Shouldn't we root for Colgate to lose today to increase UW's chances of getting a home ice NCAA game? Since they are ranked ahead of Wisconsin right now? Or is the idea that we need them to advance in their tournament and then lose to someone else?
The key to the whole thing is how the Pairwise works, the Pairwise comparisons between UW-Minn and Minn-Colgate, and getting Minn 'right next to' Wisconsin.
Most Pairwise comparisons revert to 'who has a better NPI?' because few team pairs have head-to-head elements to the comparison. If you look at the Pairwise ranking page right now, Minnesota is in 3rd with 39 wins, Colgate 4th with 38, Northeastern 37, Wisconsin 36.
The assumption of Northeastern losing the HE final to Vermont and Wisconsin beating Minn in the WCHA semi (I assume) would drop NE's NPI down enough to cause them to start losing the comparison to Wisconsin (NE's NPI lead over UW isn't very big; 62.50 to 62.28). Losing to UW would also likely drop Minn's NPI such that they start losing the comparison to Colgate. That would make it Colgate 3rd with 39 wins, Minn 4th with 38, and UW 5th with 37, getting Minn 'right next to UW'.
Wisconsin's NPI is is far enough behind that of Colgate and Minn such that UW is never going to catch them and win a comparison on NPI alone (at least not without winning the WVHA outright). But that's where the head-to-head between Wisconsin and Minn comes in. Wisconsin is two wins, zero losses, two ties over Minn. A third head-to-head win gets Wisconsin the Pairwise comparison win over Minn, despite having a worse NPI. And that would move UW ahead of Minn, 38 wins to 37.
But ONLY if Minn is 'right next to' UW, 38 and 37; that is only if Colgate stays ahead of Minn in NPI. A Colgate loss today keeps Minn ahead of Cogate in NPI, even with a loss to UW next week. That would make the Pairwise wins a three-way tie at 38. And as always, all ties are broken by 'who has the better NPI?'. And that would keep Wisconsin at 5th.
Simple, no? LOL
Wisconsin CAN get ahead of Colgate (and Minn, for that matter) if they win the WCHA tournament outright. But that requires two 'upset' wins next weekend. The 'easiest' way to get UW to 4th is for Colgate to get/stay ahead of Minn, and then beat Minn such that UW win the comparison based on head-to-head.