I see questions on here all the time of “I got (33/34/1550/1500) score on my ACT/SAT. My first choice is (insert ivy/Stanford/MIT). Should I take it again?” Nearly every time, the response is no don’t bother, and someone claims that schools don’t actually care about those couple point differences at the top of the scores tables.
I did some research though, and it looks like (at least some of) the schools say otherwise. Here ( http://ephblog.com/2006/06/08/academic-ranks/ ) is a link that outlines Amherst’s academic rating system. Their cut off to be in the top tier of their academic rating system is a 1520 (old SAT, no writing), which converts to a 1550 on the new SAT. That means, assuming the system is still the same from a few years ago, getting a 1540 vs getting a 1560 can be the difference between getting in and not getting in.
Here’s a similar one from Williams ( http://ephblog.com/2014/10/21/academic-rating-details/ ). Again, their ‘1’ rating is only available to those with a 35-36, so a 34 vs a 35 can mean the difference between being rated a 1 and being rated a 2. While they don’t publish the acceptance rates for the different groups, I would wager the acceptance rate for 1s is significantly higher than for 2s.
You can read those articles for more information on the specific schools and their rating system, but the main point I am drawing is that schools clearly do care about a 34 vs 35, 1500 vs 1560, etc. Again, this is only for Amherst/Williams, but I would wager Ivies and other highly selective schools are in the same boat.