I'm not quite sure how Academic Index factors into admissions or making of the team. Someone who knows a lot about Ivy League athletics please explain. I've heard something about how the team has to have an average AI to compete, so that would mean a sub-par athlete with good test scores and GPA could make the team, but I'm not sure of the veracity of that.
It matters on the sports where keeping the team AI close to the school's average AI is required. Those sports are football and men's/women's basketball, I believe--maybe men's ice hockey as well?
So a HS valedictorian with 1600/1600 on the SAT and a 4.0 unweighted GPA might make a school's football team--even if he would never play a down in a game--because his above-average AI would create space for a lesser academic light (but great football player) on the squad.
On track and cross-country teams, I'm pretty sure that the League has no such close-to-the-overall-AI rule. Most t&f/xc kids are strong students anyway.