Going to interpret this as asking the opinion of the athletic conference and say, does anyone really care?
It is kind of interesting that while Stanford, a school that is equal or greater in prestige and selectivity to most Ivies, is a powerhouse in football and other D1 athletics, and "Southern Ivy" Duke is known for its basketball program, the Ivy League schools themselves have chosen to be athletically irrelevant. I'm curious as to why that is. The Ivies are smaller schools, granted, but not smaller than schools like TCU and SMU; and it's not as if most of the people who root for schools like Duke actually went to Duke themselves.
The Ivies don't give out athletic scholarships.