A detailed look at NMU’s chances

Assuming all game outcomes are equally likely, Northern Michigan stands something like a 15% chance of making that tournament.

From my previous PWR possibilities article, Northern Michigan’s overall possible final PWR rankings:

Possible PWR outcomes for NMU

PWR	Number of scenarios	Percent of scenarios
13	15297	1.3%
14	120251	10.2%
15	388264	32.9%
16	610668	51.8%
17	45168	3.8%

Because 13-16 are all on the bubble, it’s most important for Northern Michigan that a limited number of conferences are won by teams that won’t be in the top 16.

Again, those are:

WCHA (2/6)
Michigan Tech
St. Cloud St

Hockey East (1/4)
Providence

ECAC (2/4)
Harvard
Colgate

CCHA (1/4)
Bowling Green

Atlantic Hockey (4/4)
RIT
Niagara
Mercyhurst
Air Force

So, while every conference could conceivably be won by a team not in the top 16, only Atlantic Hockey is guaranteed to be so. So, the last at-large team will be somewhere between PWR 11 and 15. If 3 conferences are won by non-top 16, #13 in the PWR will be in. If 2 conferences are won by non-top 16, #14 PWR will be in. If only AHA is won by a non-top 16, #15 PWR will be in.

Odds of NMU advancing, based on final PWR rank

PWR	Odds of NMU having rank	Odds of rank advancing	Odds of rank or better advancing	Odds of NMU advancing via this scenario
15	32.90%	18.75%	18.8%	6.169%
14	10.20%	40.63%	59.4%	6.056%
13	1.30%	30.21%	89.6%	1.165%
12		9.4%	99.0%
11		1.0%	100.0%
Total odds of NMU advancing				13.39%

Note that the odds of each rank advancing assume that each team has an equal shot at winning each game; in other words, they’re actually the share of outcomes in which each rank advances. That table also naively assumes the outcomes that determine NMU’s final PWR are completely independent from the outcomes that determine which PWR ranks advance. That is, of course, not true. But, because none of the scenarios (described below) require unranked teams to advance, it’s a fine rough estimate.

What influences NMU’s final PWR

Because NMU doesn’t have any games remaining, the Wildcats are the mercy of others.

Looking at NMU’s PWR Details, there are two very obvious comparisons that NMU is currently losing but could take (because the comparison is close enough and the other team is still playing):

• Cornell
• Western Michigan

It’s also apparently helpful for RIT to defeat Air Force. It’s not immediately obviously why this is the case (both are TUCs over whom NMU is winning the comparison, but so are all the other teams NMU is trying to gain on), but the models say NMU finishes noticeably higher in those scenarios.

A deeper dive into the scenarios

Miami defeating Western Michigan is huge for NMU. Note that it would eliminate a huge number of the #16-17 scenarios, while preserving all of the #13 scenarios and most of the #14 scenarios.

PWR outcomes for NMU if Miami defeats Western Michigan

PWR	Number of scenarios	Percent of scenarios
13	15297	2.6%
14	102442	17.4%
15	246385	41.8%
16	200993	34.1%
17	24707	4.2%

Western Michigan losing a second game is also pretty helpful. It drops a big majority of the #16-#17 outcomes and about half of the #15. This isn’t completely necessary, in that about 1/3 of the #13 outcomes and about 40% of the #14 outcomes exist outside this scenario, but this is a very attractive scenario for NMU.

PWR outcomes for NMU if Western Michigan also loses the consolation game

	To Michigan			To Bowling Green
PWR	Number of scenarios	Percent of scenarios		Number of scenarios	Percent of scenarios
13	4992	5.1%		4992	5.1%
14	30630	31.2%		30685	31.2%
15	61242	62.3%		61153	62.2%
16	1440	1.5%		1474	1.5%

Harvard defeating Cornell looks useful for NMU. It eliminates a lot of the 15-17 scenarios while leaving most of the 13-14 scenarios in tact.

PWR outcomes for NMU if Harvard defeats Cornell

PWR	Number of scenarios	Percent of scenarios
13	15297	2.6%
14	75380	12.8%
15	221000	37.5%
16	257768	43.7%
17	20379	3.5%

However, what’s not obvious from that table is that almost all the good scenarios come about when Cornell loses a 2nd game and almost all the bad scenarios come about when Cornell wins the 2nd game (after losing the 1st).

PWR outcomes for NMU if Cornell also loses the consolation game

	To Union			To Colgate
PWR	Number of scenarios	Percent of scenarios		Number of scenarios	Percent of scenarios
13	12993	13.2%		2304	2.3%
14	30915	31.4%		29014	29.5%
15	48434	49.3%		66923	68.1%
16	5959	6.1%		63	0.1%
17	3	0.0%

Note that I haven’t said anything about the RIT/Air Force outcome mentioned above. While it does indeed shift NMU’s chances of a 13-14 up quite a bit, about 2/3 of the #13 scenarios and 3/4 of the #14 scenarios exist outside of this outcome.

PWR outcomes for NMU if RIT defeats Niagara, Air Force defeats Mercyhurst, and RIT defeats Air Force

PWR	Number of scenarios	Percent of scenarios
13	4942	3.4%
14	30972	21.0%
15	54783	37.2%
16	53420	36.2%
17	3339	2.3%

So, Air Force defeating RIT is a nice outcome for NMU, but by no means necessary.

Too long, didn’t read

Bottom line? NMU’s best shot is for Cornell to lose twice and Western Michigan to lose at least once (though twice is a little better). That scenario includes all of the #13 possibilities, about 1/3 of the #14 possibilities, about 1/5 of the #15 possibilities, and a miniscule chance of being #16.