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.

  • Erpeldingj

    That was awesome.  Thanks!

  • Daddy

    How does all this affect Michigan State 

  • RamboWildcat

    Great work. With odds like that though, I’d rather play the Michigan Lottery this weekend!

  • Farley

    Wow Jim, nice work. It’s hard to believe you were a History major in college 😉

  • UNHfan

    Of all the teams on the bubble, NMU is the least deserving of getting in.  They finished sixth in their conference and lost in the opening round to the last place team, BG.  For NMU to get and not Cornell means six for CCHA and only one for ECAC.  This demonstrates the weakness of the RPI dominated pairwise comparisons.  I hope the committee looks at the game records to determine what bubble teams get in.  Cornell deserves to, NMU does not.

  • Matt Wellens

    Jim, I think I figured out the RIT over Air Force connection. It has little to do with NMU, but a lot to do with Michigan State.

    Three teams seem to hold the Spartans fate: North Dakota, Maine and RIT.

    If RIT beats Air Force, North Dakota can beat Minnesota and Maine wins Hockey East, then the Spartans drop to No. 17 and make room for NMU, which edges Merrimack ever so slightly in the RPI.