“Just the stats” are an incomplete picture.
An LOA can be given for many reasons - perhaps there haven’t been appointees from a certain geographic area in some time, or some other aspect of the whole candidate/score multiple that triggers the SA to offer an LOA.
The SAs fill out a class looking to balance a number of aspects that meet all kinds of goals. It’s not just “you have the best test scores/grades on the planet, we want you.”
You can drive yourself crazy trying to extrapolate your chances from another’s stats - and equally crazy if you try to use that in a comparative analysis of who got appointments or prep offers and who did not.
There are plenty who have more ho-hum stats (as compared to the group of typical SA-qualified candidates), no LOA, who get an appointment, and soar to the top of the class, blowing right by classmates who had better incoming grades and test scores.
The SA is picking its appointees based on ability to handle the academics, military life and other aspects of 4 years at an SA, but their primary focus is choosing those whom they see as having the most potential to develop into junior officers. It’s an art and a science to do that, and they have decades of experience in putting together a class each year.
Like most have said here there are many reasons why SAs give LOA. I am no expert but I believe LOAs are given to candidates that the SAs are certain they want to admit anyways either now or later if all required conditions are met; given that the candidate has met the qualities SAs seek. Must also pass and have DODMERB Nom and CFA. And supply and demand of Candidate mix they are seeking in that region, both historically and currently.
I would take the Asian Minority out from the equation. Asians are no longer minorities in this country. And has not been for many years by colleges. In fact, Asians make up the highest race after Caucasian and at many top schools; in UC Schools and MIT, Asians appear to be the majority of include international students. Among the Ivies and Stanford, Columbia and Harvard are home to large Asian student body. And West Point and Annapolis are no different with Asians and mixed Asians making up double digit student body.
So Asian Card doesn’t work at colleges and SAs. However, I can see that being an Asian female is quite rare to attend SAs so given your stats and depending on what geographic region you are from can make a real difference getting an Appointment later on.