I've always viewed Tulane as one of the "non-Ivy Ivies": the schools with a high academic reputations who chose to continue playing big-time football in the two platoon era, usually with dire on-the-field results. Duke, Wake Forest, Northwestern, Vanderbilt, Tulane,. Rice and Stanford. You can usually find them at the bottom of the standings of their respective conferences. I never put SU in that group because we tended to be better in football and especially basketball and I didn't think our academic reputation was quite on a par with theirs.
I've always thought it would make some sense for the non-Ivy's to leave their current conferences and join up with the service academies to form a new conference: Air Force, Army, Duke, Navy, Northwestern, Rice, Stanford, Tulane, Vanderbilt and Wake Forest. That would have been a good conference over the years and the academic competitions would have been dynamite.