Author Archives: jim

First 2019 PWR forecast available (and, what is it?)

After the holiday break is generally considered a good time to start paying attention to the PairWise Ranking (PWR). Remember that PWR is a ranking whose calculation mimics the NCAA’s tournament selection process, so the final PWR ranking perfectly predicts the teams that will be selected for the NCAA tournament. The 2014 article, When to start looking at PWR (revisited), examines how today’s PWR is reasonably predictive of the final PWR.

Current PWR Ranking

The reason you’re really interested in the PWR is because you want to know who is going to make the NCAA tournament. So what you really want to know is what the PWR is going to be at the end of the season. To help bridge the gap from today’s PWR to the end of season PWR, I’ve developed a forecast that shows you what the PWR is likely to be at the end of the regular season. It’s explained in the 2017 article, New forecast presentation—PWR by wins, and can be used to answer questions such as:

How many wins does my team need to make the tournament?
Can my team make the top 4?
What are some unlikely tournament seeding outcomes that could occur?

PWR By Wins (What does it take for each team to finish at each PWR ranking?)

The table on the PWR By Wins page shows you how many wins each team needs to likely finish at each PWR ranking.

So, for example, if Mass. wins half its remaining scheduled games (7 of the 14), it will probably end the regular season in the 10-12 range, and thus likely to make the tournament.

If you want more detail on a specific team, you can click a team name to see the probability curves of how likely that team is to end the regular season with each PWR ranking with a given number of wins in its remaining scheduled games.

That helps you see, for example, that though Mass. has a decent change of finishing anywhere from #3 to #9 with 8 more wins, #5-#7 are much more likely.

The forecasts are usually updated in the first half of the week. You can always browse all the data any time, but I’ll also scour the data and post interesting results and observations in this space in coming weeks.

How it works

The page notes when the forecast was last run (assume that it includes all games that had been completed as of that time).

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.

KRACH predicts the NCAA tournament

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Everyone’s favorite college hockey ranking scheme, KRACH, is also a favorite way to predict the odds of each team winning a game. As in past years, I used KRACH to predict each tournament team’s odds of winning it’s first round game, advancing out of the regional, winning a semifinal game, and winning the national championship.

For the first time in modern NCAA tournament history (the modern bracket came into existence when the field was expanded to 16 in 2003), all four 4-seeds are conference tournament champs who otherwise wouldn’t have been selected at-large.

That results in a very balanced bracket, minimizing “regions of death” for the top seeds.
KRACH gives all the 1-seeds a 70-85% chance of winning their opening round game. In fact, it further gives all four an 11-20% chance of taking the national championship. Cumulatively, straight KRACH probabilities result in a 63% chance of the tournament being won by a 1-seed, but only a 3.5% chance of it being won by a 4-seed.

The 2-3 seeds also have similar outlooks with most having a 2-3% chance of winning the national championship. The only exceptions are that slightly stronger performance out of the West this year gives 2-seed Minnesota St a 6% chance of taking the national championship, and 2-seed Denver almost a 10% chance.

West	Game 1	Game 2 (Region Champ)	Game 3 (Frozen four semifinal)	Game 4 (National Champ)
1. St Cloud St	85.46%	54.96%	33.36%	20.06%
4. Air Force	14.54%	3.43%	0.74%	0.16%)

2. Minnesota St	56.16%	24.72%	12.13%	5.90%
3. Duluth	43.84%	16.89%	7.27%	3.11%

Midwest
1. Ohio St	71.15%	39.11%	19.77%	10.62%
4. Princeton	28.85%	9.65%	2.90%	0.95%

2. Denver	63.40%	35.53%	17.94%	9.62%
3. Penn St	36.60%	15.71%	5.90%	2.39%

Northeast
1. Cornell	68.25%	43.77%	24.16%	12.58%
4. Boston U	31.75%	14.42%	5.39%	1.83%

2. Michigan	54.07%	23.56%	10.19%	4.06%
3. Northeastern	45.93%	18.25%	7.22%	2.60%

East
1. Notre Dame	79.99%	55.83%	35.06%	19.82%
4. Michigan Tech	20.01%	7.33%	2.23%	0.56%

2. Providence	48.38%	17.48%	7.33%	2.62%
3. Clarkson	51.62%	19.37%	8.42%	3.13%

Who can make the NCAAs – Saturday morning outlook

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I’ve crunched through the remaining 192 possible outcomes, and here’s what I think happens tomorrow for each team.

In for sure

St Cloud St
Notre Dame
Cornell
Ohio State
Denver
Mankato
Northeastern
Providence
Michigan
Clarkson
Penn State

Can still get autobid by winning conference

Atlantic Hockey – Robert Morris or Air Force
ECAC – Princeton (plays Clarkson, already in)
Hockey East – Boston University (plays Providence, already in)
WCHA – Northern Michigan or Michigan Tech

So at least two conferences will be won by a team that takes an autobid, leaving at most 3 at-large spots. Two additional conferences can be won by teams that wouldn’t otherwise make it, which would leave just a single spot.

Can make it at-large

Minnesota Duluth (plays in consolation game)
Minnesota
North Dakota (plays in consolation game)
Boston College

The following analysis of what each team needs is much more of a pencil and paper exercise than the automated forecasts, so please point out any inconsistencies or inaccuracies.

If neither Boston University nor Princeton win, then there will be three slots remaining. Minnesota and Minnesota Duluth each get one and North Dakota and Boston College will be vying for the final slot. UND gets it with a win or a tie; with a loss, UND can still claim it if Michigan Tech wins.

If just one of Boston University or Princeton win, there will be two spots remaining and Minnesota and Minnesota Duluth will get them and North Dakota and Boston College will be left out.

If both of Boston University and Princeton win, there will only be slot remaining. Again, North Dakota and Boston College will be out, but only one of Minnesota or Minnesota Duluth will be selected. To get the upper hand, Minnesota needs UND and any of SCSU, NMU, OSU, or RMU to win.

How many teams will each conference send to the NCAAs?

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Of the remaining possible scenarios that could come out of this weekend’s conference tournaments, here’s a breakdown of the share of scenarios of how many teams each conference sends:

	0	1	2	3	4	5	6
Atlantic Hockey	0%	100%	0%	0%	0%	0%	0%
Big 10	0%	0%	0%	2%	23%	75%	0%
ECAC	0%	1%	62%	37%	0%	0%	0%
Hockey East	0%	0%	46%	54%	0%	0%	0%
NCHC	0%	0%	2%	60%	38%	0%	0%
WCHA	0%	0%	100%	0%	0%	0%	0%

Atlantic Hockey

1 team – 100%

No teams from Atlantic Hockey will make the tournament at-large, so only the winner of the conference tournament will make the NCAAs. That will be either #20 Mercyhurst, #43 Robert Morris, #30 Air Force, or #34 Canisius.

Big 10

3 teams – 2%
4 teams – 23%
5 teams – 75%

Notre Dame, Ohio State, and Michigan are guaranteed to make the NCAAs. The Big Ten’s representation won’t be increased by the conference tournament’s winner, as the winner will be one of Notre Dame or Ohio State.

Penn State and Minnesota are both idle and both stand a pretty good chance of making the NCAAs (in 98% and 76% of scenarios, respectively). Because both are idle, there is significant overlap between Penn State and Minnesota making the tournament (both need conference tournaments won by high PWR teams to move the cutline and poor performance by other teams in search of an at-large bid, such as North Dakota). Because of that, The Big Ten puts all 5 possible teams in the NCAAs in 75% of remaining scenarios.

ECAC

1 team – 1%
2 teams – 62%
3 teams – 37%

Only #3 Cornell is guaranteed a tournament appearance, but it’s very unlikely they will be the ECAC’s only representative.

Clarkson is guaranteed an appearance with just one win, and makes the tournament in 73% of scenarios in which they don’t win at all.

Princeton and Harvard can each make the NCAAs by winning the ECAC tournament, but only by winning the ECAC tournament, so both can’t make it.

So, it’s possible, but very unlikely, for Cornell to win the conference tournament and be the only ECAC team to advance. If Clarkson wins the conference tournament, both Cornell and Clarkson will go to the NCAAs. If either of the other two win, the ECAC will have three representatives if Clarkson makes it at-large or two if not.

Hockey East

2 teams – 46%
3 teams – 54%

Providence and Northeastern are guaranteed to make the NCAAs.

If either Boston University or Boston College win the Hockey East tournament, that winner will also advance, giving Hockey East three teams.

There are also a very small number of scenarios in which BC or BU make the NCAAs despite Providence or Northeastern advancing (generally having to do with favorable cutlines and some quirky RPI luck; see How Boston University can make the NCAAs without winning Hockey East for more details).

NCHC

2 teams – 2%
3 teams – 60%
4 teams – 38%

St Cloud St and Denver are guaranteed bids.

While one might guess that #8 Duluth is a lock, especially knowing that #9 Providence and #10 Michigan are, reader of CollegeHockeyRanked – NCAA tournament possibilities know that Duluth misses in about 11% of scenarios in which they lose the semifinal. So, the NCHC advances only 2 teams in about 2% of possible scenarios, or 3 teams in about 60%.

North Dakota also stands some chance of advancing, either by winning the NCHC tournament (25% of possible scenarios) or at-large.

WCHA

2 teams – 100%

Minnesota State is guaranteed a bid.

But, Minnesota State has already been eliminated from the WCHA tournament. Neither of the remaining two teams–Northern Michigan and Michigan Tech–can make the NCAAs at-large. So, the winner is guaranteed to be the WCHAs second team in the NCAAs.

How Boston University can make the NCAAs without winning Hockey East

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An example of Boston University making the NCAA tournament at-large (that is, without winning the Hockey East tournament) follows:
https://goo.gl/UJMXKt

Generalizing that individual scenario, two things need to happen for Boston University to make the NCAAs at-large:

Game outcomes need to be such that BU gets pushed up to #14 PWR, despite a loss
Only two conference tournaments can be won by low PWR teams, so the #14 PWR team gets selected at-large

Getting BU to #14

One mandatory outcome for the Terriers to advance without winning the conference tournament seems to be North Dakota losing two games. Any win or tie by the Hawks, even if it doesn’t result in UND getting a bid, eliminates any chance of BU getting an at-large bid.

Beyond that, it takes one of a few particular combinations of outcomes to land BU at #14. There are 41 such combinations in the 12,288 possible outcomes in which Boston University wins the opening game versus Boston College but loses the Hockey East championship.

Getting #14 into the tournament

Even if Boston University gets to #14 in the PWR, as described above, only two conference tournaments can be won by teams ranked #15 or lower for the #14 team to get an at-large bid.

Because the WCHA (#17 Northern Michigan vs #24 Michigan Tech) and Atlantic Hockey (#20 Mercyhurst, #43 Robert Morris, #30 Air Force, and #34 Canisius) can only be won by teams that will finish #14 or lower, all other conference tournaments must be won by teams that finish in the top 14.

That’s guaranteed in the Big Ten, where only #2 Notre Dame and #4 Ohio State are vying for the championship. Also in a Hockey East tournament in which BU doesn’t win, a winner from among #15 Boston College, #9 Providence, and #7 Northeastern is guaranteed to be in the top 14.

So, from the ECAC, #3 Cornell or #11 Clarkson must take the championship rather than #22 Princeton or #26 Harvard. And, in the NCHC, #1 St Cloud St, #5 Denver, or #8 Minnesota Duluth must win (though #14 North Dakota losing is already a mandatory condition to get BU to #14, as stated above).

Summary

To get to #14 but not win the Hockey East championship, Boston University needs to win vs. Boston College but lose the championship game. The Terriers also need some help from North Dakota, which must lose in both the semifinal and consolation games.

Also, for the #14 team to advance to the NCAA tournament, the above must hold and Cornell or Clarkson must win the ECAC tournament.

BU wins 1 game, loses championship
North Dakota loses two games
Cornell or Clarkson wins ECAC tournament

Those conditions leave 1024 remaining possible scenarios, in which 41 of them see BU hold onto the #14 slot and get an NCAA bid.

NCAA tournament possibilities

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This article describes what teams might make the NCAA hockey tournament based on the data in the College Hockey Tournament Possibilities table:
College Hockey Tournament Possibilities

Because of a new conference tournament schedule this year, there are only 15 games remaining and thus only 49,152 possible outcomes remaining (the NCHC consolation game can end in a tie). That’s a dramatic simplification from past years, and there are thus few surprises in the possible outcomes.

16 teams make the tournament. The winner of each conference tournament is selected with what I sometimes call an “autobid”, then the remaining slots are filled in order of final PWR rank. Thus, teams that don’t make the tournament with an autobid but end up in “bubble” PWR ranks of 12-15 want conference tournaments won by high ranking teams so there are still slots available for them to get selected at-large. Teams that can’t finish in the top 16 of PWR can only be selected for the NCAA tournament by winning their conference tournaments and getting an autobid.

In

9 teams are guaranteed to make the NCAA tournament regardless of outcome next weekend.

#1 St Cloud St
#2 Notre Dame
#3 Cornell
#4 Ohio St
#5 Denver
#6 Mankato (idle)
#7 Northeastern
#9 Providence
#10 Michigan (idle)

A lock with a win

Minnesota-Duluth and Clarkson both stand a good chance to make the NCAA tournament regardless of outcome (in 89% of scenarios in which they go 0-2 for Duluth and 73% of scenarios in which they lose for Clarkson), but can lock up at-large bids with a single win. If either should lose, they just need enough of the teams above to advance to leave at-large spots available for them.

#8 Duluth
#11 Clarkson

At-large possible

Much like Duluth and Clarkson, these teams hoping for an at-large bid want conference tournaments to be won by teams that have already locked up a bid (above). If a team that wouldn’t otherwise make the tournament wins a conference tournament and gains an autobid, that would leave one fewer at-large slot for these teams.

Penn State is quite likely to advance, in 98% of remaining scenarios. Minnesota faces a more perilous 76% of scenarios remaining that allow the Gophers to advance.

Of course, the 3 teams that are still playing have varying amounts of control over their own destinies:

North Dakota gets selected in 14% of scenarios in which they’re winless, 25% of scenarios in which they win 1, and can get an autobid.
Boston College faces less favorable 3% and 9% chances with zero or one wins.
Boston University can’t make it without a win, and even with 1 win faces a tiny chance of being selected at-large (under 1% of scenarios in which they win just 1 game).

#12 Penn St (idle)
#13 Minnesota (idle)
#14 North Dakota
#15 Boston College
#18 Boston University

Need to win the conference tournament

#17 Northern Michigan
#20 Mercyhurst
#22 Princeton
#24 Michigan Tech
#26 Harvard
#30 Air Force
#34 Canisius
#43 Robert Morris

March 9-11 weekend PWR outlook

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This article discusses who is likely to make the NCAA tournament based on potential outcomes this weekend. It’s largely based on the following forecast:
Wins needed to emerge at PWR rank

Now that we’re in conference tournament play, note that the forecast is for one week.

Near locks for the NCAA tournament

It would take highly unlikely (though not mathematically impossible!) bad luck for any of the current top 6 to miss the NCAA tournament.

#1 St Cloud through #6 Denver should emerge from the weekend in the top 8, even if they fail to advance. It would be exceedingly unlikely for any of them to then fall to #12 or below while idle AND have conference tournaments won by enough low ranked teams that teams in the #12 range fail to make the NCAA tournament at-large.

#1 St Cloud St
#2 Nore Dame
#3 Cornell
#4 Ohio St
#5 Minnesota St
#6 Denver

Almost a lock?

A similar case can be made for #7 Michigan, who should fall between #7-#12 if they lose. But, it’s just possible enough to hit #12 (or below) and miss that I don’t yet dare call the Wolverines a lock.

#7 Michigan

Control their own destiny

#8 Clarkson through #12 Providence can drop to the bubble with loss(es), or position themselves well with win(s). None of these teams would be outright eliminated if they fail to advance this weekend, but would become dependent on others’ performances and some luck.

#8 Clarkson
#9 Minnesota-Duluth
#10 Northeastern
#11 Penn St
#12 Providence

Watching from the sidelines

#13 Minnesota has already been eliminated from the Big Ten tournament, so is not playing this weekend, and is likely to emerge from the weekend between #10-14. Nothing is likely to change for the Gophers this weekend–they’re not yet eliminated, but will be dependent on others’ performances and some luck.

#13 Minnesota

Need to win

It’s tough to imagine #14 Nebraska-Omaha or below making the NCAA tournament unless they advance this weekend. The Mavericks show some chance of emerging #15, with a slim remaining chance of an at-large bid, from a winless weekend; but even that hope doesn’t seem to extend to #15 North Dakota and below.

How it works

Resources

PWR Rankings (CollegeHockeyRanked.com)
Forecasted PWR by team wins (CollegeHockeyRanked.com)
CHN PWR Rankings (CollegeHockeyNews.com)
USCHO PWR Rankings (USCHO.com)
Explanation of how PWR mimics NCAA tournament selection (CollegeHockeyNews.com)

Conference tournament play-in weekend outlook

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With all conferences except the NCHC in the opening round of conference playoffs, many teams have the weekend off while others play in a best-of-3 play-in series.

Here’s where teams could end up after this weekend’s play:
PWR Forecast By Wins

View from the top

#1 St Cloud St isn’t going anywhere. Even though the Huskies play a pair of games, #2 Notre Dame and #3 Cornell are idle so can’t do enough to overtake St Cloud. They’re also both nearly guaranteed to stay in the top 4.

#4 Minnesota St, #5 Denver, and #6 Ohio St are all playing and all vying to fill spots 4-6.

Above the bubble

Idle teams #7 Clarkson, #11 Northeastern, and #12 Providence should all stay at 13 or above.

#8 Minnesota-Duluth, #9 Minnesota, and #10 Michigan can stay top 10 with a pair of wins (though even with a pair of wins Michigan could stumble out of the top 10, most likely in the condition that they also get a loss in the best of 3 series).

On the bubble

#13 Penn State, #14 North Dakota, ad #15 Nebraska-Omaha all have the potential to climb into the single digits with a pair of wins, or fall to 16 or below with no wins on the weekend.

Of other teams, only #17 Northern Michigan and #18 Bowling Green stand a significant chance of climbing to 13 with a pair of wins.

How it works

Resources

PWR Rankings (CollegeHockeyRanked.com)
Forecasted PWR by team wins (CollegeHockeyRanked.com)
CHN PWR Rankings (CollegeHockeyNews.com)
USCHO PWR Rankings (USCHO.com)
Explanation of how PWR mimics NCAA tournament selection (CollegeHockeyNews.com)

Weekend outlook for February 23-25

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First, let’s review last weekend’s prognostications.

#1 St Cloud St didn’t need to sweep to hold onto the #1 spot because #2 Notre Dame stumbled with a pair of losses. Nonetheless, the Irish held onto #2 as predicted (#5 Denver could have overtaken them with a strong performance, but the Pioneers split on the weekend).

Those stumbles allowed #4 Mankato to climb into the top 4, as was noted could happen in that scenario.

None of the potential big movers came to fruition, as none pulled off the required sweeps.

Now, let’s look ahead to the coming weekend.

Potential 1 seeds

Because of stumbles by both St Cloud and Notre Dame last weekend, there are now 4 teams vying to emerge #1 from this weekend. In addition to the Huskies and Irish, #3 Cornell and #5 Denver stand a change of emerging from the weekend #1.

St Cloud is pretty much guaranteed to hold the #1 spot with a sweep of Denver. But, the same series gives Denver the best opportunity to take over the #1 spot if the Pioneers manage to pull off the sweep.

Above the bubble

Only the top 8 teams are pretty certain to emerge from the weekend in the top 12. Including those mentioned above, those teams are:

#1 St Cloud
#2 Notre Dame
#3 Cornell
#4 Minnesota State
#5 Denver
#6 Ohio State
#7 Clarkson
#8 Minnesota

It’s too early to call them all locks for the NCAA tournament (disaster in conference tournament play could easily push one of the bottom few onto the bubble), but they’ll be well positioned heading into the conference tournaments.

On the bubble

Almost all teams through #24 Wisconsin have a chance to emerge from the weekend in the top 14, thus on the bubble for an at-large bid for the NCAA tournament.

Those include:

#14 Nebraska-Omaha
#15 Western Michigan
#16 Northern Michigan
#17 Penn State
#18 Bowling Green
#20 Union
#21 Boston College
#22 Harvard
#23 Colorado College
#24 Wisconsin

#19 Boston University is the one exception. Hosting a pair of games against #47 Vermont just doesn’t give the Terriers much upside, with #16 looking like the best likely weekend outcome (and even that isn’t very likely).

On the outside, looking in

#25 Maine and below just aren’t very likely to climb onto the bubble, regardless of their performance this weekend. Those teams will be looking for success in their conference tournaments to gain access to the NCAA tournament.

Other interesting potential moves

#11 Michigan is the highest ranking team facing a precipitous cliff. Getting swept by #55 Arizona St could push the Wolverines as low as #22, with the #17-19 range most likely. A sweep isn’t particularly helpful, with a #10-11 ranking the most likely outcome of a sweep.

Perhaps more likely, #14 Nebraska-Omaha faces similar downside in a pair of games against #23 Colorado College. Getting swept could push the Mavericks as low as #24, though #19-21 are most likely. UNO, however, faces some upside potential from a sweep, with a climb to #11-12 most likely.

How it works

Resources

PWR Rankings (CollegeHockeyRanked.com)
Forecasted PWR by team wins (CollegeHockeyRanked.com)
CHN PWR Rankings (CollegeHockeyNews.com)
USCHO PWR Rankings (USCHO.com)
Explanation of how PWR mimics NCAA tournament selection (CollegeHockeyNews.com)

Interesting potential PWR movements the weekend of Feb. 16

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Will there be a new #1?

#1 St Cloud State is almost, but not quite, guaranteed to hold onto #1 with a sweep (the Huskies stay #1 in about 98% of scenarios in which they sweep), but with a single loss would become vulnerable to #2 Notre Dame overtaking them if the Irish can pull off a sweep. Neither has an easy matchup, with St Cloud State facing #12 Western Michigan and Notre Dame facing #15 Michigan.

Who’s vying for a 1-seed position?

In addition to St Cloud St and Notre Dame, the rest of the top 6 are also likely to be vying for top 4 slots this weekend.

#3 Cornell is unlikely to climb, but is hoping not to fall as low as #7.

#4 Denver could climb to #2 with stumbles by those ahead of them, but could also fall as low as #7 with a poor performance.

#5 Mankato could climb to #3, but could fall as low as #8.

#6 Ohio State could climb as high as #3, or slip a little to #7.

Biggest upside potential of the weekend

#24 Colorado College is the big upside team of the week. If the Tigers sweep and all goes well, they could climb as high as #12 and firmly onto the bubble. The #14-16 range is more likely with a sweep, but even that would represent a tremendous one week climb.

Biggest downside potential of the weekend

As often seems to be the case this time of year, around the #10-12 range can be precarious. These teams face a lot of downside potential if swept, and usually not much upside potential with a sweep. They generally need to win just to hang on, or rely on significant losses above them to climb.

#8 Providence could fall as low as #16 if swept, though #13-14 is a bit more likely.

#10 Nebraksa-Omaha could fall as low as #18 if swept, though #14-15 is more likely.

#11 Minnesota-Duluth could fall as low as #19 if swept, though #16-17 are a bit more likely.

Biggest range of outcomes for the weekend

This usually comes from the 30s, where win-loss records and RPI are both in the .500 range and there’s lots of potential to climb or fall out of the pack.

This week’s biggest potential mover is #30 Yale. The Bulldogs could climb as high as about #21 with two wins or fall as low as #39 with two losses, a range of 18 positions of likely outcomes!

How it works

Resources

PWR Rankings (CollegeHockeyRanked.com)
Forecasted PWR by team wins (CollegeHockeyRanked.com)
CHN PWR Rankings (CollegeHockeyNews.com)
USCHO PWR Rankings (USCHO.com)
Explanation of how PWR mimics NCAA tournament selection (CollegeHockeyNews.com)