Tag Archives: North Dakota

How Cornell, Notre Dame, North Dakota, or Providence could miss the NCAAs

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For each of Cornell, Notre Dame, North Dakota, and Providence, missing the tournament requires a poor PWR ranking because of the success of the others.

All but idle Providence control their own fates, being able to guarantee an at-large bid with a single semi-final win.

With no additional wins, each is likely to land somewhere in the 9-16 range in PWR. To miss the NCAA tournament requires landing at the bottom of that range, requiring other teams in that range to do well. In addition to the other teams in this list doing well, Penn State, Ohio State, Air Force, and Boston College all have opportunities to move ahead of one of these teams that remains winless.

How Cornell misses

Cornell misses in about 6% of the scenarios in which they lose their semifinal game.

Here’s a scenario that pushes Cornell down to #16, so out of contention:
https://goo.gl/hFduxl

In this scenario, Cornell’s RPI falls enough and teams just below Cornell are successful enough that they pass Cornell in RPI and take the PWR comparison. Notre Dame, North Dakota, Providence, Penn State, Ohio State, Air Force, and Boston College each take the comparison, moving Cornell from 51 comparisons won to 44, enough to fall to #16 and out of contention.

Note that in that scenario, only the WCHA is won by a team that doesn’t finish in the top 15 in PWR. If only some of those teams pass Cornell, such that Cornell lands somewhere in the #12-15 range, enough conferences would need to be won by teams outside the top 15 for Cornell to still miss it.

How North Dakota misses

North Dakota misses in about 11% of the scenarios in which they lose their semifinal game.

Here’s a scenario that pushes North Dakota down to #16, so out of contention:
https://goo.gl/o7E4Pz

In that scenario, North Dakota’s RPI falls enough and teams just below the Hawks are successful enough that they pass North Dakota in RPI and take the PWR comparison. Providence, Penn State, Ohio State, Air Force, and Boston College each take the comparison, moving North Dakota from 49 comparisons won to 44, enough to fall to #16 and out of contention.

Note that in that scenario, only the WCHA is won by a team that doesn’t finish in the top 15 in PWR. If only some of those teams pass North Dakota, such that UND lands somewhere in the #12-15 range, enough conferences would need to be won by teams outside the top 15 for North Dakota to still miss it.

How Notre Dame misses

Notre Dame misses in about 4% of the scenarios in which they lose their semifinal game.

Here’s a scenario that pushes Notre Dame down to #16, so out of contention:
https://goo.gl/cUZqLw

In that scenario, Notre Dame’s RPI falls enough and teams just below the Irish are successful enough that they pass Notre Dame in RPI and the PWR comparison. North Dakota, Providence, Penn State, Ohio State, Air Force, and Boston College each take the comparison, moving Notre Dame from 50 comparisons won to 45, enough to fall to #16 (due to losing the RPI tie-breaker w/Providence) and out of contention.

Note that in that scenario, only the WCHA is won by a team that doesn’t finish in the top 15 in PWR. If only some of those teams pass Notre Dame, such that Notre Dame lands somewhere in the #12-15 range, enough conferences would need to be won by teams outside the top 15 for Notre Dame to still miss it.

How Providence misses

Providence is the only idle team with a shot at an at-large bid, though its scenario highly resembles those of Cornell, North Dakota, and Notre Dame with a semifinal loss. Providence misses the NCAA tournament in about 4% of possible scenarios.

Here’s a scenario that pushes Providence down to #16, so out of contention:
https://goo.gl/NVhyEE

In that scenario, Providence’s RPI actually rises a bit but teams just below Providence are successful enough that they pass Providence in RPI and take the PWR comparison. Penn State, Ohio State, and Air Force each take the comparison, moving Providence from 47 comparisons won to 44, enough to fall to #16 and out of contention. (Note that Providence already loses the comparison to BC, but BC moves ahead of Providence in PWR ranking in this scenario on the basis of Providence’s decline in comparisons won).

Note that in that scenario, only the WCHA is won by a team that doesn’t finish in the top 15 in PWR. If only some of those teams pass Providence, such that Providence lands somewhere in the #12-15 range, enough conferences would need to be won by teams outside the top 15 for Providence to still miss it.

What to watch for in PWR this weekend

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This article looks at the most interesting outcomes of games this weekend, with a focus on what PWR might look like next Monday. If you want a more general analysis of the remaining regular season and NCAA tournament likelihood, check out the article, NCAA tournament outlook as conferences enter final regular season weekend, and the table, Wins needed to likely end regular season at PWR rank.

Biggest upside potential

#20 Wisconsin, visiting the red hot #4 Gophers in Minneapolis, has an opportunity to surge. The Badgers could climb to the 9-11 range with a sweep (as high as 7 is realistic), but will likely just stay put if swept. Of course, in the long run staying put is not good enough for the Badgers who needs 3-4 wins in their final 6 games to climb to the bubble (see NCAA tournament outlook).

#18 Boston College has a similar opportunity facing #8 Mass.-Lowell for a home-and-home series. Sweeping would provide a broad range of possible outcomes, from #8-#15 quite possible. Getting swept would likely result in a modest decline to the 19-20 range.

Biggest downside potential

As past readers of these articles know, just as teams around #20 usually have the most upside potential, teams around #10 usually have the most potential to fall.

#10 Cornell faces the most downside potential, with ranks 15-21 possible if swept by Rensselaer and Union. Given that these are the last two games of the regular season for Cornell, that would put the Big Red firmly on the bubble.

#9 Providence faces a similar outlook, with ranks 15-20 possible with a pair of losses to Massachusetts.

All of #8 Mass.-Lowell, #11 Penn State, #12 St Cloud St, #13 Ohio St, and #14 North Dakota face similar chances of a slightly more modest plunge with a pair of losses. Only Mass.-Lowell’s regular season ends this weekend, so others would have some opportunity to recover.

Top seeds?

#1 Denver and #2 Minnesota-Duluth each look unlikely to leave the weekend outside of the 1-3 range, regardless of outcome, and one of the two is almost certain to come out #1. Denver doesn’t quite control its own destiny, as Minnesota-Duluth stands about a 10% chance of sneaking into #1 even if both sweep. Other teams fighting for spots in the top 4 this weekend are #3 Harvard, #4 Minnesota, #5 Western Michigan, and #6 Boston University.

Methodology

Forecasts include the results of games played through Tuesday of this week.

Each forecast is based on at least one million monte carlo simulations of the games in the described period. For each simulation, the PairWise Ranking (PWR) is calculated and the results tallied. The probabilities presented in the forecasts are the share of simulations in which a particular outcome occurred.

The outcome of each game in each simulation is determined by random draw, with the probability of victory for each team set by their relative KRACH ratings. So, if the simulation set included a contest between team A with KRACH 300 and team B with KRACH 100, team A will win the game in very close to 75% of the simulations. I don’t simulate ties or home ice advantage.

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A few top teams are starting to look like locks for NCAA tournament

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For the first time this season, the top PWR teams are starting to look like locks for the NCAA hockey tournament. Aside from current PWR ranking, the biggest determinant in how possible it is for a top team to fall out of contention is how many games it has remaining (because when looking for the worst case, each is a potential loss). Some teams are down to 4 regular season games remaining while others have as many as 8 (plus up to 2 conference tournament losses, in the worst case, for most teams).

While it’s tough to imagine #1 Quinnipiac or #2 St Cloud St losing out, including a pair in the conference tournament, even that probably wouldn’t be enough to bump them (dependent on how many conferences’ tournament champions come from outside the top of the PWR).

quinnipiac scsu

While #3 North Dakota is mathematically vulnerable, getting swept 4 more weekends (including into the conference tournament) seems unlikely.

und

With only 4 games remaining, #4 Boston College and #5 Providence are near locks (again, dependent on how many conferences’ tournament champions come from outside the top of the PWR).

bc providence

#6 Michigan is the highest ranked team with a significant chance of falling to the bubble, largely by virtue of having more games remaining than any other similarly ranked team.

michigan

Despite a brutal schedule of series against #5 Providence and #11 Boston University, #7 Notre Dame won’t fall much with only 4 regular season games remaining. But, 11-12 going into the conference tournament would leave the Irish vulnerable to being excluded with a poor performance.

notredame

With 6 regular season games remaining for each, it’s too early to call #8 Denver and #9 Nebraska-Omaha safe. It would take a slump for either to miss the NCAA tournament, but they do play each other head-to-head and the Mavericks have a particularly brutal schedule (#8 Denver, #3 North Dakota, and #2 St Cloud).

denver uno

North Dakota eyeing taking #1 from Quinnipiac, but don’t count out St. Cloud

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#1 Quinnipiac has held the top PWR ranking for as long as it has been calculable this season, and the top three have been unchanged for about a month. However, the Bobcats haven’t been perfect and last week’s forecast revealed the first possibility of a new leader. QU held onto its top ranking with a win and a tie, but the odds of someone overtaking them continued to increase.

history

Though Quinnipiac hasn’t lost since December 12, a string of ties (4 out of 7 games in 2016, including 3 of the last 5) has chipped away at their once formidable PWR lead.

On a 5-0-1 streak until last weekend, #2 St. Cloud St. has been nipping at the Bobcats’ heels the last couple weeks. However, St. Cloud’s position also weakened a bit with a split last weekend.

#3 North Dakota, in contrast, has continued to strengthen its position with a 12-1-1 run since Thanksgiving. With St. Cloud St. idle this weekend, UND is the most likely beneficiary of any additional stumbling by Quinnipiac. Not only do the Fighting Hawks stand their first measurable chance of taking #1 this weekend, but it’s a pretty realistic chance.

Even if Quinnipiac wins both its games this weekend, North Dakota can give itself about a 28% chance of taking #1 by also sweeping. A complicated mix of other game outcomes would determine the RPI leader between QU and UND, who would then also win the PWR comparison, and take #1.

If Quinnipiac loses one of its two games this weekend and North Dakota sweeps, the Fighting Hawks are almost certain (over 99% of scenarios) to take #1. A single win doesn’t seem likely to do it for UND, as that would make it difficult to overtake idle St. Cloud St.

If the Bobcats keep up their undefeated streak, but earn another draw, that will also open the door for North Dakota. Those scenarios give UND about a 95% chance of taking #1 with a sweep.

Finally, though they don’t control their own fate, St. Cloud St. still stands a chance of taking #1. If UND loses one, the Huskies would have about a 33% chance of taking #1 with one Quinnipiac loss, or about a 94% chance with two losses by QU (again, those would come down to complicated RPI movements based on other games).

qu scsu und

A new #1 in KRACH

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Unlike PWR (which mimics the tournament selection process) , KRACH is just for fun. But, a lot of people like it and it’s what I use to estimate team strength when simulating game outcomes.

When writing yesterday’s post, I noticed there’s a new king of the hill in PWR – #2 North Dakota.

Only once this season has #1 Minnesota State been knocked out of first place in KRACH, on Dec. 29 by then second-in-PWR Harvard. The following week Harvard also took over first place in PWR. Harvard’s reign was short-lived, as Minnesota State took back the top rankings in both PWR and KRACH on January 12 and have held both until this week.

krach

pwr

Big PWR games of the week

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#10 Minnesota appears in the Big PWR Game of the Week for a second time. Buoyed by a road split last weekend, the Gophers probably need a better performance hosting #33 Michigan State to avoid falling back down to the bubble.

Getting swept could incite numerous “Time to get rid of the stupid PWR?” forum threads, as Minnesota would likely fall 8-9 places.

minnesota_oneweek

The runner-up, #22 Northeastern, could provide a shock in the other direction by appearing on the bubble if they sweep #6 Boston University.

northeastern_oneweek

Finally, #1 Minnesota State faces the biggest threat to its ranking in weeks with a series hosting #5 Michigan Tech. The Mavericks need a sweep to hold off #2 North Dakota.

mankato_oneweek

michtech

Big PWR game of the week

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The big PWR game of the week is #14 Yale vs. #10 Quinnipiac. They only play one game vs. each other, but then another each vs. #56 Princeton and #48 Brown, respectively.

A single win this weekend for either most likely results in a small decline in ranking. The interesting outcome is if the loser of the head-to-head also loses their other game, which could result in falling of at-large bid position in the PWR.

yale

quinnipiac

The runner-up big PWR game is #23 Western Michigan vs. #2 North Dakota. North Dakota isn’t moving much, even if they get swept; it doesn’t seem possible to overtake idle #1 Minnesota State this weekend. However, Western Michigan could jump just below the bubble with a sweep.

westernmichigan

northdakota

Methodology

Forecasts include the results of games played through Sunday of this week, unless otherwise noted.

Each forecast is based on at least one million monte carlo simulations of the games in the described period. For each simulation, the PairWise Ranking (PWR) is calculated and the results tallied. The probabilities presented in the forecasts are the share of simulations in which a particular outcome occurred.

The outcome of each game in each simulation is determined by random draw, with the probability of victory for each team set by their relative KRACH ratings. So, if the simulation set included a contest between team A with KRACH 300 and team B with KRACH 100, team A will win the game in very close to 75% of the simulations. I don’t simulate ties or home ice advantage.

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Saturday morning update

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This is a big article will in four parts:

  • Changes from yesterday
  • A new summary of the overall outlook
  • Specific scenarios that determine which of the at-large candidates make it
  • A table of all remaining PWR possibilities

As we near the end, I want to remind everyone that there’s a noticeably higher than other years chance that this information is wrong. The NCAA changed its selection process this year. While USCHO, CHN, and I have attempted to faithfully implement it and came up with identical PWR rankings, it wouldn’t be shocking if something different came out of the committee than what’s in our final PWR tables.

Changes from yesterday

Colgate is a lock
Cornell is out
Northeastern is out

Overall outlook

In

  • Minnesota
  • Boston College
  • Union
  • Ferris St
  • Wisconsin
  • Quinnipiac
  • Mass.-Lowell
  • Notre Dame
  • St Cloud (added Thursday)
  • Colgate (added Friday)

In the running at large

  • Providence (about 94%)
  • Michigan (about 17%)
  • Mankato (can also get auto bid, about 75% with loss)
  • North Dakota (about 28% with win)
  • Vermont (about 93%)

Can make it with a conference championship

  • New Hampshire
  • Ohio St
  • Denver (playing Miami)
  • Miami (playing Denver)
  • Robert Morris (playing Canisius)
  • Canisius (playing Robert Morris)

Scenarios of interest to at-large teams

North Dakota

UND makes it in about 28% of the scenarios in which it wins. UND seems to need:

UND and Mass.-Lowell win and either (Wisconsin wins) or (Canisius, Ferris St, and Miami win)

The Mass.-Lowell, Wisconsin, and Ferris St wins prevent the cut line from moving by giving auto bids to teams already above the cut. In the case of UML + Ferris, UND needs a little PWR help from the other two wins.

Minnesota State

Minnesota State is in with an auto bid with a win.

Minnesota State also makes it in about 75% of scenarios in which it loses. Those scenarios are a bit complex.

Mankato misses if:
Ferris St, Ohio State, New Hampshire win and (North Dakota, or Canisius, or Denver win)

or

Ferris St, Ohio State, Mass.-Lowell, North Dakota, Canisius, and Miami win

Michigan

Michigan makes it in about 17% of scenarios.

Michigan is in if:
Wisconsin and Mass.-Lowell win and UND either ties or loses.

Wisconsin and Mass.-Lowell wins prevent the cut-line from moving, and a UND tie should keep them below Michigan in the PWR.

Providence

Providence makes it in about 94% of scenarios.

Providence only misses if:
New Hampshire, Mankato, Colgate, and Ohio State win.

Vermont

Vermont makes it in about 93% of scenarios.

Vermont only misses if:
Ohio State, New Hampshire, Western Michigan, Ferris St, Robert Morris, and Miami win

OR

Ohio State, New Hampshire, Mankato, and Union win

Both scenarios require Ohio State and New Hampshire to move the cutline; the other games are about keeping other teams from taking all the available at-large bids.

Remaining PWR possibilities

Team PWR Possibilities
Overall By number of wins
UMN #1 100.0%
Tournament invites: 100.0%		 n/a
Boston College #2 91.1%
#3 8.9%
Tournament invites: 100.0%		 n/a
Union #2 8.9%
#3 91.1%
Tournament invites: 100.0%
PWR Win 0 Win 1
#2   17.7%
#3 100.0% 82.3%
Tournament invites: 100.0% 100.0%
Ferris State #4 74.0%
#5 22.4%
#6 0.0%
#7 3.6%
Tournament invites: 100.0%
PWR Win 0 Win 1
#4 47.9% 100.0%
#5 44.8%  
#6    
#7 7.3%  
Tournament invites: 100.0% 100.0%
UW #4 25.0%
#5 50.0%
#6 25.0%
Tournament invites: 100.0%
PWR Win 0 Win 1
#4   50.0%
#5 50.0% 50.0%
#6 50.0%  
Tournament invites: 100.0% 100.0%
Quinnipiac #6 75.0%
#7 25.0%
Tournament invites: 100.0%		 n/a
Mass.-Lowell #4 1.0%
#5 27.6%
#6 0.0%
#7 71.4%
Tournament invites: 100.0%
PWR Win 0 Win 1
#4   2.1%
#5   55.2%
#6    
#7 100.0% 42.7%
Tournament invites: 100.0% 100.0%
Notre Dame #8 100.0%
Tournament invites: 100.0%		 n/a
Providence #10 12.5%
#11 38.5%
#12 36.5%
#13 12.5%
Tournament invites: 93.8%		 n/a
SCSU #9 100.0%
Tournament invites: 100.0%		 n/a
Michigan #14 64.6%
#15 34.4%
#16 1.0%
Tournament invites: 16.7%		 n/a
Mankato #10 50.0%
#11 0.0%
#12 2.6%
#13 45.3%
#14 2.1%
Tournament invites: 87.5%
PWR Win 0 Win 1
#10   100.0%
#11    
#12 5.2%  
#13 90.6%  
#14 4.2%  
Tournament invites: 75.0% 100.0%
UND #13 2.1%
#14 31.3%
#15 4.2%
#16 18.2%
#17 18.8%
#18 17.2%
#19 8.3%
Tournament invites: 9.4%
PWR Win 0 Win 1
#13   6.3%
#14   93.8%
#15 6.3%  
#16 27.3%  
#17 28.1%  
#18 25.8%  
#19 12.5%  
Tournament invites: 0.0% 28.1%
Vermont #11 11.5%
#12 49.5%
#13 39.1%
Tournament invites: 92.7%		 n/a
Colgate #10 37.5%
#11 50.0%
#12 11.5%
#13 1.0%
Tournament invites: 100.0%
PWR Win 0 Win 1
#10 25.0% 50.0%
#11 50.0% 50.0%
#12 22.9%  
#13 2.1%  
Tournament invites: 100.0% 100.0%
Cornell #16 8.3%
#17 34.4%
#18 41.1%
#19 16.1%
Tournament invites: 0.0%		 n/a
New Hampshire #14 2.1%
#15 10.9%
#16 12.0%
#17 13.5%
#18 36.5%
#19 25.0%
Tournament invites: 50.0%
PWR Win 0 Win 1
#14   4.2%
#15   21.9%
#16   24.0%
#17   27.1%
#18 50.0% 22.9%
#19 50.0%  
Tournament invites: 0.0% 100.0%
Northeastern #15 36.5%
#16 40.1%
#17 18.2%
#18 5.2%
Tournament invites: 0.0%		 n/a
Western Michigan #21 66.7%
#22 33.3%
Tournament invites: 0.0%
PWR Win 0 Win 1
#21 50.0% 100.0%
#22 50.0%  
Tournament invites: 0.0% 0.0%
Ohio State #15 14.1%
#16 20.3%
#17 15.1%
#18 0.0%
#19 27.6%
#20 22.9%
Tournament invites: 50.0%
PWR Win 0 Win 1
#15   28.1%
#16   40.6%
#17   30.2%
#18    
#19 54.2% 1.0%
#20 45.8%  
Tournament invites: 0.0% 100.0%
Bowling Green #24 14.1%
#25 8.3%
#26 77.6%
Tournament invites: 0.0%		 n/a
AA #27 100.0%
Tournament invites: 0.0%		 n/a
Denver #23 50.0%
#24 0.0%
#25 50.0%
Tournament invites: 50.0%
PWR Win 0 Win 1
#23   100.0%
#24    
#25 100.0%  
Tournament invites: 0.0% 100.0%
Mercyhurst #32 100.0%
Tournament invites: 0.0%		 n/a
Miami #29 27.6%
#30 22.4%
#31 50.0%
Tournament invites: 50.0%
PWR Win 0 Win 1
#29   55.2%
#30   44.8%
#31 100.0%  
Tournament invites: 0.0% 100.0%
Michigan State #37 18.8%
#38 81.3%
Tournament invites: 0.0%		 n/a
Robert Morris #44 50.0%
#45 0.0%
#46 0.0%
#47 0.0%
#48 50.0%
Tournament invites: 50.0%
PWR Win 0 Win 1
#44   100.0%
#45    
#46    
#47    
#48 100.0%  
Tournament invites: 0.0% 100.0%
Canisius #44 7.3%
#45 21.9%
#46 14.6%
#47 6.3%
#48 50.0%
Tournament invites: 50.0%
PWR Win 0 Win 1
#44   14.6%
#45   43.8%
#46   29.2%
#47   12.5%
#48 100.0%  
Tournament invites: 0.0% 100.0%
Niagara #49 21.9%
#50 78.1%
Tournament invites: 0.0%		 n/a
Penn State #51 49.5%
#52 50.5%
Tournament invites: 0.0%		 n/a

Friday morning update

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With the first two Big Ten games down, there are only minor changes to the overall tournament outlook.

St Cloud St now appears to be a lock for an at-large bid.

Michigan has taken on the expected “0 win” scenario from previous columns (about a 22% chance of making the tournament at-large).

Each of the bubble teams — Mankato, UND, Vermont, Colgate, and Cornell — improved their one win at-large chances by about 10% (idle Vermont’s overall chances increased by about 10%).

Unlikely outcomes — how BC and Union could swap; Providence and SCSU could miss; and UND, Colgate, and Cornell could make it without any more wins

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In previous columns this week I presented what tournament selection outcomes are most likely, every possible tournament selection outcome, and what determines the fate of teams with the most uncertainty as to outcome. Today, I’ll dive into the nooks and crannies of the most unlikely outcomes to explain how they could come about.

How Union could climb to #2 and Boston College could fall to #3

The key to swapping #2 Boston College (idle) and #3 Union is for Union to overcome BC’s current RPI advantage. That would change the comparison, currently 2-0 in BC’s favor, to 1-1 with the RPI tie-breaker going to Union. Though the current RPI gap is only .5892 for BC to .5810 for Union, it’s difficult for Union to overcome because BC isn’t playing so can’t move down much.

Obviously, the best thing Union can do to improve its own RPI is win two games. To further maximize the benefit, Union prefers to play #6 in RPI Quinnipiac over #16 in RPI Colgate (though Colgate’s better opponent win% somewhat offsets Quinnipiac’s better win%, the quality win bonus for defeating Quinnipiac tips the scales).

The next most important thing for Union’s RPI is to further improve its quality win bonus by having teams it has defeated climb in the RPI ranks. New Hampshire is the most obvious candidate, capable of climbing from its current #18 in RPI to as high as #12. In addition to the benefit it would receive from two wins, New Hampshire would be helped by losses from teams immediately above it such as #15 Colgate, #16 Cornell, #13 North Dakota, #12 Mankato, and #11 Michigan.

Finally, Union can pick up a few other quality win bonus points by having Bowling Green become a contender.

Here’s an example of one such scenario:
http://goo.gl/qs5CXO

When such factors all come together Union can climb to #2 in about .5% of remaining possible outcomes, or about 2% of the scenarios in which Union wins its conference tournament.

How Providence could miss the NCAA tournament

The two keys to Providence missing the NCAA tournament are for Providence to fall in the PWR and for conference autobids to go to teams that wouldn’t make it at large. Combined, the two can push Providence down and move the line for an at-large bid up enough such that Providence doesn’t make the tournament.

For Providence’s PWR to fall sufficiently, Providence must exit winless by losing its first game. Second, a combination of teams below Providence must rise sufficiently to further push Providence down.

Here’s one such example in which #16 Cornell, #10 St Cloud St, and #14 Vermont pass Providence, pushing it to #12. This scenario additionally features 5 of the 6 conference autobids going to teams below the cutoff, thus denying #12 Providence an at-large bid.

http://goo.gl/uevH6G

Similar factors come together for Providence to miss the NCAA tournament in about 1.3% of remaining outcomes, or about 2.6% of scenarios in which Providence loses its first game.

How St. Cloud State could miss the NCAA tournament

The principles for St. Cloud State missing are the same as for Providence — St. Cloud St’s PWR must fall and conference autobids must go to teams that wouldn’t make it at large.

Because SCSU is idle, it’s a little harder to move their PWR. The biggest lever available to do so is the quality win bonus. St. Cloud St currently enjoys QWB’s from wins over #3 RPI Union, #12 RPI Minnesota State, #13 RPI North Dakota, #16 RPI Colgate, and #19 RPI Western Michigan. Poor performances from those teams, and resulting drops in SCSU’s QWB, are key to St. Cloud St missing.

Here’s one such scenario in which each of the above loses as many as possible, pushing SCSU down to #12. This scenario additionally features 5 of the 6 conference autobids going to teams below the cutoff, thus denying #12 St Cloud St an at-large bid.

http://goo.gl/slBcnQ

Similar factors come together for SCSU to miss the NCAA tournament in only 80 of the 3,145,728 remaining possible scenarios (about .003%).

How North Dakota makes the NCAA tournament without any more wins

A quirk of this year’s revised conference tournaments is that only the NCHC has a consolation game, thus an opportunity for a team to go winless across two conference tournament games.

For North Dakota to make the tournament without any additional wins, the principles are familiar — maximize UND’s PWR ranking while having as many conference autobids as possible go to teams that would otherwise make the tournament at large.

Another quirk of consolation games is that they can end in ties. To maximize UND’s PWR without a win, North Dakota needs a loss in the opening game but a tie in the consolation game. Even with a loss and a tie, UND’s PWR is almost certain to fall, so the key is for teams around UND to perform poorly enough that UND’s fall is minimal.

There are a few ways that could happen, but here’s one such scenario in which only two teams (#18 Northeastern and #14 Vermont) rise above UND but only one (#11 Michigan) falls below, resulting in a net loss of only one position to #14. This is dependent on poor performance by #15 Colgate, #16 Cornell, and #17 New Hampshire. This scenario additionally features only two conference tournaments going to non-autobid teams, thus allowing #14 UND to get an at-large bid despite no additional wins.

http://goo.gl/HS0PSQ

Similar factors come together for UND to make the NCAA tournament in about .5% of outcomes in which UND loses the first game, or about 1.5% of outcomes in which UND loses the first game then ties the consolation game.

How Colgate makes the NCAA tournament without any more wins

The principles for Colgate making the NCAA tournament without another win are similar to those for North Dakota — maximize Colgate’s PWR and have as many conference autobids as possible go to teams that would otherwise make the tournament at large.

Because we’ve already stipulated that Colgate must lose a game, maximizing its PWR relies primarily on poor performance from the teams around it and an improvement in its quality win bonus.

There are a few ways to do that, but here’s one such scenario in which #15 Colgate passes two teams (#12 Mankato and #13 North Dakota) while being passed by only one (#17 Northeastern) resulting in a rise to #14. While this is dependent on poor performances by North Dakota and Northeastern, it is also helped by a poor performance from Cornell and a mixed performance from New Hampshire to prevent those teams from overtaking Colgate. Colgate’s PWR is also helped in this scenario by a modest rise in its quality win bonus from good performances by Ferris State, Quinnipiac, and Union. This scenario additionally features only two conference tournaments going to non-autobid teams, thus allowing #14 Colgate to get an at-large bid despite no additional wins.

http://goo.gl/WjT4bM

Similar factors come together for Colgate to make the NCAA tournament in about 2.1% of scenarios in which it loses its lone conference tournament game.

How Cornell makes the NCAA tournament without any more wins

The principles for Cornell making the NCAA tournament without winning are the same as for North Dakota and Colgate — maximize Cornell’s PWR and have as many conference autobids as possible go to teams that would otherwise make the tournament at large.

Because we’ve already stipulated that Cornell must lose a game, maximizing its PWR relies primarily on poor performance from the teams around it and an improvement in its quality win bonus.

Though #16 Cornell has a slight RPI edge on #15 Colgate (Cornell is currently one PWR rank lower because it loses the comparison between the two because of their H2H results), it has a much tougher time improving its PWR this weekend because it doesn’t have the wins versus Ferris State and Union that give Colgate the opportunity to improve its quality win bonus. While wins by Quinnipiac help a bit, Cornell’s RPI seems doomed to fall.

So, to actually rise in the PWR (#16 won’t make it at large because the AHA autobid will go to someone not in the top 16), Cornell needs more teams above it to fall than teams below it rise. Here’s a scenario in which only one team (#15 Colgate) dips below Cornell while no teams below Cornell rise, resulting in Cornell taking the #15 spot. To make the tournament from #15, this scenario also features only one team outside the top 15 winning its conference tournament.

http://goo.gl/GJlLTr

Such a set of outcomes useful to Cornell is quite unusual, occurring in only 182 of the 1,572,864 scenarios in which Cornell loses its lone game (about .01%).