I'm going to start right here by saying this premise is so incredibly far-fetched that it almost doesn't bear writing about. I posted the other day about getting a bye in the Big East tournament to set up a 3-in-3 run like it was a pipe dream, and that's frankly still the most likely hope.
Just for grins, let's just lay out the best-case, non-auto bid scenario for Xavier and see where that lands them.
First, you've obviously gotta have X winning out in the regular season. That's wins over Nova and St. John's at home and St. John's and Butler on the road. KenPom gives Xavier an above 50% chance of winning just one of those games, the 52% against St. John's at home. The win probability math on all four of them gives X something like a 1.3% chance of going 4-0. Whatever, we'll take it.
That leaves Xavier with work to do in the Big East tournament, namely winning two games but not three.
We'll pivot to Bart Torvik's website here because he lets you project conference tournaments. Installing Xavier as the 3 seed thanks to their scalding finish to the season and run the numbers to find... about a 14% chance to make the final before falling.
If that happens, where does it leave Xavier? They would be around 15-11 in Q1 and Q2 games with probably something on the order of a 5-8 Q1 record depending on how opponents finish their season. They would be 20-14 overall with a 10-8 regular season conference record. Would that get them in?
It obviously depends on a whole host of other moving parts. For what it's worth, Bart Torvik would give that resume about a 10% chance at an at-large bid.
That's what we're looking at without the auto bid: a 1.3% chance to sweep the regular season to get a 14% chance to win two in the BET for a 10% chance to hear Xavier called on Selection Sunday.
Works for me.