Tournament cutlines, revisited

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It’s been about a month since my First look at the tournament cutlines. Since then, things have firmed up just a little bit, so it’s worth revisiting.

First a couple of things to keep in mind while looking at the pictures: 1) there are still about 250 games remaining in the regular season alone, so we should fully expect some of the “1% likelihood” events to happen; and 2) teams have wildly different numbers of games remaining in their regular season, from 6 to 12, so their potentials to make big moves will also differ accordingly.

Is anyone a lock?

Mathematically, still no. But the top four teams would need to win just one or two of their remaining games to fall out:
#1 Minnesota State
#2 North Dakota
#3 Boston University
#4 Nebraska-Omaha

#5 Minnesota-Duluth and #6 Bowling Green could each fall out with a particularly bad performance—winning about 1/3 of their remaining games.

Who controls their own destiny?

Teams that should make it if they continue to do we’ll are from #7 Michigan Tech down to about #18 Merrimack, which approaches the bubble with a bit over .500 in its remaining games. Those include:
#8 Miami
#9 Denver
#10 Providence
#11 Harvard
#12 Boston College
#13 Mass.-Lowell
#14 Michigan
#15 Quinnipiac
#16 Vermont
#17 Yale

#19 Minnesota approaches the bubble by winning about 2/3 of its remaining regular season games.

#20 Colgate needs to win about 3/4 to climb to the bubble. Teams down through about #23, Western Michigan, have a similar outlook.

That includes:
#21 St. Lawrence
#22 Penn State
#23 Western Michigan

#24 Robert Morris has a tough, but mathematically possible, road to the bubble.

Down through #31 Dartmouth have a similar outlook. That group includes:
#24 Robert Morris
#26 Cornell
#27 Northeastern
#29 Northern Michigan
#30 Union

Note that I left out #25 St Cloud St and #28 Bemidji St, each of which stand a slightly better (though still difficult) chance than their neighbors at climbing to the bubble.

Who needs to win their conference tournament?

From #32 Alaska down are unlikely to make the bubble at-large, even if they win out. That group includes
#33 Clarkson
#34 Michigan State
#35 Connecticut
#36 Ohio State
#37 Notre Dame
#38 Bentley
#39 Ferris St
#40 Mercyhurst
#41 Canisius
#42 Rensselaer
#43 Maine
#44 New Hampshire
#45 Alabama-Huntsville
#46 Massachusetts
#47 Colorado College
#48 RIT
#49 Alaska-Anchorage
#50 Holy Cross
#51 Lake Superior
#52 Air Force
#53 Sacred Heart
#54 Brown
#55 Wisconsin
#56 Princeton
#57 Army
#58 American Int’l
#59 Niagara

How are last month’s predictions holding up?

Finally, let’s do a results check on last month’s predictions. The two movements that seem most surprising looking back are Harvard and Bemidji State.

I noted that no one was a lock, and that even #1 Harvard could fall to the bubble if they won only about half of their remaining games. Since then, Harvard has gone 2-6 and has fallen to #11. The current forecast matches the original pretty well—that Harvard would now need to win about 5 of its remaining 9 games to end the regular season on the bubble.

I noted that Bemidji State was the cutoff for being unlikely to advance without a major run. A 5-2-1 run since then has helped propel Bemidji State from #37 to #28. The forecasts now show that they stand a slightly better chance of making the tournament than seemed possible a month ago, but that they’d still need a run of winning at least 8 if not 9 of their remaining 10 to hit the bubble.

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)

How many teams will each conference put into the playoffs?

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Repeating a similar post that was inspired by message board chatter last year, I ran simulations of the remaining games and tracked how many teams each conference had in the top 14 at the end of the regular season (a reasonable guess as to the PWR rank that would guarantee an invitation to the NCAA tournament).

Let’s start with the current PWR.

Number of teams in top 14 of PWR right now
Atlantic Hockey	0
Big 10	1
ECAC	1
Hockey East	4
NCHC	5
WCHA	3

A far cry from last year when the post was inspired by inquiries about whether the NCHC was underperforming.

Now for the results of the simulations. Each chart shows the likelihoods of how many teams a conference will have in the top 14 at the end of the regular season.

Remember that the simulations assume each team will continue to perform similarly to how it has to date. So, it’s not surprising that each conference is predicted to finish with about the same number of teams in the top 14 as they have today.

More interesting is seeing how easy (or not) it is for conferences to move up or down. Atlantic Hockey is pretty unlikely to get an at-large bid. The Big Ten is more likely to fall to 0 at-large bids than climb to 2.

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)

A first look at the at-large tournament cutlines

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A couple of weeks ago in When to start looking at PWR (revisited), I noted that the PWR as of early January does give us some idea as to which teams might make the tournament at large. I noted that any top team can still fall out of contention, though that it takes a notable collapse for the top few. More interestingly, I observed that its unusual (though definitely possible) for a team rated much lower than 20 to climb into an at-large bid.

To see how those general historical observations will hold up this season, I ran simulations for the rest of the regular season and generated some statistics about where teams are likely to finish based on their performance over their remaining games. (Specific details about the simulations are available in the methodology section at the end).

Before we jump into the data, I want to warn that starting simulations this far out makes it pretty likely that some of the 1% events will happen. Remember that PWR cares how each team’s opponents perform, so the analysis for each team implicitly assumes that all other teams will continue to perform as they have to date. As teams’ fortunes change in the 2nd half of the season, it will affect not only their own PWR but also their opponents’. With about 450 games remaining, we should see a lot of outcomes we didn’t expect.

Is anyone a lock for the tournament?

Not completely. Even #1 Harvard could slip to the bubble if it wins only 6-7 of its remaining 14 games. That’s not particularly likely (the odd shape of the “win 6” curve and complete absence of the “win 4” curve are because those scenarios occurred so infrequently in the simulations).

Who can still make the tournament at-large with a good regular season performance?

From #1 Harvard (as described above) down to about #27 Northern Michigan have realistic scenarios for at-large bids. It would take a good run for Northern Michigan to climb into an at-large bid; they would need at least 12 wins in their remaining 16 games to stand a good chance.

From #28 Notre Dame to #37 Bemidji State, it appears possible to make the tournament at-large, but only with an amazing run (e.g. one or two losses at the most). These teams aren’t mathematically eliminated, but it’s a decent guess that being below #28 today means success in a conference tournament will be required for an NCAA tournament bid.

#38 New Hampshire and below look like the only path to the NCAA tournament is through the conference tournaments.

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)

When to start looking at PWR (revisited)

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Five years ago I wrote a post for SiouxSports.com, When to start looking at PWR. I want to revisit that post because we now have five more seasons of data, including the first full season with last year’s PWR revisions.

It’s been noted countless times on message boards (by people presumably offended that others enjoy looking at PWR?) that PWR is only calculated once at the end of the conference tournaments. So why do we calculate “as if the season ended today” versions of PWR before that?

We look at PWR before the end of the season because we think it’s going to provide some insight into what that final PWR might be and what our favorite teams need to do to make the tournament. When to start looking depends what insight you’re looking for.

In this article I’ll look at how stable PWR is over time and how well it predicts the final PWR. The PWR starts containing useful information about what each team needs to do for an at-large bid as early as November. Front-runners start to become more entrenched by January. But as readers of this blog know, only the top few teams going into the conference tournaments are absolute locks, and teams as low as the mid-20s still stand a chance.

Week-to-week stability of PWR

My previous article started with a look at how stable PWR is. My thinking was that if next weekend’s games have the potential to completely upend the PWR table, then this week’s PWR table may not be particularly interesting.

The above chart shows the average PWR movement (in rank positions) of teams ranked over consecutive weeks. Consistent with the last article, PWR exhibits wild swings (an average or 4+ positions week-to-week) until the December break (movements in December are lower because teams play so many fewer games over holiday breaks). By January, movement has settled into an average of 2-3 positions per weekend for ranked teams, and down to 1-2 positions by March.

PWR’s ability to predict the final PWR

So we know when PWR stabilizes week-to-week, but what we really want to know is how good a predictor a weekly PWR is of the one true final PWR.

Though PWR seems relatively stable in January, because week-to-week movements have settled down, those movements add up enough over the weeks that January’s PWR isn’t a spectacular predictor of the final PWR. On January 1 (about 90 days before the final PWR) teams have been an average of 3-8 ranks off from their final rank. Even 30 days out teams are only within 2-4 positions on average of their final rank.

Likelihood of teams finishing in the top 12 of PWR

That’s where I stopped five years ago. Let’s go a little further—the reason we care about PWR is we want to know if a team is going to make the tournament. Let’s look at how many teams in the top 12 of PWR are still in the top 12 at tournament selection time.

From 50%-85% of top 12 teams as of January 1 (90 days out) have finished in the top 12. At 60 days out, that has climbed to roughly 60%-85% holding onto a top 12 spot. By 30 days out, that has climbed to 75%-100%.

Also interesting is knowing how much a team’s performance to date has set their fate. Let’s look at how highly ranked you must be at given times to be a pretty good lock for the tournament and how lowly ranked you can be and still stand a chance.

At 90 days out (January 1) anyone can fall out of contention, though it takes a notable collapse by a previously top-performing team. In the last ten years, we’ve never seen a team that was top 4 at 60 days out (February 1) miss finishing top 12. We’ve seen a season where the top 12 are locked at 42 days out, but also one where only 6 of the top 12 at 28 days out manage to finish top 12.

On the flip side, every year in the past 10 has seen a team ranked #17 or lower 90 days out climb into the top 12. It’s most common for a team around #20 at 90 days out to be the lowest rank from which anyone climbs to finish top 12. But, there has been a recent season in which a team unranked until Feb. 22 and ranked #25 until Mar. 15 made it to the top 12.

Effects of the new formula

It’s really too early to tell based on the empirical data if the new PWR formulas is more or less stable than the previous one. It’s a reasonable guess that the removal of the TUC cliff and introduction of sliding RPI bonuses would lead to less severe movements, but that’s not obviously the case from the available results.

I should note that the 2013 line in the first two charts isn’t directly comparable to those from earlier seasons. The 2013 PWR ranks all teams so the line represents an average of all teams, while the earlier lines only include those teams that were ranked at both times.

Some notes on statistics

Feel free to skip this paragraph if you don’t care about statistics.

I’m not a statistician and would happily take some advice from one. I didn’t calculate proper correlations in the past because I wasn’t sure what to do with the teams dropping in and out of being ranked. Giving the unranked teams the average rank of the tied group, as I’ve seen done with Spearman, struck me as potentially exaggerating those teams’ rises and declines as they fall in and out of being ranked. I suppose I could have run a standard Pearson on the teams ranked in both periods rather than just report the mean difference, but I didn’t.

But the new formula ranks every team, so without further ado here’s the Spearman rho correlation between the PWR for each week and the final PWR. Not surprisingly, you can see that even the earliest PWR rankings make a statistically significant contribution to the final PWR (with a reasonably high degree of confidence).

The tournament that could have been

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For better or worse, the NCAA changed the hockey tournament selection criteria this year. While the formulas were carefully crafted to produce a nearly identical outcome for last year, things could have been a little different this year if the change hadn’t been made.

The PairWise Rankings that could have been

First, the collegehockeyranked supercomputers have produced a table of where this year’s top 20 would have ranked under last year’s formula.

	PWR	Old PWR
Minnesota	1	1
Boston College	2	3
Union	3	2
Wisconsin	4	8
Ferris State	5	9
Quinnipiac	6	5
Mass.-Lowell	7	4
Notre Dame	8	11
St Cloud St	9	7
MSU-Mankato	10	13
Providence	11	6
Colgate	12	12
Vermont	13	15
North Dakota	14	10
Michigan	15	16
Northeastern	16	19
Cornell	17	14
New Hampshire	18	18
Ohio State	19	20
Yale	20	22

As we should have expected, the tournament field doesn’t change much (after announcing the changes last Fall, the NCAA issued a statement noting that the tournament field wouldn’t have changed at all the previous year under the new formula).

Vermont is out at #15 while Cornell is in at #14. North Dakota fans would have been a little less worried and MSU-Mankato fans a little more, but both teams would still make the field.

But, the order is different enough to change the bracket quite a bit. My strength is statistics and rankings, not bracket-making, so I’ll walk you through a straight serpentine bracket then note the interesting aspects:

West (St Paul)
1. Minnesota vs 16. Robert Morris
8. Wisconsin vs 9. Ferris St

Northeast (Worcester)
3. Boston College vs 14. Cornell
6. Providence vs 11. Notre Dame

East (Bridgeport)
2. Union vs 15. Denver
7. St Cloud St vs 10. North Dakota

Midwest (Cincinnati)
4. Mass-Lowell vs 13. Mankato
5. Quinnipiac vs 12. Colgate

Problem #1 – Which #1 do you put in Cincinnati?
Problem #2 – Providence v Notre Dame is no good.
Problem #3 – St Cloud St vs North Dakota is no good.
Problem #4 – Attendance at Cincinnati would be in the double digits.

We can solve #2 and #3 by swapping North Dakota and Notre Dame.

I have no idea what the committee would do about #1 and #4.

It would be nice to get Quinnipiac in Bridgeport but Union is already there and swapping St Cloud St to Cincinnati may not help Cincinnati much. A three way move could instead land Wisconsin in Cincinnati and St Cloud St in St. Paul.

Instead of just swapping UND and ND, you could also imagine a three way move that put Colgate in Worcester, Notre Dame in Bridgeport, and UND in Cincinnati.

The matchups and outlook would certainly be different (and North Dakota fans would undoubtedly be delighted for another stop in Worcester on the B.C. revenge tour).

Like I said, I’m a rankings guy, not a bracket guy, so feel free to let me know what I did wrong.

KRACH predicts the NCAA tournament

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Everyone’s favorite college hockey ranking scheme, KRACH, can be used to predict game outcomes. Here’s what KRACH thinks of the NCAA tournament field.

KRACH thinks Minnesota has the easiest path to the Frozen Four, with a better than 60% of emerging from its regional.
SCSU vs Notre Dame is the most balanced game, with KRACH given about a 1% edge to St Cloud St.
Wisconsin is the weakest 1-seed facing the 2nd toughest 4 seed, resulting in only a 56-44 advantage over North Dakota.
The Midwest is also the most balanced regional overall, with each team having between a 20-30% chance of advancing.

KRACH	West	Game 1	Game 2 (Region Champ)	Game 3 (Frozen four semifinal)	Game 4 (National Champ)
359.406	1. Minnesota	93.19%	61.16%	40.70%	23.41%
26.2834	4. Robert Morris	6.81%	0.84%	0.11%	0.01%

190.458	2. St Cloud St	50.60%	19.36%	9.95%	4.20%
185.96	3. Notre Dame	49.40%	18.65%	9.47%	3.94%

	Midwest
198.286	1. Wisconsin	56.35%	29.51%	12.39%	5.35%
153.57	4. North Dakota	43.65%	20.08%	7.25%	2.70%

199.632	2. Ferris St	55.70%	29.49%	12.43%	5.38%
158.776	3. Colgate	44.30%	20.93%	7.71%	2.93%

	East
352.088	1. Union	69.46%	45.44%	26.41%	15.61%
154.823	4. Vermont	30.54%	13.88%	5.35%	2.11%

197.646	2. Quinnipiac	53.26%	22.42%	9.93%	4.49%
173.439	3. Providence	46.74%	18.26%	7.52%	3.17%

	Northeast
350.585	1. Boston College	76.88%	49.23%	28.98%	17.10%
105.457	4. Denver	23.12%	8.11%	2.50%	0.77%

159.696	2. Minnesota St	41.36%	15.71%	6.28%	2.52%
226.442	3. Mass.-Lowell	58.64%	26.94%	13.02%	6.32%

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%).

A more in-depth look at the at-large chances for teams on the bubble

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With this year’s simplification of PWR (primarily moving the good wins bonus into RPI), there are far fewer fluky outcomes that push teams up or down. Teams trying to make the tournament from the #12-16 range are looking for two things:

maximizing the number of teams that make the tournament on the basis of PWR
maximizing their own PWR

The first is accomplished by minimizing the number of autobids that go to teams with lower PWRs.

Because of the new PWR’s simplicity, the second is usually accomplished by teams with rankings near the team in question is losing. If the team in question wins, it is helped by teams around it losing to clear a path. If the team in question loses, it is mostly focused on teams below it also losing so as not to be overtaken.

PWR Rankings (SiouxSports.com)

Autobids to high ranking teams

If you think of the tournament as having 6 autobids (for conference tournament winners) and 10 at-large bids, then each autobid that goes a team that would have made it at-large essentially frees up the at-large bid for the next lower ranked team.

So, if four autobids go to teams that otherwise would have made the tournament, then #14 in PWR will get a bid. If only two autobids go to teams that otherwise would have made the tournament, then only through #12 in PWR will get a bid.

So, the teams on the at-large bubble of #12-#16 want as many conferences tournaments as possible to be won by teams that were going to make the tournament regardless. Those are:

Big Ten

#1 Minnesota
#5 Wisconsin

ECAC

#3 Union
#6 Quinnipiac

WCHA

#4 Ferris State

Hockey East

#7 Mass.-Lowell
#8 Notre Dame
#9 Providence

#2 Boston College and #10 St Cloud St are idle.

As teams like #11 Michigan and the teams featured in this article advance to the point that they’re pretty much guaranteed a tournament spot, it may similarly benefit the featured teams for those teams to continue to succeed and claim conference championships. However, the Atlantic Hockey tournament autobid guarantees that at most the top 15 in PWR will make it, so teams featured in this article have to be cheering for at least some of the others to lose.

Minnesota State

#12 Minnesota State makes the tournament in 54% of scenarios in which it wins 1 game and 6.4% of scenarios in which it has no wins.

Minnesota State is most helped by #16 Cornell, #17 New Hampshire, #13 North Dakota, and #15 Colgate losing (note that #14 Vermont is not playing).

Minnesota State, like all teams featured in this article, is also helped by autobids going to highly ranked teams as described above.

North Dakota

#13 UND makes the tournament in 42% of scenarios in which it wins 1 game and .5% of scenarios in which it has no wins (a tie in the consolation game seems to be required).

Because the NCHC has a consolation game, UND could exit the tournament with one win either by winning then losing, or by losing then winning. The two have slightly different outlooks.

If UND wins its first game, it makes the tournament in about 46% of scenarios in which it loses the championship game. Most useful to UND in this situation seems to be #12 Minnesota State, #16 Cornell, #15 Colgate, and #11 Michigan losing (note that #14 Vermont is not playing).

If UND loses its first game, it makes the tournament in about .5% of scenarios in which it ties the consolation game or about 36% of scenarios in which it wins the consolation game. Most useful to UND in this situation seems to be #17 New Hampshire, #21 Ohio State, #16 Cornell, and #15 Colgate losing (note again that #14 Vermont is not playing).

North Dakota, like all teams featured in this article, is also helped by autobids going to highly ranked teams as described above.

Vermont

#14 Vermont has no opportunity for an auto bid but makes the tournament at large in 69% of scenarios.

Because Vermont is idle, it’s counting on others to clear it a path. Its own PWR is most helped by losses from #11 Michigan, #15 Colgate, #16 Cornell, #12 Mankato, and #13 North Dakota.

Vermont, like all teams featured in this article, is also helped by autobids going to highly ranked teams as described above.

Colgate

#15 Colgate makes the tournament in 77% of scenarios in which it wins a game, but only 2% of scenarios in which it has no wins.

Colgate is most helped by #12 Minnesota State, #16 Cornell, #13 North Dakota, and #17 New Hampshire losing (remember that #14 Vermont is idle).

Colgate, like all teams featured in this article, is also helped by autobids going to highly ranked teams as described above.

Cornell

#16 Cornell makes the tournament in 85% of scenarios in which it wins a game, but under 1% of scenarios in which it has no wins.

Cornell is most helped by #15 Colgate and #13 North Dakota losing (remember that #14 Vermont is idle).

Cornell, like all teams featured in this article, is also helped by autobids going to highly ranked teams as described above.