It doesn’t. Assume you mean the other 4 service academies for “other institutions.”
While all the SAs are looking for top performers well-rounded in academics, athletics and leadership, they all have their own way of evaluating candidates and weighting skills attributes and traits they value. They also fully expect and don’t mind candidates are also applying to other academies, ROTC, and civilian colleges. They want each and every candidate to find a good two-way fit with an academy, and most importantly, with the service they will be in for a minimum of 5 years after graduation.
And if a candidate is offered an appointment to say, USAFA, that does not guarantee an offer from any other SA. Much depends on the competition in your nom categories.