I hope I don't screw this up too bad. It is mostly done by highest WCSs get the appointments, but I think that admissions can really do whatever they want to make the class they want. My dad was an ALO, and he said that he's heard of the academy bargaining with MOCs to take someone on their slate instead of taking their principle nom. And if Timmy the basketball star has a WCS of X and Johnny Eagle Scout has a score of X-1, they can still pick Johnny Eagle Scout instead of Timmy basketball star for "intangible" reasons that they see. Maybe they like Johnny's leadership. Maybe Timmy admitted to smoking marijuana. Maybe Johnny comes from an Air Force family. Maybe they already have their basketball team filled.
So for the most part we can live in peace believing that principle noms always get appointments, and the highest WCS will win; all that is true most of the time. But there are weird exceptions, admissions will make the class how they want.
P.S. and as an added note, I'm kind of counting on intangibles to win me an apppointment at this point. My ALO told me my WCS is about 95% of what it needed to be for her to confidently tell me i'm "competitive". But my dad was an Air Force officer, and an ALO, and my recommendation letters were from Military guys and a West Point grad. According to my ALO and my dad, these are the things that might help to push me over that line.