They open the flood-gates for Americans.
I'm currently studying International Relations there, I've been in tutorials where I've been the only UK Student. I've never been in a class in the department which wasn't at least 1/4 yank - and it's often closer to 3/4. The university actively targets American schools, sends ambassadors out there regularly, (especially to the elite private schools), and even held a gala dinner in New York (with Will & Kate) to solidify it's status as 'internationally Scottish' i.e. follow the American money. I've met absurdly rich people here.
I've heard statistics which say that 1/32 UK applicants are admitted for our program, 1/64 Scottish, and 2/3 for the Americans. That is to say that for every 32 UK students who apply, there is only one place. For Americans entry requirements are lower, and they'll respond to you first to let you know you've got a place. After all the internationals have been decided upon, they then decide which RUK and Scottish kids are offered a place. It's pretty shocking behaviour tbh - but in comparision with other elite universities St Andrews just doesn't have the money - and the incentive of £17,000 a year from a international students (plus that nice tradition Americans have of donating to their Alma Mater) is just too hard to turn down. As a former history tutor of mine quipped : 'the IR school is a cash cow for the university.' ... The marketisation of education is a wonderful thing.
Don't get me wrong, some of the Americans work very hard and are incredibly bright individuals completely deserving of a space here - and it definitely makes for a unique student experience. However, I can't shake the feeling that this comes at a cost to local students - the Scots in particular. In four years I haven't met a single state-school educated Scottish student in IR. The new Principal says she's going to work on widening-access... but I'm not sure how much of that is window-dressing rather than a sincere commitment. ... And after saying all of that, I have heard from a New Yorker friend that a couple of students from her school have been rejected from St Andrews (previously unheard of).
Sorry this largely irrelevant ranting - if you apply, do your research, write a good statement, and meet the entry criteria I would be surprised if you weren't offered a place. The town can get a bit claustrophobic, but it's beautiful, the education is top class, you'll meet wonderful people, and many doors will be opened for you. Wish you all the best, but I wouldn't fret too much about getting a place.