 95% go to the academy.
I don't know what the numbers are for foundation prep school, but that's another avenue for h.s. students needing more academic prep.
(Maybe you'll get more answers from some Smartest-Guy-In-The-Room-type eager to fine tune my numbers.)
If you get as far as a BGO interview, make sure you explain that you'd be happy to attend prep school in order to get to the Academy. Good luck to you.