PWR game of the week – Can #31 Maine climb into the mid-teens this weekend?

Long time followers of PWR know that despite seeming pretty stable overall, individual teams’ PWR rankings can move substantially under the right conditions. An 8-10 position swing in a single weekend’s pair of games is a relatively common possibility, though it often takes both an unusual outcome for the team and a lot of other things going just right around the league.

This week, however, the #31 Maine Black Bears face a stunning 18 position upside potential in their series against #5 Boston College. While the full 18 position climb is exceedingly unlikely, occurring in only 1.1% of scenarios in which Maine sweeps BC, Maine’s likely PWR ranking if they sweep are centered around #16, a 15 spot climb!

Digging into why such a big move is possible for Maine, there’s nothing unique about their situation, there are just lots of known little things about PWR and RPI adding up just right for the Black Bears facing a series they’re supposed to lose.

Warning, thar be math below!

At 10-9-4, Maine has a win percentage of .5217, and winning two more would move that to 12-9-4 and .5600. But, because of RPI game weightings (in which road wins and home losses count more than road losses and home wins), Maine’s current weighted percentage is actually .5490 and would rise to .5965 with a pair of road wins this weekend. Maine is undefeated at home, but home wins only count as 4/5 of a game, as do road losses. But, road wins would count as 6/5 of a game, giving them 50% more impact on Maine’s ratings, giving these games (if wins) outsized influence on Maine’s ratings. The other components of Maine’s RPI would also rise a bit because of BC’s strong schedule, though much more modestly (oppponents’ win% from .4927 to .5197, and opponents’ opponents’ win% from .4958 to .5012). Finally, Maine’s quality win bonus would climb from .0019 to .0057 with a pair of road wins against Boston College.

Adding all of that up, Maine’s RPI would climb from .5103 to about .5346 with a pair of road wins this weekend.

Maine’s position near the bottom of a dense cluster of RPI rankings would result in an RPI climb of .0243 leading to a substantial climb in PWR ranking. Looking at the current RPI rankings, an RPI of .5346 would be good for #16 today, 15 spots higher than Maine’s current ranking. For comparison, if Maine were .0243 lower, at .4860 RPI, they would still be #40, only 9 positions lower.

Is this really going to happen?

Of course, a road sweep against #5 Boston College (15-5-0) is a tall order. Assuming no home ice advantage, KRACH predicts Maine as only having a 19% chance of winning each game, or a 3.7% chance of the sweep (if the games were independent). But, if Maine pulled off this signature sweep, RPI and PWR would statistically reward the Black Bears for being a different team than their results to date would predict.

First look at which teams are likely to make the 2020 NCAA hockey tournament

With 10-12 regular season games remaining for most teams, we can start to get some picture of what teams need to do to end the regular season in position for an NCAA tournament bid (we generally think of ending the regular season in the top 10 as likely being in the tournament, anywhere from 10-15 as on the bubble, and 16 or below as unlikely to make it at-large).

If you’re new to this site or missed last week’s article, First PWR Forecast of 2020 (and why you might care), read that first for some background.

You can always browse the weekly forecast yourself, and might find it useful to follow along with this article, at PWR by wins forecast.

Who’s a lock?

This far out, there are no mathematical locks. Even #1 North Dakota could miss if the Hawks improbably strung together 12 losses to end their regular season. But, in 1,000,000 simulations, none of #1 North Dakota, #2 Minnesota State, or #3 Cornell dipped below #13 (with 2, 4, and 5 being the minimum number of wins simulated for each, respectively). It would take an unprecedented collapse for any of the three to miss.

Unless something fundamentally changes that makes their success to date not predictive of future results, it would take a 1 in a 1,000,000 collapse for any of the following teams to miss the NCAA tournament:
#1 North Dakota
#2 Minnesota State
#3 Cornell

Who’s in if they keep performing as they have to date?

Surprisingly, in addition to the above, only #4 Denver seems almost assured an at-large berth if they win half their remaining games.

The lone team likely to be assured a berth if they keep winning is:
#4 Denver

Who controls their own destiny?

From #5 Boston College down to about #34 St Cloud State can put themselves in bubble position or better with sufficiently good performance over the remainder of the regular season.

Those teams include:
#5 Boston College
#6 Massachusetts
#7 Ohio State
#8 Clarkson
#9 Penn State
#10 Providence
#11 Arizona State
#12 Minnesota-Duluth
#13 Mass.-Lowell
#14 Northeastern
#15 Quinnipiac
#16 Michigan State
#17 Northern Michigan
#18 New Hampshire
#19 Dartmouth
#20 Harvard
#21 Notre Dame
#22 Michigan Tech
#23 Bemidji State
#24 Michigan
#25 Army
#26 Western Michigan
#27 Bowling Green
#28 Nebraska-Omaha
#29 Alaska
#30 Boston University
#31 Maine
#32 Wisconsin
#33 Minnesota
#34 St. Cloud St

Of course, teams near the top of that list have an easier path (winning about 50% of remaining games for #5 Boston College) than teams near the bottom of that list (winning about 80% of remaining games for #34 St. Cloud St).

Who needs help

From #35 down, there aren’t a lot of opportunities to climb onto the bubble. Quite a few in the #35-45 range seem to have a possibility of climbing just onto the bubble with a perfect or near perfect remainder of the regular season. But, even if that unlikely outcome were to occur, anything short of a conference tournament championship would result in a season ending loss that would likely push them back out of contention for an at-large bid. If you like super long shots, the teams with the best chance of that scenario are #35 Sacred Heart, #36 Connecticut, #37 Colorado College, #39 Colgate, and #41 Yale.

The following teams should plan to win their conference tournaments if they want to make the NCAAs:
#35 Sacred Heart
#36 Connecticut
#37 Colorado College
#38 American International
#39 Colgate
#40 RIT
#41 Yale
#42 Miami
#43 Rensselaer
#44 Air Force
#45 Robert Morris
#46 Holy Cross
#47 Lake Superior
#48 Merrimack
#49 Canisius
#50 Bentley
#51 Vermont
#52 Ferris State
#53 Princeton
#54 Union
#55 Niagara
#56 Alaska Anchorage
#57 Brown
#58 Mercyhurst
#59 St. Lawrence
#60 Alabama-Huntsville

What next?

The forecasts are updated weekly, usually Monday or Tuesday, so you can always browse them yourself. I’ll also try to post interesting interpretations here, with increasing frequency as we near the end of the regular season. Meanwhile, you can explore more of the data yourself:

First PWR forecast of the 2020s (and why you might care)

If you care about what teams will make the NCAA hockey tournament, keeping an eye on this site between now and the selection show in March will give you a wealth of insight on how each team’s chances play out between now and then. Unlike in most other sports, the hockey tournament selection committee uses known calculations to determine the tournament participants; so, college hockey fans have long been able to calculate with certainty who is going to be selected for the NCAA tournament once all the games have been played.

The PairWise Rankings (PWR) were developed to mimic the NCAA’s tournament selection criteria, so the final PWR ranking perfectly predicts the teams that will be selected for the NCAA tournament. Calculating the PWR rankings before all the games have been played is interesting because it can be used to help predict the final PWR. Most people start to find that calculation interesting shortly after winter break, as examined in the 2014 article, When to start looking at PWR (revisited).

Current PWR Ranking

But, the reason you care about PWR is because you’re interested in who’s going to make the NCAA tournament, and this site can give you even more insight into that. Because the PWR formula is well known, you could get the current rankings from numerous sources. But, as mentioned above, the value in today’s PWR is that it helps you guess at the final PWR. This site helps you get there by calculating how the remaining games could affect PWR and forecasting what the PWR is likely to be at the end of the regular season. The presentation of the forecasts is 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 forecast (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 the regular season at each PWR ranking.

So, for example, if #1 North Dakota wins half its remaining games (8 of 16), the Fighting Hawks are likely to finish in the #5-9 range and thus make the tournament. If UND wanted to finish in the top 4 to get a one seed, winning at least 12 games seems advisable to be most likely to go into conference tournaments in the top 4.

You can get more detail on a specific team by clicking the team name in the table 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 even though #5-9 is UND’s likely range if it wins 8 of 16, #5-7 are most likely. Similarly you can see that 12 wins would be very likely to result in a top 4 finish, while 10 wins might or might not. You can also switch from the “End of season” view to a “One week” view to see just how much the PWR is likely to change based on the outcomes of the coming weekend’s games.

The forecast data will usually be updated in the first half of the week. You can always browse all the data yourself any time, but I’ll also scour the data (including some of the background calculations that don’t yet appear on the site) and post interesting results and observations (more frequently, as the tournament approaches).

How the forecast works

The forecast 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

Everyone’s favorite college hockey ranking scheme, KRACH, has the feature that it can be used to predict the likelihood of a team winning a matchup against another team. So, it is possible to use KRACH likelihoods to determine the likelihood of each team advancing through each game of the NCAA hockey bracket.

KRACHWestGame 1Game 2
Game 3
Game 4
768.0431. St Cloud St91.92%66.64%48.55%34.19%
67.5264. American Int’l8.08%1.52%0.30%0.05%
284.913. Ohio St48.92%15.36%7.70%3.65%
297.5052. Denver51.08%16.47%8.43%4.08%
359.9521. Massachusetts63.42%36.72%14.74%7.83%
207.5864. Harvard36.58%16.18%4.62%1.84%
249.2973. Notre Dame47.69%21.90%7.05%3.11%
273.4192. Clarkson52.31%25.20%8.60%3.99%
392.3781. Minnesota St65.86%39.54%22.02%10.13%
203.3694. Providence34.14%14.96%5.97%1.88%
230.8413. Cornell44.51%18.94%8.12%2.77%
287.7612. Northeastern55.49%26.56%12.79%4.98%
438.3721. Minnesota Duluth70.53%45.04%26.81%13.03%
183.1974. Bowling Green29.47%12.56%4.82%1.42%
204.1913. Arizona St41.87%15.89%6.51%2.05%
283.4632. Quinnipiac58.13%26.51%12.96%5.00%

On paper, there’s a tremendous advantage to being the #1 seed overall. Not only does St Cloud St have, by about 2-1, the highest KRACH overall; but, they’re also matched up against the lowest KRACH-rated team in the tournament, Atlantic Hockey champ American International. That gap gives the Huskies a formidable 92% chance of winning their opening game, a 67% chance of making the Frozen Four, and a 34% chance of winning the National Championship.

The remaining three regions are reasonably balanced, with each having something between a 17%-22% chance of producing the national champ.

The 1 seeds are reasonably strong, as rated by KRACH, with a 65% chance overall that one of them becomes the national champ.

The NCAA tournament field is nearly set going into the last day of conference tournaments

Though 7 conference tournament games remain, there’s not a lot of drama left around who will make the NCAA tournament.

You can always follow along on your own:
College Hockey Tournament possibilities

Who’s in?

These 12 teams are in for sure:

  • St Cloud St
  • Massachusetts
  • Minnesota St
  • Minnesota-Duluth
  • Quinnipiac
  • Denver
  • Ohio St
  • Northeastern
  • Clarkson
  • Arizona St
  • Cornell
  • Harvard

Who else can make it

Both participants in the NCHC and ECAC tournaments are already in.

The winner of the Big Ten tournament will also make it (and the loser will not):

  • Penn State or
  • Notre Dame

The winner of Atlantic Hockey will also make it (and the loser will not):

  • American International or
  • Niagara

That’s 14 teams in, and leaves 2 slots.

There are two more conference championships, Hockey East and the WCHA, whose winners can secure an invitation. These teams can lock up an invitation with a win:

  • Bowling Green
  • Boston College

But, we’re already counting their opponents, Minnesota St and Northeastern as in. So, if Minnesota State or Northeastern win, that leaves an additional slot and an opportunity for another team to make it at-large.

If BC loses, Bowling Green and Providence make it at large
If BC wins, Bowling Green makes it if they win, otherwise Providence makes it

What needs to happen for my team to make it?

Restated in terms of what they need to do to make it:

  • Penn State needs to win
  • Notre Dame needs to win
  • American International needs to win
  • Niagara needs to win
  • Boston College needs to win
  • Bowling Green needs to either win or have Northeastern defeat Boston College
  • Providence needs either Northeastern to defeat Boston College or Minnesota St defeat Bowling Green

What will be the conference representation in the NCAA tournament

The ECAC is likely to place the most teams into the NCAA tournament this year. Here’s a complete rundown of the possibilities.

Big Ten0%0%100%0%0%0%
Atlantic Hockey0%100%0%0%0%0%
Hockey East0%0%6%72%22%0%

As you know from Who can make the NCAA tournament?, the winner of the Atlantic Hockey tournament is the only team from that conference that will make the NCAAs.

Similarly, the winner of the Big Ten tournament is the only team that will join Ohio State in representing the Big Ten, guaranteeing the Big Ten two representatives.

Arizona State will be the lone independent in the NCAA tournament.

The NCHC is guaranteed to get St Cloud St, Denver, and Minnesota Duluth in, and will most likely have 3 representatives. But, if (and only if) Colorado College wins the tournament, the Tigers will get an automatic bid, giving the NCHC 4 teams in the NCAAs.

The WCHA is only guaranteed one team, Minnesota State, and it is possible that the Mavericks will be the WCHA’s only representative. But, the WCHA is more likely to get 2 in by having Bowling Green join them (which could happen even if Minnesota State wins the conference tournament).

Hockey East is only guaranteed two teams, Massachusetts and Northeastern, but 3 or 4 is much more likely. Boston College or Boston University can make it by winning the conference tournament, and Providence can make it at-large.

The ECAC has the most possible different permutations of teams that could make the NCAAs, though landing 4 teams in the NCAAs is by far most likely. Quinnipiac and Clarkson are the only teams in for sure, but there is no situation in which they are the only two who make it. Brown can also make the NCAAs by winning the conference tournament. Cornell and Harvard can make it either by winning the conference tournament, or possibly by earning an at-large bid depending on other outcomes. The ECAC should see no fewer than 3 teams and no more than 5 in the NCAAs.

Who can make the NCAA tournament?

This post explains the data in the PWR tournament possibilities page. You can follow along there if you’d like to browse the raw data yourself:

NCAA Tournament Participation Probabilities

Who’s in?

The following 10 teams are guaranteed an invitation to the NCAA tournament on the basis of their PWR.

  • #1 St Cloud State
  • #2 Massachusetts
  • #3 Minnesota St
  • #4 Minnesota-Duluth
  • #5 Quinnipiac
  • #6 Denver
  • #7 Ohio State
  • #8 Northeastern
  • #9 Clarkson
  • #10 Arizona St

Who else can get in?

The winner of each conference tournament can get in:

Atlantic Hockey

  • American International (*)
  • Robert Morris (*)
  • Niagara (*)
  • RIT (*)

Big Ten

  • Notre Dame (*)
  • Penn St (*)

Hockey East

  • Massachusetts (in)
  • Boston College (*)
  • Boston University (*)
  • Northeastern (in)


  • Cornell
  • Brown (*)
  • Harvard
  • Clarkson (in)


  • St Cloud St (in)
  • Colorado College (*)
  • Denver (in)
  • Minnesota Duluth (in)


  • Minnesota St (in)
  • Bowling Green

Those marked with a (*) can only get in if they win their conference tournament. Those marked with (in) will make the tournament regardless of conference outcome. But, what about the rest?

There are 16 spots in the NCAA tournament. 10 participants are already known (see above). The winners of the Atlantic Hockey and Big Ten tournaments are not only guaranteed spots, but are the only teams from those conference tournaments that will get spots, so you can think of those two spots as reserved for one of the 4 AH teams and one of the 2 AH teams, respectively.

That leaves 4 spots total for a combination of the champions of the remaining 4 conferences and the 5 teams that can make it at-large (there is some overlap between those two groups). How many teams are selected at-large depends how many of the 4 remaining slots are taken by teams that aren’t already in by virtue of their PWR. For each of Hockey East, ECAC, NCHC, and WCHA that are won by a team that is already counted as being in, an additional spot is available for a different team to make it at-large.

The following teams can make it at-large:

  • Cornell (64% of scenarios in which they win 0, 97% in which they win 1)
  • Harvard (81% of scenarios in which they win 0, 94% in which they win 1)
  • Bowling Green (29% of scenarios in which they lose)
  • Providence (not playing, 65% of scenarios)
  • Union (not playing, <.1% of scenarios)

More predictions coming soon, and the perils of fan-made tools

Update Mar 21, 9am — USCHO has updated its PWR Predictor so it now produces results that match the predictions on this site and the results of CHN’s calculators. Results from that calculator from before today should be disregarded and recalculated.

There’s some chance the final PWR on this site and CHN will differ from that on USCHO, and someone will be wrong about who is going to make the NCAA tournament. Keep that in mind when considering forecasts from any source.

I’m a bit slow this year at posting analysis in what is usually the busiest week for discussing who will make the NCAA tournament. That’s because I wasn’t completely confident in my analysis; my forecasts did not agree with the results generated by the calculators at CollegeHockeyNews and USCHO, and I wanted to understand why before making predictions that I knew would be interpreted as fact.

I’m happy to say that I feel that I now understand the issues, and hope to provide some interesting analysis in the next couple days. To start, here’s a summary of all 49,152 remaining possible outcomes to the season:

College Hockey Tournament Possibilities

The biggest known difference between the online calculators centers around whether to treat the on-campus conference championships for the Big Ten and WCHA as home games for the hosts. That matters in RPI. Forecasts on this site, and now CollegeHockeyNews, treat them as home games. USCHO treats them as neutral site games.

That means that the forecasts on this site can only be tested and confirmed with the CHN calculator. It also means there’s some chance the final PWR on this site and CHN will differ from that on USCHO, and someone will be wrong. Keep that in mind when playing with these tools!

Will Arizona State make the NCAA tournament?

The number question I still get every week is, “Will Arizona St make the NCAA tournament?” The answer to that question is still, “very likely”, but it’s not quite “definitely”.

Because Arizona St is done with regular season play, any movement in its PWR will be because of the movement of other teams. To understand what might happen, the place to start is with the teams around #10 Arizona St, because those are the teams that will either climb above or fall below the Sun Devils and change their ranking.

Arizona State’s PWR Rankings Details

PWR comparisons are usually won on the basis of RPI. Looking at the teams around Arizona St, there is significant potential for movement:

#5 Quinnipiac.5715
#6 Ohio St.5594
#7 Denver.5572
#8 Northeastern.5517
#9 Providence.5508
#10 Arizona St.5494
#11 Clarkson.5492
#12 Cornell.5473
#13 Western Michigan.5445
#14 Harvard.5434
#15 Notre Dame.5388

Note the big gaps between #5 Quinnipiac and #6 Ohio St, and between #14 Harvard and #15 Notre Dame. The range #10 Arizona State is likely to operate in is between #6 Ohio St and #14 Harvard. But remember that there’s a little bit more to PWR than RPI; if you look at ASU’s PWR details (linked above), you’ll see that the comparison with #6 Ohio St wouldn’t be flipped by Arizona St surpassing them in RPI, so Arizona St’s real likely range is #7-#14.

To understand what’s going to make ASU moves around within that range, it helps to start by looking at what is likely to happen this week.

Arizona State’s one-week PWR outlook

Unlike last week, when I noted that ASU had a lot more downside potential than upside (and indeed they fell 2 spots), their outlook this week is a pretty balanced bell curve around their current #10 ranking.


(Note that those predictions rely on KRACH weighting for likelihood of game outcomes, so that is not a share of possible outcomes or an assumption that each outcome is equally likely).

Where Arizona St will land after this weekend comes down to the performance of the teams listed above. If teams around Arizona St falter, the Sun Devils will climb. If teams around Arizona St succeed, ASU will fall. Arizona St fans should cheer for the following:

  • Boston College to defeat #9 Providence
  • Maine to defeat #8 Northeastern
  • UND to defeat #7 Denver
  • Yale to defeat #11 Clarkson
  • Union to defeat #12 Cornell

In the world of 1% outcomes, the simulations say that Dartmouth beating #14 Harvard is more important than #13 Western Michigan’s games, but I’m not sure why.

The more of those that occur, the better for Arizona St; the fewer, the worse.

Of course, more games will played after this weekend but before NCAA tournament selection. Because we’re in conference tournament play now, the games above have an additional impact on Arizona St’s fortunes beyond their immediate impact on PWR. Winning teams will get more games, whereas losing teams will not. That’s why I’m comfortable saying Arizona St is likely to make the NCAA tournament—if the teams around ASU lose this weekend, not only will Arizona St have a better PWR, but their potential to fall will diminish significantly because those teams who could most harm ASU’s PWR won’t have any more games; further, even if the teams around ASU do win this weekend, pushing the Sun Devils into a worse PWR, those teams will play again with some chance of losing and falling back below Arizona St.

Conference tournament play-in weekend PWR outlook

This weekend most teams are playing best of 3 conference tournament play-in series, with the exception of two Big Ten semifinal games. The range of likely outcomes isn’t particularly broader than usual, because the best a team can do is still two wins and the worst two losses. But, this weekend’s interesting twist is that the worst outcome would also result in no additional games until NCAA tournament selection, so some teams will start to lose control of their own PWR destiny this weekend.

Follow along with the one-week forecast:

Wins needed to likely have PWR rank on March 18, 2019

#1 St Cloud is probably going to be #1 a week from now, no matter what happens this weekend. The Huskies’ RPI of .6175 is simply unassailable, with #2 Massachusetts at a distant .5827.

The top 6—#1 St Cloud, #2 Mass, #3 Minn St, #4 Minn Duluth, #5 Quinnipiac, and #6 Ohio St—should all still be top 10 after this weekend. Their worst case scenarios for the weekend would also mean the end of their conference tournament play, so a top 10 finish this weekend would make it very likely that they would still be positioned to receive at-large bids to the NCAA tournament by the time conference tournaments are over.

It might appear that Ohio State really belongs in the group below this one, with its RPI of .5595 being much closer to #7 Denver’s .5572 than #5 Quinnipiac’s .5714. But, because Ohio State can lose at most one more game, it’s difficult for them to drop much below #10 at the worst (i.e. under a 1% chance). Even then, everything below them would have to go just wrong for the Buckeyes to miss out on an NCAA bid from there.

From #7 Denver down to #12 Cornell could end the weekend on the bubble, with a chance of making the NCAA tournament at-large, even with losses this weekend.

Those teams include:

  • #7 Denver
  • #8 Northeastern
  • #9 Providence
  • #10 Arizona St
  • #11 Clarkson
  • #12 Cornell

From #13 Western Michigan down to #22 Lake Superior St can keep their hopes of an at-large bid alive by winning this weekend, but will probably move out of position for an NCAA bid if eliminated.

Those teams include:

  • #13 Western Michigan
  • #14 Harvard
  • #15 Notre Dame
  • #16 Bowling Green
  • #17 Union
  • #18 North Dakota
  • #19 Penn State
  • #20 Mass.-Lowell
  • #21 Minnesota
  • #22 Lake Superior St

#23 Northern Michigan and below stand little chance of making the NCAA tournament at-large, so their only likely paths to the NCAAs are through a conference tournament championship and automatic bid.