Our Congressman has 15 constituents at USAFA right now./QUOTE]
While there may 15 constituents at USAFA now, I would expect that only 5 of them are charged to his nomination. (Disclaimer -I don't know anything about USAFA: I believe USAFA has a different authorization statute, but suspect the nomination rules are the same for all service academies). The remainder may be charged to the two Senators and/or the various alternative nomination sources USMA1994 identifies above. As noted above, most Appointees themselves don't necessarily know, or care, what nomination source they are charged t0.
So 10 candidates may be competing for 1 to 5 spots within their district? If that is accurate -it sounds like there may also be an opportunity for other "at-large"spots if not all states / districts around the country fill all their spots? Is that in the ballpark?
Keep in mind, thats 5 appointees in the academy at any given time, or 1.25 every year (or 1 most years, with 2 occasionally). It's probably pretty rare to have no qualified candidates from an Congressional District... It happens, but not enough for a candidate to even think about.