Published by Jim Dahl on 14 Mar 2012 at 09:42 am
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:
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 1316 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 atlarge team will be somewhere between PWR 11 and 15. If 3 conferences are won by nontop 16, #13 in the PWR will be in. If 2 conferences are won by nontop 16, #14 PWR will be in. If only AHA is won by a nontop 16, #15 PWR will be in.
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 #1617 scenarios, while preserving all of the #13 scenarios and most of the #14 scenarios.
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.
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 1517 scenarios while leaving most of the 1314 scenarios in tact.
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).
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 1314 up quite a bit, about 2/3 of the #13 scenarios and 3/4 of the #14 scenarios exist outside of this outcome.
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.

Erpeldingj

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Farley

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Matt Wellens