Ivies don't give athletic scholarships (or any scholarships). They have an Academic Index, and athletes must meet a minimum number. The team average A.I. has to be not too different than the overall student body average A.I. (maybe within a standard deviation - I don't remember).
That being said, if you are a big impact player for a certain sport, you can get away with the minimum A.I. Ivies sometimes then "recruit" athletes that are good players, not great, but have a high A.I. to boost the team average.
There was a classmate of one of my kids who was a big impact player in her sport, and she was probably on the low end of A.I. Kid had a 1200 SAT, and managed the academics (in a not too demanding major).
However, that is about as low as they will go. Said kid had a sibling who played the same sport at a public Ivy, and had lower scores - that kid struggled with the academics.
