Tag Archives: Michigan

Six teams have an opportunity to dramatically increase NCAA at-large odds this weekend

Likely in—#7 Yale, #8 Michigan, #9 Boston University, #10 Notre Dame

These teams are in good shape and likely to get an at-large bid if they win more than they lose in the coming two weekends.

If swept this weekend, their worst likely outcomes are falling to the 11-12 range, which would require keeping an eye out for potential additional downward movement and the cutlines (that is, how many of the at-large spots are taken away by autobids ranked lower than 16 in the PWR).

Of course, for Yale, Boston University, and Notre Dame, a pair of wins means another game. A loss in that game would probably result in giving back up some ground. But, that would still probably result in a safe position unless a lot of low ranked teams win their conference tournaments.

Note that Michigan’s position is slightly different because the Big Ten is still in regular season play. Even if swept by Penn State this weekend, the Wolverines would still have an additional game in the Big Ten tournament to either climb or fall. That worst possible outcome this weekend could drop Michigan as low as #12, from which another loss could push them out of position for an at-large bid.

Likely in if they win—#11 Harvard, #12 Mass.-Lowell

These teams would be in trouble if swept this weekend. Harvard’s likely fall could be to as low as 16, and Mass.-Lowell as low as 15. While it’s possible to climb a little bit while idle and have the cutline low enough to sneak into an at-large bid, it would be a bit of a longshot. I’ll also note that there are some extremely unlikely cases that could push these teams as low as 18 and 17 respectively if swept.

Sweeping, on the other hand, has the possibility of putting either in great shape — as high as 8 or 9 (though 9 to 11 more likely) with only 1 potential loss remaining.

One more team you should expect to see in the NCAA tournament

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The first five—Quinnipiac, St Cloud St, Boston College, North Dakota, and Providence

On Feb. 23, I called the top 5 “starting to look like locks” for the NCAA tournament (in order of their ranking at the time)—#2 Quinnipiac, #3 St Cloud St, #5 Boston College, #1 North Dakota, and #4 Providence. While those 5 have shuffled a bit amongst themselves, they obviously remain the top 5, and are even more certain locks.

None of them are likely to drop out of the top 7 in this weekend’s conference tournament play. Because a worst case scenario for any of those teams would also mean no more games before NCAA selection, there would be limited opportunity for additional downward movement.

Almost had it—Michigan

In that Feb. 23 article, I called (then #6) #8 Michigan too close and too many games remaining to call. The Wolverines have rewarded me for my caution, going 1-3, dropping two spots, and being at risk of hitting the bubble if they continue to lose.

The new “next one”—Denver

But what about the new #6 Denver (then #8)? They’ve been the hottest PWR team of 2016 with a 14-1-3 record since the New Year, including a 4-0 run since that article.

The Pioneers are facing an elimination best-of-3 that is likely to result in no worse than a #8 PWR ranking, I’m comfortable saying you should expect to see Denver in the NCAA tournament.

Note, however, that Denver has not mathematically secured the bid. In very obscure scenarios, they could fall as low as 9 this weekend if swept (about a .1% of KRACH-weighted outcomes in which Denver goes 0-2). It’s conceivable, though incredibly unlikely, that the then idle Pioneers could slip enough further to fall below the cutline if almost all of the conference tournaments are won by teams outside the top 16. That scenario is extremely unlikely to still be in play after this weekend, but if it is, I’ll give full details of the likelihood and how it could happen.

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).

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

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).

#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.

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.

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).

Friday morning’s PWR headlines today

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There are two Big Ten games today, so while people will be poring over PWR tables and running simulations tonight, I’ll predict their headlines now:

[OSU or Penn St] and [Michigan or UW] advance in first round of Big Ten tournament, knocking [Penn St or OSU] and [UW or Michigan] out of NCAA contention. Share of remaining scenarios in which Minnesota advances with one win [cut in half/double].

That is pretty much it. The primary tournament effects appear to be that the teams that lose are eliminated, which you probably already knew. The possibilities of other teams advancing in certain scenarios will shift a few percentage points here and there, with the only significant shift being Minnesota’s chance of advancing with 1 win going from 35% as of now to 50-55% if Michigan wins or 16-18% if Wisconsin wins.

No teams other than those playing today seem to have any potential scenarios closed off as a result of today’s action.

A look at the bubble teams

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If you haven’t read them yet, you might want to start with my articles from earlier this week, Who’s a lock for the NCAA tournament? and Who might fall out of contention for the NCAA tournament? Having visited those two extremes, this article goes into a little more depth on the teams in between.

Background on how PWR matters for tournament selection

Because we get lots of new readers during the tournament season, here’s some background information that my posts generally assume you know:

The PWR rankings are not a poll or computer model, but are instead an implementation of the same process the NCAA uses to select its tournament participants. They have correctly predicted the NCAA tournament participants for a decade or two.
Each conference gets to send one tournament winner to the NCAA tournament. So, we don’t need to look at the PWR of a team that wins its conference tournament.
The remaining 10 slots are given to top teams as ranked by the process implemented in PWR. So, PWR ranks 1-10 are in for sure; but, for 11-16 to make it requires some of the autobids to have gone to teams ranked above them (e.g. if an autobid goes to the team ranked #3, then an extra slot is open for the team ranked #11, and so on).

Because of that structure, we think of teams that are going to finish in the 12-15 range as “on the bubble”. Teams’ prospects are dependent not only on their final ranking, but also on how many lower ranked teams wins conference tournaments. Bubble teams’ chances for an at-large bid increase as slots are freed up by more conference tournaments being won by teams that would have made the NCAA tournament at-large.

A look at the bubble teams

#9 Providence would be on the bubble if eliminated from their conference tournament this weekend. They’d then need a bit of luck to make the NCAA tournament, needing to either climb a bit while idle and/or have a lot of conference tournaments won by top ranked teams.

If Providence wins this weekend, they’ll be in pretty good shape. A semifinal loss would probably push them back down to the high end of the bubble, while a win would nearly lock up a bid.

#10 Boston College is in a very similar position to Providence. They’d be on the bubble if eliminated this weekend and would be watching the other conference tournaments carefully.

If they advance this weekend, they’ll be in pretty good shape — favored, though probably not mathematically secure, for an NCAA bid.

#11 Bowling Green would likely be pushed down below the bubble if eliminated this weekend. It would take a lot of luck to climb back onto the bubble while idle and have most of the conference tournaments won by top ranked teams.

If Bowling Green advances, they would still probably need a semifinal win to stay on the bubble.

#12 Quinnipiac has a chance of staying on the bubble if eliminated this week, but would have to watch future tournament results carefully.

If they advance, another win would probably be needed to stay atop the bubble.

#13 Yale is likely to be pushed just below the bubble if eliminated this weekend, but would stand a slim chance of climbing onto it dependent on other tournament results.

Advancing this weekend would position them well, but not secure a spot in the NCAAs. With an additional win, Yale would be favored to secure a spot.

#14 Minnesota hasn’t entered conference tournament play yet, so does not face elimination. Getting swept this weekend would put them in a bad spot for an at-large bid, but would also probably force them to play in the Big Ten quarterfinals. The extra game would give them the chance to go 2-1 in the conference tournament and possibly get back onto the bubble.

#15 Mass.-Lowell is likely to end well below the bubble if eliminated this weekend. It would take a very unlikely confluence of events for them to move into an at-large bid from that position.

Advancing puts them in a precarious spot on the bubble, such that a subsequent loss would probably push them off.

#16 St Cloud St is currently at 11-12-1 so needs one more win than loss in its remaining games to meet the .500 requirement for consideration for the NCAA tournament. So, the Huskies won’t be considered if eliminated this weekend. If they advance (either 2-1 or 2-0), they’ll be in a decent bubble position, but probably need at least one more win.

#17 Harvard will be below the bubble if eliminated this weekend and it’s very unlikely they could slide into position for an at-large bid while idle.

Advancing would put them right on the bubble, such that they’d probably want another win to stay there.

#18 Colgate is out if eliminated this weekend. Advancing puts them on the low end of the bubble, such that a subsequent loss would probably push them off. Best to advance and win one more.

#19 Vermont is very likely out if eliminated this weekend. Advancing would put them right on the low end of the bubble, such that another win would probably be required to make the tournament at-large.

#20 Michigan is not yet in its conference tournament so is not facing elimination this weekend. Two losses would likely put an at-large bid out of reach, while two wins would bring the bubble within sight. A first round bye, though, would reduce their opportunities to climb in the PWR.

#21 Bemidji State is out if eliminated this weekend. It’s possible, though not particularly likely, that Bemidji State could position itself for an at-large bid by advancing to the conference tournament final and losing.

#22 St. Lawrence is almost identical to Bemidji State. They’re out if they lose this weekend. It’s possible, though not particularly likely, that St. Lawrence could position itself for an at-large bid by advancing to the conference tournament final and losing.

#23 Dartmouth is out if they fail to advance. Dartmouth is better positioned than the teams above it to get an at-large bid by winning a few games then losing the conference final. Winning the conference tournament would be a safer bet.

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.

Resources

Current PWR Rankings (SiouxSports.com)
Current RPI Rankings (SiouxSports.com)
CHN PWR Rankings (CollegeHockeyNews.com)
USCHO PWR Rankings (USCHO.com)
Explanation of how PWR mimics NCAA tournament selection (CollegeHockeyNews.com)

Tournament cutlines and weekend PWR outlook

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Welcome new visitors. You might want to start with my introductory post, Hello world, to see what this blog is about. It may not be for everyone.

Review of last week’s cutlines

I don’t report on the cutlines (the rankings above which teams are locks for the tournament and below which teams are unable to make the tournament at-large) weekly, because their movements are usually pretty intuitive. If I reported that a team needs to win 5 out 8 and it subsequently wins 2 games, it then needs to win 3 out of 6; the PWR curves usually look about same, just the curve labels change from “5 more wins” to “3 more wins” and so forth. To illustrate that, let’s quickly review a few of the teams that had charts in last week’s article (you may want to open its charts side-by-side for comparison if you can).

By winning 2 games, #4 Minnesota-Duluth made the old “win 0” curve drop off and now just needs 1 or 2 more wins to stay on or above the bubble.

#5 Bowling Green also won 2 games, so now just needs about 4 wins to go into conference tournaments on the bubble.

Further down the chart, #14 Minnesota shifted all of its curves with a pair of wins — the Gophers now need about 6 or 7 wins out of 10 (consistent with last week’s 8 or 9 out of 12) to climb onto the bubble before conference tournaments.

#30 Bemidji State, which I said last week could only afford about 2 losses, has racked up 2 losses. They would pretty much need to win out for a shot at an at-large bid.

Interesting potential movements this weekend

First, is this the week #1 Minnesota State falls out of first? It only seems possible if they get swept (which KRACH gives about a 2.6% chance of happening), and even then someone nipping at their heels (North Dakota seems the only possibility) has to do well. You can’t see the “Win 1” curve because it’s in exactly the same place as “Win 2″—100% at 1.

The matchup of the weekend is definitely #12 Michigan vs #14 Minnesota. Neither has much upside potential, but if either sweeps the other will plummet up to 10 spots.

#15 Mass.-Lowell needs a sweep to hang on, but pair of losses could send them into the twenties.

Remember when #16 Harvard was ranked 1st and I said that a “not particularly likely” bad 2nd half could still push them out? Two more losses this weekend could push them into the twenties.

#22 St Cloud State, mentioned last week as the lowest ranked team with a good chance of climbing into contention, can make up some ground this weekend. An unlikely sweep of #5 Minnesota-Duluth could catapult them up onto the bubble, while even a split could result in a climb of a position or two.

#26 Western Michigan is also poised for huge jump with an also unlikely sweep over #4 Nebraska-Omaha.

Methodology

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

Resources

Current PWR Rankings (SiouxSports.com)
Current RPI Rankings (SiouxSports.com)
CHN PWR Rankings (CollegeHockeyNews.com)
USCHO PWR Rankings (USCHO.com)
Explanation of how PWR mimics NCAA tournament selection (CollegeHockeyNews.com)

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

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)

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

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%

#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

#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%).