Packer; if you want to use averages you can, but the reality is that the reason 5 is the max is because it's possible for a cadet to have to leave and come back. So it's basically 1 per year, with the occasional 5th. Remember; air force is young. However; army and navy have been around a long time. The rules apply to all 3. But a cadet could have left for medical, religious, family emergency, etc...
Also; there really are some MOCs who might have 2 available slots open, but CHOOSE to not try and fill both slots. They might not feel they have 2 guaranteed worthy applicants. There's a lot of reasons.
Also, you have to realize that both the academy and the MOC are playing games with each other. Last year, I/we had an individual who had a presidential and received an EARLY appointment. (October-November). Obviously it was using the presidential. However; one of the senators nominated him anyway. When the spring came, the academy had MOVED his allocated slot FROM the presidential slate to the senator's slate. This meant our state got one less appointment because the academy wanted to use the presidential for someone else. With the cutbacks and appointments not coming out until spring, it's not a big deal, but when there are early appointments, I tell the candidate as well as the MOC's that if a candidate has an actual APPOINTMENT in hand using a presidential, ROTC, or similar; do NOT give the candidate a nomination.
So while mathematically, you can say that 668 of the "X" amount of appointments will come from reps/senators, this isn't necessarily true. Neither is the rounded off 535 for 1 for each rep/senator. My state has the 2 senators, but we only have 1 representative for the entire state. Yet, the year my son started his freshman year at the academy, our state had 6 candidates with appointments. 1 presidential; 1 from the prep-school; one senator had 2 slots; one had NONE available; 1 for a representative; and another from the national pool. Bottom line: No amount of math or what a senator or representative in another state/district does; will have any affect on a person's odds/chances of receiving an appointment. More than half of the qualified individuals who don't receive an appointment are good enough to get accepted to some of the finest universities in the country. The truth is: There's simply not enough spots in the academies for everyone who wants to come here. Same with harvard, yale, princeton, stanford, purdue, MIT, Cornell, etc... They only have room for so many. Same with the academies.