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Big PWR games of the week

#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.

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

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.

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.

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.

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)

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.

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)

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

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.

In contention teams’ tournament probabilities by outcome

1 Reply

Here are some more detailed probabilities for teams with a possibility of making the NCAA tournament at-large.

The following conclusions are based on an exhaustive search of all possible remaining outcomes (about 3,145,728 of them). Any percentages given are not weighted by likelihood or team strength, but instead represent the share of remaining scenarios in which that outcome occurs.

See the previous post—Conference tournament weekend PWR outlook—for a less statistical, more descriptive explanation.

I’ll dive deeper into some of the more interesting teams in coming days.

Team

PWR Possibilities

Overall

By number of wins

UMN

#1 100.0%
Tournament invites: 100.0%

PWR	Win 0	Win 1	Win 2
#1	100.0%	100.0%	100.0%
Tournament invites:	100.0%	100.0%	100.0%

Boston College

#2 99.5%
#3 0.5%
Tournament invites: 100.0%

n/a

Union

#2 0.5%
#3 99.5%
Tournament invites: 100.0%

PWR	Win 0	Win 1	Win 2
#2			2.0%
#3	100.0%	100.0%	98.0%
Tournament invites:	100.0%	100.0%	100.0%

Ferris State

#4 42.8%
#5 33.9%
#6 19.2%
#7 3.9%
#8 0.2%
Tournament invites: 100.0%

PWR	Win 0	Win 1	Win 2
#4	23.2%	32.3%	92.3%
#5	43.3%	41.4%	7.7%
#6	27.4%	21.9%
#7	6.0%	3.6%
#8	0.0%	0.8%
Tournament invites:	100.0%	100.0%	100.0%

#4 22.3%
#5 17.6%
#6 22.6%
#7 27.0%
#8 8.6%
#9 1.9%
Tournament invites: 100.0%

PWR	Win 0	Win 1	Win 2
#4		9.5%	79.7%
#5	7.2%	37.0%	18.9%
#6	24.9%	39.2%	1.4%
#7	47.4%	13.2%	0.1%
#8	16.7%	1.1%
#9	3.8%
Tournament invites:	100.0%	100.0%	100.0%

Quinnipiac

#4 12.6%
#5 19.9%
#6 28.2%
#7 32.3%
#8 6.7%
#9 0.3%
#10 0.0%
Tournament invites: 100.0%

PWR	Win 0	Win 1	Win 2
#4		2.2%	48.1%
#5	7.9%	23.6%	40.4%
#6	29.5%	43.1%	10.6%
#7	50.0%	28.4%	0.9%
#8	11.9%	2.8%
#9	0.7%
#10	0.0%
Tournament invites:	100.0%	100.0%	100.0%

Mass.-Lowell

#4 8.9%
#5 9.9%
#6 8.8%
#7 24.3%
#8 37.7%
#9 10.3%
#10 0.1%
Tournament invites: 100.0%

PWR	Win 0	Win 1	Win 2
#4			35.5%
#5		1.3%	38.5%
#6	0.5%	16.4%	17.5%
#7	20.6%	47.6%	8.5%
#8	58.3%	34.4%
#9	20.4%	0.2%
#10	0.2%
Tournament invites:	100.0%	100.0%	100.0%

Notre Dame

#4 13.4%
#5 12.7%
#6 9.3%
#7 6.1%
#8 44.1%
#9 14.0%
#10 0.4%
Tournament invites: 100.0%

PWR	Win 0	Win 1	Win 2
#4		0.3%	53.3%
#5		13.0%	37.8%
#6	0.0%	29.0%	8.3%
#7	4.6%	15.0%	0.0%
#8	69.5%	36.7%	0.6%
#9	25.1%	5.9%
#10	0.8%
Tournament invites:	100.0%	100.0%	100.0%

Providence

#4 0.1%
#5 5.9%
#6 11.9%
#7 6.3%
#8 0.0%
#9 21.5%
#10 21.8%
#11 21.7%
#12 8.9%
#13 1.7%
#14 0.2%
#15 0.0%
Tournament invites: 98.7%

PWR	Win 0	Win 1	Win 2
#4			0.4%
#5			23.7%
#6			47.5%
#7			25.4%
#8			0.0%
#9	1.8%	79.3%	3.0%
#10	33.5%	20.1%
#11	43.0%	0.6%
#12	17.9%
#13	3.5%
#14	0.3%
#15	0.0%
Tournament invites:	97.4%	100.0%	100.0%

SCSU

#8 0.1%
#9 36.2%
#10 48.8%
#11 13.5%
#12 1.3%
#13 0.0%
Tournament invites: >99%

n/a

Michigan

#6 0.1%
#7 0.0%
#8 2.6%
#9 7.1%
#10 3.0%
#11 10.4%
#12 17.2%
#13 15.9%
#14 17.8%
#15 16.2%
#16 8.0%
#17 1.5%
#18 0.2%
Tournament invites: 59.9%

PWR	Win 0	Win 1	Win 2	Win 3
#6				0.6%
#7				0.0%
#8				20.6%
#9			0.1%	56.6%
#10			2.2%	22.2%
#11	0.0%	22.0%	38.9%
#12	2.7%	43.4%	40.0%
#13	14.8%	25.5%	16.8%
#14	31.4%	7.5%	2.0%
#15	31.6%	1.5%
#16	15.8%	0.1%
#17	3.0%
#18	0.5%
Tournament invites:	22.7%	95.9%	96.5%	100.0%

Mankato

#9 0.1%
#10 4.1%
#11 14.1%
#12 10.7%
#13 10.0%
#14 13.3%
#15 15.9%
#16 15.4%
#17 7.8%
#18 7.7%
#19 0.8%
#20 0.0%
Tournament invites: 41.7%

PWR	Win 0	Win 1	Win 2
#9			0.4%
#10			16.3%
#11		2.9%	53.7%
#12	0.2%	16.1%	26.4%
#13	2.8%	31.3%	3.1%
#14	11.9%	29.3%	0.0%
#15	24.5%	14.7%
#16	28.4%	4.6%
#17	15.0%	1.1%
#18	15.5%
#19	1.7%
#20	0.0%
Tournament invites:	6.4%	54.1%	100.0%

UND

#10 1.0%
#11 9.6%
#12 16.4%
#13 16.6%
#14 14.4%
#15 9.6%
#16 7.0%
#17 16.4%
#18 7.9%
#19 1.0%
#20 0.0%
Tournament invites: 42.7%

PWR	Win 0	Win 1	Win 2
#10		0.0%	4.0%
#11		2.4%	34.2%
#12		13.4%	43.4%
#13	0.0%	30.0%	16.5%
#14	0.8%	32.9%	1.9%
#15	6.9%	17.5%
#16	16.5%	3.7%
#17	49.1%
#18	23.7%
#19	2.9%
#20	0.0%
Tournament invites:	0.5%	42.0%	100.0%

Vermont

#10 0.8%
#11 6.7%
#12 23.3%
#13 34.2%
#14 24.7%
#15 9.1%
#16 1.3%
Tournament invites: 69.2%

n/a

Colgate

#9 0.1%
#10 9.1%
#11 14.6%
#12 12.1%
#13 8.1%
#14 5.5%
#15 7.9%
#16 16.6%
#17 18.9%
#18 6.7%
#19 0.4%
Tournament invites: 45.4%

PWR	Win 0	Win 1	Win 2
#9			0.3%
#10		1.7%	34.8%
#11		14.5%	44.1%
#12	0.0%	30.2%	18.0%
#13	0.2%	29.2%	2.6%
#14	2.7%	16.4%	0.1%
#15	12.5%	6.4%
#16	32.4%	1.7%
#17	37.8%
#18	13.5%
#19	0.9%
Tournament invites:	2.1%	77.1%	100.0%

Cornell

#9 8.5%
#10 10.9%
#11 9.4%
#12 9.3%
#13 7.6%
#14 3.4%
#15 2.0%
#16 11.1%
#17 29.0%
#18 8.2%
#19 0.6%
Tournament invites: 46.2%

PWR	Win 0	Win 1	Win 2
#9			34.1%
#10		1.4%	42.1%
#11		17.2%	20.4%
#12		34.2%	3.2%
#13		30.1%	0.2%
#14	0.1%	13.3%
#15	2.3%	3.4%
#16	22.0%	0.4%
#17	58.0%
#18	16.4%
#19	1.1%
Tournament invites:	< 1%	84.7%	100.0%

New Hampshire

#12 0.3%
#13 2.2%
#14 6.1%
#15 8.6%
#16 5.9%
#17 5.6%
#18 12.8%
#19 20.0%
#20 28.2%
#21 9.2%
#22 1.1%
Tournament invites: 25.0%

PWR	Win 0	Win 1	Win 2
#12			1.4%
#13			9.0%
#14			24.4%
#15			34.2%
#16			23.7%
#17		16.4%	6.1%
#18		49.9%	1.1%
#19	24.7%	30.5%
#20	54.8%	3.2%
#21	18.3%	0.0%
#22	2.2%
Tournament invites:	0.0%	0.0%	100.0%

Northeastern

#12 0.3%
#13 3.5%
#14 13.9%
#15 29.1%
#16 32.3%
#17 13.9%
#18 6.6%
#19 0.3%
Tournament invites: 8.8%

n/a

Western Michigan

#15 0.0%
#16 0.0%
#17 4.1%
#18 14.8%
#19 22.5%
#20 30.4%
#21 18.3%
#22 6.8%
#23 2.3%
#24 0.7%
#25 0.2%
Tournament invites: 25.0%

PWR	Win 0	Win 1	Win 2
#15			0.0%
#16			0.1%
#17		0.5%	15.5%
#18		3.2%	53.8%
#19		37.4%	27.6%
#20	30.5%	46.8%	3.0%
#21	40.1%	11.8%
#22	20.2%	0.2%
#23	6.8%
#24	2.0%
#25	0.5%
Tournament invites:	0.0%	0.0%	100.0%

Ohio State

#13 0.1%
#14 0.7%
#15 1.6%
#16 2.4%
#17 2.8%
#18 6.5%
#19 6.7%
#20 5.9%
#21 10.3%
#22 10.9%
#23 14.1%
#24 22.6%
#25 11.8%
#26 3.2%
#27 0.3%
Tournament invites: 12.5%

PWR	Win 0	Win 1	Win 2	Win 3
#13				1.1%
#14				5.7%
#15				13.0%
#16				19.1%
#17				22.8%
#18			22.2%	29.4%
#19			44.5%	9.0%
#20		9.6%	27.6%	0.0%
#21		38.4%	5.7%
#22	0.0%	43.6%	0.0%
#23	24.0%	8.3%
#24	45.3%	0.0%
#25	23.7%
#26	6.4%
#27	0.6%
Tournament invites:	0.0%	0.0%	0.0%	100.0%

Bowling Green

#19 0.4%
#20 6.7%
#21 14.1%
#22 3.8%
#23 1.8%
#24 11.6%
#25 19.2%
#26 24.8%
#27 17.7%
Tournament invites: 25.0%

PWR	Win 0	Win 1	Win 2
#19			1.5%
#20			26.7%
#21			56.3%
#22			15.3%
#23		6.9%	0.2%
#24	4.9%	36.6%
#25	20.0%	36.7%
#26	40.9%	17.4%
#27	34.1%	2.4%
Tournament invites:	0.0%	0.0%	100.0%

#18 0.0%
#19 0.3%
#20 6.7%
#21 12.4%
#22 4.6%
#23 5.5%
#24 8.2%
#25 12.5%
#26 31.0%
#27 18.8%
Tournament invites: 25.0%

PWR	Win 0	Win 1	Win 2
#18			0.0%
#19			1.0%
#20			27.0%
#21			49.5%
#22		0.1%	18.4%
#23		17.8%	4.1%
#24	0.2%	32.4%
#25	3.2%	43.7%
#26	59.2%	5.6%
#27	37.4%	0.4%
Tournament invites:	0.0%	0.0%	100.0%

Denver

#20 0.0%
#21 8.5%
#22 10.5%
#23 5.0%
#24 4.5%
#25 16.6%
#26 7.6%
#27 12.1%
#28 18.1%
#29 16.5%
#30 0.6%
#31 0.0%
Tournament invites: 25.0%

PWR	Win 0	Win 1	Win 2
#20			0.0%
#21			34.0%
#22			42.2%
#23			19.9%
#24		8.5%	3.9%
#25		39.8%
#26	0.2%	18.1%
#27	5.0%	25.0%
#28	43.8%	8.4%
#29	49.1%	0.3%
#30	1.8%
#31	0.1%
Tournament invites:	0.0%	0.0%	100.0%

Mercyhurst

#27 0.2%
#28 0.9%
#29 23.6%
#30 0.4%
#31 32.1%
#32 35.1%
#33 7.1%
#34 0.6%
#35 0.0%
Tournament invites: 25.0%

PWR	Win 0	Win 1	Win 2
#27			0.9%
#28			3.7%
#29		0.0%	94.5%
#30		1.2%	0.3%
#31	31.4%	64.9%	0.7%
#32	54.8%	30.7%
#33	12.6%	3.1%
#34	1.3%
#35	0.0%
Tournament invites:	0.0%	0.0%	100.0%

Miami

#27 0.2%
#28 0.5%
#29 6.4%
#30 14.4%
#31 15.7%
#32 20.3%
#33 7.8%
#34 17.3%
#35 8.2%
#36 4.9%
#37 4.4%
Tournament invites: 25.0%

PWR	Win 0	Win 1	Win 2
#27			0.9%
#28			2.0%
#29			25.6%
#30		0.0%	57.6%
#31		29.8%	13.1%
#32	0.0%	48.2%	0.7%
#33	1.1%	17.7%
#34	46.4%	4.3%
#35	24.7%	0.0%
#36	14.7%
#37	13.1%
Tournament invites:	0.0%	0.0%	100.0%

Michigan State

#27 1.0%
#28 2.0%
#29 4.6%
#30 3.0%
#31 2.0%
#32 1.5%
#33 2.3%
#34 4.8%
#35 7.2%
#36 6.8%
#37 31.0%
#38 33.8%
Tournament invites: 12.5%

PWR	Win 0	Win 1	Win 2	Win 3
#27				8.0%
#28				15.9%
#29				37.1%
#30				24.0%
#31			3.9%	12.4%
#32			9.6%	2.4%
#33			18.3%	0.2%
#34		0.9%	36.5%
#35		12.9%	31.7%
#36		27.1%
#37	32.5%	59.1%
#38	67.5%
Tournament invites:	0.0%	0.0%	0.0%	100.0%

Robert Morris

#44 20.4%
#45 4.6%
#46 0.0%
#47 14.4%
#48 49.7%
#49 10.8%
#50 0.0%
Tournament invites: 25.0%

PWR	Win 0	Win 1	Win 2
#44			81.4%
#45			18.5%
#46		0.0%	0.1%
#47	5.3%	47.2%
#48	74.6%	49.7%
#49	20.1%	3.1%
#50	0.1%
Tournament invites:	0.0%	0.0%	100.0%

Canisius

#44 0.1%
#45 7.4%
#46 9.7%
#47 7.8%
#48 17.0%
#49 36.5%
#50 19.6%
#51 1.9%
Tournament invites: 25.0%

PWR	Win 0	Win 1	Win 2
#44			0.5%
#45			29.5%
#46			38.8%
#47			31.2%
#48	12.1%	43.8%
#49	47.9%	50.0%
#50	36.1%	6.2%
#51	3.9%
Tournament invites:	0.0%	0.0%	100.0%

Niagara

#45 2.6%
#46 6.1%
#47 24.6%
#48 8.0%
#49 7.3%
#50 41.4%
#51 9.9%
Tournament invites: 25.0%

PWR	Win 0	Win 1	Win 2
#45			10.5%
#46			24.4%
#47		33.2%	65.0%
#48		32.0%	0.1%
#49	0.4%	28.6%
#50	79.8%	6.2%
#51	19.8%
Tournament invites:	0.0%	0.0%	100.0%

Penn State

#45 0.0%
#46 0.2%
#47 2.8%
#48 9.2%
#49 2.2%
#50 2.7%
#51 11.2%
#52 69.7%
#53 2.0%
Tournament invites: 12.5%

PWR	Win 0	Win 1	Win 2	Win 3
#45				0.0%
#46				1.3%
#47				22.3%
#48			4.0%	70.0%
#49			11.0%	6.4%
#50			21.4%
#51		13.2%	63.6%
#52	95.9%	86.8%
#53	4.1%
Tournament invites:	0.0%	0.0%	0.0%	100.0%

The calculation ambiguity mentioned in the previous post has been resolved.

Conference tournament weekend PWR outlook

2 Replies

The following teams will make the NCAA tournament regardless of what happens this weekend:

#1 Minnesota
#2 Boston College (not playing)
#3 Union
#4 Ferris State
#5 Wisconsin
#6 Quinnipiac
#7 Mass.-Lowell
#8 Notre Dame

The following teams are extremely likely to make the NCAA tournament, but there are some outlier scenarios that could knock them out:

#9 Providence (in for sure with a win, selected in 97% of 0 win scenarios)
#10 St. Cloud St (not playing, selected in over 99% of scenarios)

The following teams have some chance of making it regardless of outcome:

#11 Michigan (selected in 21% of scenarios with no wins, selected in 96% of scenarios with 1 win)
#12 Minnesota State (selected in 6% of scenarios with no wins, selected in 54% of scenarios with 1 win)
#14 Vermont (not playing, selected in 69% of scenarios)
#15 Colgate (selected in 2% of scenarios with no wins, selected in 77% of scenarios with 1 win)
#16 Cornell (selected in <1% of scenarios with no wins, selected in 85% of scenarios with 1 win)
#18 Northeastern (not playing, selected in 8% of scenarios)

The following teams need a win to make it:

#13 North Dakota (out with two losses, selected in 41% of scenarios with 1 win). UND is an outlier from the group above because the NCHC has a consolation game, so no wins actually means two losses instead of one.

The following teams need to win the conference tournament to get a bid:

#17 New Hampshire
#19 Western Michigan
#21 Ohio State
#24 Bowling Green
#25 Alaska Anchorage
#26 Denver
#31 Mercyhurst
#32 Miami
#37 Michigan State
#47 Robert Morris
#48 Canisius
#49 Niagara
#52 Penn State

Note – as of this writing there seems to be some discrepancy between the USCHO PWR calculator and CHN PWR calculator that I’m trying to work out. I feel pretty good about these numbers so wanted to get them out there rather than wait, but there’s a possibility of small revisions if new information comes to light.