No way to predict chances for appointment, though the fact you have an LOA is a nice boost.
Presidential noms are not competitive, so as many are eligible get them, but the Academy has a limit on how many appointments are charged to Presidential noms. There are usually more who are eligible for those than are offered appointments. I think it’s 100 of those per class.
Principal (not principle) nom - time to do your research. MOCs have the choice of a few different methods to rack and stack their slates. A principal nom is part of some of the methods. Assuming you have applied for your elected officials’ noms, their websites or staffers should be able to tell you the method used.
Since I am feeling Sirialexa-like today, here is:
https://www.usna.edu/Admissions/Apply/US-Senators-Representatives-and-Delegates.php
If you have not yet read every page, dropdown and link on USNA.edu, or re-read them, it’s always a good thing to consult the primary source when doing your own research. Most answers are there.
For detailed reading, find the most recent copy of the Congressional Guide to Admission to the United States Service Academy:
https://www.usma.edu/admissions/Shared Documents/Congressional Guide (2016).pdf
Go over to the Nominations Forum here on SAF - read Sticky, browse.
In general, someone who has met all the requirements of the LOA, continues to remain eligible and is the principal nominee on a slate, will be offered an appointment. That is actually not required at USNA, different from the other SAs, but will generally be the case.