Great post, great questions, Ramblerguy. You have been thinking about some of the same things I've been thinking about.
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it sure seems like the NCAA finds schools outside the P5 or 6 to be an annoying presence at this event
YES! I pointed out last week that there are exactly 75 total teams in the P5+Big East. Their new way of keeping mid-major teams out of the tournament is this new "Quadrant" system that "replaces" consideration of top 50 and top 100 wins. And it's the number of Q1 and Q2 wins that matters--- the LOSSES DO NOT MATTER AT ALL. So where do they draw the line to consider what is a Q1 and Q2 win? For road games, it's at 75 for a Q1 win, and for home games the cutoff is 75. To me, that says "we won't consider any of your wins worthwhile unless they come against teams that are or should be in the top 6 conferences" without actually saying it. Also, they consider a team that 6 wins and 11 against Q1/Q2 teams to be far superior to a team that is 4-3 against Q1/Q2. Losses don't matter if they're against Q1/Q2 (or teams that would be in the P5+BE if RPI merit were the only consideration).
Something needs to be done about under-.500 conference teams getting at large bids, because they have no incentive to ever play decent teams outside their conference. They can play all MEAC or SWAC or the bottom of the WAC and Summit and Big Sky in guarantee games on their home court. They'll mix in an MTE, or a conference challenge game to make it look respectable and get another chance at a Q1/Q2 win. But there is a huge disincentive to play respectable teams.
So how to fix it?
1. Teams under .500 in conference need to have a better than .500 record in their conference tournament, or they are not eligible for consideration. (Example: If you're 8-10 in the Big 12 or SEC, you have to go at least 2-1 in your conference tournament).
2. Consider road victories as a factor equal to Q1/Q2 or strength of schedule, OR add a bonus similar to the RPI bonus for road victories when calculating SOS.
3. Also consider Q1/Q2 losses, so a team that is 6-13 against Q1/Q2 is actually worse off than a team that is 4-3, not BETTER off.
4. Adjust the Q1/Q2 cutoffs (e.g. make the neutral site cutoffs the home game cutoffs, and bump the cutoffs for road games up by 10-15%, and split the difference for neutral games). In other words, add 15 or so to all the Quadrant cutoff numbers.
5. If you're going to punish mid-major schools for not scheduling up, then you have to do that to major schools, too. Michigan, Michigan State, Houston, Texas A&M, West Virginia, NC State, Creighton, Florida State, and Nebraska all had Non-Con SOS numbers about where Loyola is or worse, and they played almost all their games at home, bought their home opponents, or bought out their promised road commitments. They had many more choices than mid-majors, and they knew they could make up their overall SOS in conference games, where they could finish below .500 and still make the tournament. This is only going to get worse with the current rewards/punishments as they are. The only way to reasonably be sure that the team you're scheduling against will have a Q1/Q2 level RPI is to schedule against a P5+BE team, but P5+BE teams refuse to schedule mid-majors, because they might lose, and because THEY DON'T HAVE TO.