An LOA is a tricky thing. Although many people say that they go to the best of the best, and imply that this relates in great part to grades or test scores, the reality is that it is actually much more complex than that. They are sent to those who, based on their file at the SA, are the best candidates for USMA. Because the SAs look at the whole person, not just testing/academics etc., what appears to be the best candidate to the average citizen looking in is not always the best candidate from the perspective of admissions.
While there is often a correlation between grades/test scores and LOA’s, many LOA recipients are not at the very top scholastically. I personally know of many LOAs who’s test/GPA etc. were around the norm or even under the norm of scores for the prior accepted class. The goal of the SAs is to appoint people who will become great officers. This requires not only scholastic success but also an aptitude for leading others. In the long run, the SAs recognize that cadets/mids must have the scholastic aptitude to succeed and graduate but they also must have the fortitude to accept the difficulties of SA life (not the academic side) as well as the character traits of a leader. Many of these are very difficult to quantify and are intangible.
To try and figure out why some applicants obtained an LOA and others did not is a exercise that cannot be successfully accomplished. Although you may know the scholastic aptitudes of some of these candidates, it is unlikely that you have seen the recommendations written by others on their behalf, reviewed the essay responses to the SA or reviewed all out of school participations (church/club/community etc.). You have each almost certainly submitted your files at different times (rolling admissions at the SAs). More LOAs are sent in the Oct/Nov time frame (even some in the summer for USMA) so if they completed their file before you, they had better odds of an LOA because of the time frame. If your file was not complete until late (Dec/Jan) then there are far fewer LOAs being given by then...
One things you state is that all of the 7 other students have an LOA or appointment to a SA but you do not note if it is the same SA that you are applying to. In reading your note it sounds like the 8 may be vying for different SAs. Each SA admissions office reviews files differently and what may get an LOA/appointment at one SA will not at another.
The best thing you can do at this point is be certain that your file is complete and reflects you to your ultimate potential. If you have not already submitted your most recent transcript, do so now. If you have participated in events/activities etc.. that would reflect well on your file then it is time to submit an updated resume of accomplishments. Good luck to you and let us know how it goes. Remember, it really is still early in the process - most appointments don’t go out for another few months.