Hey! You finally asked an intelligent question!
Not an easy question to answer however, CP Thomas on the Big Soccer forum probably has the best solution which is just a slight tweak to what they are doing now.
The tough pill to swallow is the automatic qualifier for champions for some very inferior conferences. they take up a lot of slots. Then you’ve got the 7th, 8th & 9th place teams from the ACC getting in just because they play in a strong conference. Maybe they need to weigh the non-conference schedule heavier than the conference schedule to discourage teams from scheduling cupcakes and not penalize teams as much who play in conferences like the WCC where the talent level really drops off after the top 3-4 teams. if Pepperdine, SC & BYU had a choice, they probably wouldn’t want to play UOP and St. Mary’s but they don’t.
how about you Carnac? What changes would you make?
If you look at the formula (WLT x .25 + Opp WLT x .5 + Opp Opp WLT x .25), the best path for a conference to follow is for everyone to schedule cupcakes for non-conference games. That helps pump up the first 25% of everybody's RPI, and once they start playing conference games against each other, everyone already has a good W-L-T record, which helps the next 50%. On the men's side, look at RPI #7 Clemson's record (they're in the ACC). They have only played only one non-conference game against a team with a winning record.
https://rpiupdatemenssoccer.blogspot.com/2019/07/clemson.html
Or look at #18 Notre Dame, also in the ACC for soccer, who beat Purdue Ft. Wayne 8-0 - PFW is currently #204 out of 206 in the RPI ranking.
https://rpiupdatemenssoccer.blogspot.com/2019/07/notre-dame.html
The NCAA selection formula for ice hockey is ridiculously complicated, unless you have computer in your lap. After the conference automatic entries are determined, every eligible team (.500 or better record, not on suspension or voluntary withdrawal, etc) is compared with every other eligible team. Factors such as head-to-head records (each game is worth a point in comparison), one point for best record against common opponents, and one point for best RPI (adjusted for freaks such as wins that reduce the RPI), with RPI as the tiebreaker if needed. The teams who win the most comparisons become the at-large selections.
I have been toying with another formula (let's all it Espola Rating Index, or ERI) with similar intent as RPI but computed differently. A win against a team with a winning record would be worth more than a win against a team with a losing record, etc., but with an adjustable scaling factor (or perhaps a non-linear scaling). I don't have time to keep up with the numbers while games are still being played, but maybe next month I will see what difference it makes. Roughly - a win would be worth the weighted average of 1 and opponent's WLT, a tie worth the weighted average of 0.5 and opponent's WLT, and a loss worth the weighted average of 0 and opponent's WLT; and the average of all those numbers would be the ERI.