Thursday night PWR possibilties update, Sioux seem a lock for NCAAs

The Sioux now seem a lock for the NCAA championship and St. Cloud State’s season is done.

With Mich. Tech and St. Cloud both eliminated, it seems the WCHA can only be won by a team in the top 16, thus only 4 slots can be taken by autobids outside the top 16. So, #12 in the PairWise Rankings should be safe.

Remembering from the Deeper dive into whether UND will make the NCAA tournament that UND can do no worse than #12 after defeating St. Cloud, the Sioux now seem a lock for the NCAA tournament.

Here are the remaining possibilities for the key 19:

Team PWR Possibilities
Overall Win none Win all
Boston College 1 76.0%
2 23.5%
3 0.5%		 1 76.3%
2 23.7%		 1 76.9%
2 23.1%
Michigan 1 0.3%
2 65.2%
3 27.9%
4 5.0%
5 1.4%
6 0.2%		 2 49.4%
3 33.3%
4 12.4%
5 4.3%
6 0.6%		 2 75.0%
3 25.0%
Miami 1 0.3%
2 2.7%
3 16.6%
4 15.3%
5 13.0%
6 12.5%
7 10.4%
8 8.6%
9 7.4%
10 7.1%
11 5.0%
12 1.2%
13 0.1%		 5 0.1%
6 3.3%
7 13.9%
8 21.0%
9 21.8%
10 21.2%
11 14.9%
12 3.5%
13 0.2%		 1 1.2%
2 10.7%
3 56.9%
4 28.1%
5 2.9%
6 0.2%
UMD 1 23.4%
2 2.7%
3 3.0%
4 8.8%
5 13.6%
6 13.0%
7 16.6%
8 13.4%
9 4.6%
10 0.8%
11 0.1%		 3 0.0%
4 1.7%
5 8.5%
6 19.7%
7 32.4%
8 26.7%
9 9.1%
10 1.6%
11 0.3%		 1 93.6%
2 6.4%
Ferris State 3 5.5%
4 17.6%
5 29.0%
6 28.8%
7 14.9%
8 4.0%
9 0.3%		 n/a n/a
Boston University 2 3.1%
3 13.6%
4 10.2%
5 7.3%
6 7.7%
7 10.8%
8 15.3%
9 16.0%
10 10.4%
11 4.4%
12 1.1%
13 0.1%		 5 0.0%
6 1.1%
7 10.6%
8 25.5%
9 30.8%
10 20.7%
11 8.7%
12 2.3%
13 0.3%		 2 12.5%
3 49.5%
4 29.5%
5 7.3%
6 1.1%
7 0.1%
UMN 2 0.6%
3 12.2%
4 12.2%
5 8.1%
6 7.7%
7 11.9%
8 17.2%
9 17.4%
10 9.7%
11 2.7%
12 0.3%
13 0.0%		 5 0.1%
6 2.5%
7 12.0%
8 27.2%
9 32.9%
10 19.3%
11 5.4%
12 0.5%
13 0.0%		 2 2.2%
3 45.2%
4 37.3%
5 12.8%
6 1.9%
7 0.5%
8 0.1%
Maine 3 1.0%
4 5.3%
5 8.7%
6 7.5%
7 2.6%
8 1.2%
9 4.9%
10 13.7%
11 24.0%
12 22.9%
13 8.1%
14 0.2%		 10 5.9%
11 34.7%
12 42.9%
13 16.1%
14 0.4%		 3 3.8%
4 21.2%
5 34.8%
6 29.8%
7 9.9%
8 0.4%
9 0.0%
UND 2 0.5%
3 10.0%
4 10.4%
5 4.3%
6 4.1%
7 7.1%
8 11.0%
9 19.1%
10 20.1%
11 11.6%
12 1.8%		 6 0.1%
7 1.8%
8 10.8%
9 27.6%
10 34.4%
11 21.7%
12 3.6%		 2 1.9%
3 40.1%
4 41.7%
5 14.5%
6 1.8%
7 0.1%
Mass.-Lowell 6 0.6%
7 3.8%
8 10.6%
9 12.3%
10 17.3%
11 27.8%
12 22.0%
13 5.5%
14 0.1%		 n/a n/a
Michigan State 13 11.4%
14 40.7%
15 38.4%
16 4.2%
17 5.3%		 n/a n/a
Western Michigan 9 0.0%
10 0.2%
11 1.7%
12 3.7%
13 13.5%
14 33.7%
15 22.6%
16 16.6%
17 8.0%		 13 1.2%
14 8.9%
15 16.2%
16 49.8%
17 23.9%		 9 0.0%
10 0.7%
11 6.8%
12 14.8%
13 35.5%
14 42.3%
Denver 3 2.1%
4 4.9%
5 7.3%
6 6.6%
7 3.6%
8 1.5%
9 4.1%
10 9.0%
11 11.8%
12 31.0%
13 15.0%
14 3.0%		 10 0.0%
11 5.9%
12 58.1%
13 29.8%
14 6.1%		 3 8.6%
4 19.7%
5 29.2%
6 26.3%
7 13.9%
8 2.2%
9 0.1%
Northern Michigan 13 1.4%
14 10.4%
15 32.5%
16 55.6%
17 0.1%		 n/a n/a
Union 2 1.8%
3 7.6%
4 10.0%
5 6.2%
6 6.8%
7 9.5%
8 10.0%
9 11.4%
10 11.4%
11 7.6%
12 6.1%
13 11.4%
14 0.3%		 6 0.0%
7 0.2%
8 1.8%
9 9.3%
10 18.1%
11 17.7%
12 17.8%
13 34.3%
14 0.8%		 2 7.1%
3 30.4%
4 38.2%
5 17.5%
6 5.4%
7 1.3%
8 0.1%
Merrimack 14 0.0%
15 1.3%
16 15.6%
17 72.2%
18 11.0%		 n/a n/a
SCSU 20 0.0%
21 0.7%
22 13.1%
23 43.9%
24 29.3%
25 11.8%
26 1.3%		 n/a n/a
Cornell 4 0.2%
5 1.2%
6 4.6%
7 9.0%
8 7.3%
9 2.5%
10 0.3%
11 3.4%
12 9.8%
13 33.5%
14 11.5%
15 5.2%
16 7.8%
17 3.8%
18 0.0%		 12 0.7%
13 24.9%
14 23.9%
15 15.5%
16 23.5%
17 11.5%
18 0.0%		 4 0.8%
5 4.7%
6 18.2%
7 35.9%
8 29.2%
9 10.0%
10 1.3%
11 0.0%
Harvard 15 0.0%
16 0.2%
17 10.7%
18 2.9%
19 23.2%
20 13.7%
21 11.7%
22 2.6%
23 4.6%
24 6.7%
25 7.4%
26 8.5%
27 7.8%
28 0.0%		 22 1.8%
23 8.8%
24 18.3%
25 22.2%
26 25.6%
27 23.3%
28 0.0%		 15 0.1%
16 0.9%
17 42.8%
18 11.4%
19 44.7%

6 thoughts on “Thursday night PWR possibilties update, Sioux seem a lock for NCAAs”

  1. In looking at Michigan’s chances, it appears that there is a scenario where if they lose a game (unsure which) they could make the #1 overall, however, if they win 2 games, they have no chance of getting the #1 overall.  Very weird.

  2.  Good catch.  This is what I love about being able to make the raw data accessible — you all catch a lot of stuff I don’t, making it much more valuable than my personal interpretation.

    The situation you described seems to be in about .3% of the remaining outcomes (860 of 294912).  It does require Michigan to win 1 game but no more.  I’ll try to pin it down tomorrow morning and let you know what I find out.

  3. Ok, here’s one scenario in that family:
    Minnesota-Duluth > Denver
    North Dakota > Minnesota
    Maine > Boston University
    Boston College > Providence
    Harvard > Cornell
    Colgate > Union
    Miami > Western Michigan
    Michigan > Bowling Green
    RIT > Niagara
    Mercyhurst > Air Force

    North Dakota > Minnesota-Duluth
    Maine > Boston College
    Union > Cornell
    Harvard > Colgate
    Bowling Green > Western Michigan
    Mercyhurst > RIT

    The only game left undecided is the CCHA championship game between Miami and Michigan.  If Michigan loses, the Wolverines get #1 overall.  If Michigan wins, they fall to #2.

    In the Michigan loses scenario, Michigan and Miami are actually tied at 29 comparisons won, with Michigan having the lead on RPI.  However, BC is breathing down their necks at 28 comparisons won (losing the comparisons to Duluth and Miami) and a stronger RPI than either.

    If Michigan wins, that harms Miami enough that BC takes the comparison, rises to 29 comparisons won to tie with Michigan, but has the RPI tie breaker.

  4. I get it that there are “possibilities” that regarding Michigan being #1, but what are the “probabilities?  Even though its possible for Michigan to attain the #1 spot, BC still has at least a 76.3% chance to be #1 verses MI’s 49%(no wins – 79% (two wins), and evidently somewhere in between if only winning one of the final two games…..mathematically lower than BC’s probability of 76.3%.  Correct?  Then UMD has a 93.6% chance for #1 if UMD wins the Broadmoor.  On 3/12, UMD probability to win the Broadmoor and get a #1 PWR was 78%.  Now 96.5%  That’s quite a jump from before the Thursday night’s two WCHA games to after. What caused that jump? 

  5. Though I sometimes lazily refer to these as probabilities, they’re actually the percent of remaining possible outcomes in which an event occurs.  Also, the 2nd and 3rd columns (apparently poorly labeled) are the shares of outcomes in which the team has a particular ranking IF they fulfill the condition in the column title.

    So, the way to read the UMD win all column is…

    UMD ends the season with a #1 ranking in 93.6% of all remaining possible scenarios in which UMD wins the Broadmoor.

    If you think each team has an equal chance of winning each game (clearly not true, but not a horrible assumption around tournament time) you can simplify that to…

    UMD has a 93.6% chance of finishing #1 in PWR if they win the Broadmoor.

  6. “i was told there would be no math.”   —i’m glad you do it, though.   thanks Jim.

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