OP, not quite sure what you are asking, since service academy applicants do not apply directly to either the service prep schools (NAPS, MAPS, USAFAPS) or to the scholarship programs to civilian prep schools such as MMI though the Naval Academy Foundation Scholar, USAFA Falcon Scholar, etc.
There are certain civilian prep schools the SA has a relationship with, and if a candidate is offered a USNA Foundation Scholarship, for example, and applies to one of those prep schools, they are going to get in to that prep school. If they successfully complete either the service prep or scholarship prep, chances are extremely high they will successfully reapply to the SA. See this link for USNA partner prep schools. Ditto NAPS - if a candidate is offered NAPS, and they accept, then they are in at NAPS.
Those options are offered to applicants Admissions thinks would benefit from the program. You can look up the profile of incoming classes that is published each year, and there will be a stat for prep school.
@nuensis gave the NAPS ballpark. You have to assume the actual number of service prep school offers and civilian prep school offers is larger than the class size, because some will decline the offer. There will also be attrition at the prep schools, voluntary and involuntary. Here’s an example of an incoming class profile; you can look for these for all the SAs each year.
Class Portrait page for Admissions at USNA.edu. Updated Tue May 21 05:06:43 EDT 2024.
www.usna.edu