I have been a teacher and college guidance counselor in schools in New England since the early 80s. I remember when I was first starting out in the "biz", I was told by a much older and experienced mentor that Princeton tended to target a certain "type" and that its academic requirements weren't really as high as Harvard and Yale -- it looked for other things, including a real demonstration of interest in Princeton. Obviously, I am not sure if that was ever true, and certainly over the past 20 years or so, the student bodies -- in terms of statistics, at least -- are practically interchangeable. All three schools today are infernally and equally hard to get into.
Interestingly enough, while kicking around the storage room of our school's library I came across some dusty old hard and soft-cover college guides, including Peterson's and Barron's from the 60s, 70s and 80s. The kind of things we had to use in the benighted period that preceded the world wide web. I have been perusing them for kicks and I really was surprised by how much lower the median SAT scores were for Princeton 30 to 40 years ago compared to H and Y. Some examples from random years:
Year, School, Average Math/Verbal SAT
1965 H 655/640 Y 650/632 P 635/590
1968 H 675/670 Y 680/665 P 630/600
1972 H 690/665 Y 670/660 P 638/620
1977 H 685/675 Y 675/675 P 640/630
When did Princeton close this "gap"? Did Princeton just get more popular, or was there an active effort to increase SATs? Obviously, Princeton scores in this period were not bad -- but they were actually below Dartmouth's scores and around Cornell's scores, and places like Bucknell and Union College. I didn't have too many kids apply to Princeton from my neck of the woods until about 1990 -- they were much more H and Y and New England LAC focused.