You're asking about something that is subjective in nature; and used mainly to validate.
Hmmm?
A letter of recommendation, unless it came personally and directly from the President of the United States, isn't going to get you into the academy. However; if one of your teachers who provides a recommendation and gives a very negative response, could have a negative affect on your chances.
Your application lists basically "FACTS". GPA, SAT/ACT, class rank, sport participation, club involvement, volunteer time, etc... The letters of recommendation are mainly used to validate all those facts and accomplishments. You can tell a lot by answers from a teacher if the accomplishments and facts of the applicant are sincere and part of that person's makeup or is it simply someone filling in squares. Most letters are going to be full of "Praise". But some use less impact words that don't sound like the person who's facts are in front of them.
So no, there isn't a lot of direct points associated with letters of recommendations; but the academy and your senators/representative can get a clearer idea of who you really are from them. That will definitely affect they score you in their process.