In the wake of Wisconsin’s 4-1 victory over North Dakota in the WCHA third-place game, Minnesota can still make the NCAA tournament, but the chances are slimmer than slim.

It was known last night that a UW win was bad for the Gophers because it caused the Wisconsin-Minnesota head-to-head pairwise comparison to flip. Minnesota still isn’t quite dead pending the Princeton-St. Lawrence outcome, though.

The following scenario taken from the PairWise Predictor illustrates that point.

CCHA Championship game: Michigan defeats Notre Dame

ECAC Championship game: Yale defeats Cornell

ECAC Consolation game: St. Lawrence defeats Princeton

Hockey East Championship game: Boston University defeats Mass.-Lowell

WCHA Championship game: Minnesota-Duluth defeats Denver

Atlantic Hockey Championship game: Mercyhurst defeats Air Force

Go ahead and see — Minnesota ends up in a tie for 13th with St. Lawrence and in the tournament. In this situation, Michigan over Notre Dame is key since it influences the Ratings Percentage Index in such a way as to give Minnesota a comparison win over Princeton.

Wild, no? But that’s the PairWise. Mercyhurst over Air Force is important for a different reason — AFA can win its head-to-head comparison with Minnesota if it wins today. That knocks the Gophers down and potentially out no matter what else happens.

If Princeton wins or ties, the Gophers’ scenario is much bleaker. I have yet to find a scenario that puts Minnesota in the NCAAs without a St. Lawrence win in the ECAC third-place game. There may be one somewhere, but I don’t know what it is.