Category Archives: forecasts

The 1 seeds – UND and three of QU, SCSU, PC, BC, DU

The 1 seeds

These teams have a shot at 1-seed:
North Dakota (lock)
St Cloud St
Boston College

Extracted from PWR Possibilities:

Team Result 1 2 3 4 5 6 7 8
UND Win 0 34% 41% 21% 4%
Win 1 63% 30% 7% < 1%
Win 2 100%
Quinnipiac Win 0 < 1% 35% 39% 25% < 1% < 1%
Win 1 4% 46% 38% 12% < 1%
Win 2 57% 42% 1%
SCSU Win 0 < 1% 29% 40% 24% 7%
Win 1 8% 18% 48% 25% 1%
Win 2 62% 27% 11%
Providence Win 0 1% 58% 32% 9%
Win 1 7% 44% 41% 7%
Win 2 14% 51% 30% 5%
Boston College Win 0 82% 18%
Win 1 < 1% 4% 81% 15%
Win 2 < 1% 29% 41% 29% < 1%
Denver Win 0 98% 2% < 1%
Win 1 1% 3% 93% 2%
Win 2 31% 36% 8% 24% < 1%

UND will finish in the top 4 and get a 1-seed.

Quinnipiac, St Cloud St, and Providence are each guaranteed a top 4 finish, and a 1-seed, if they win their conference tournament.

Quinnipiac is nearly (but not quite!) a lock for a 1-seed regardless of outcome, and St Cloud St is nearly (but not quite!) a lock for a 1-seed if they win 1.

Boston College and Denver each need at least one win, preferably two.

BC to #1 overall

An example:

Obviously Boston College needs to win and North Dakota, Quinnipiac, St Cloud St, and Providence need to lose enough to be passed by BC. Finally, it takes an unusual combination of other outcomes to give BC a small RPI advantage over those teams (note, for example, that the linked scenario actually has Providence win one then lose one to give BC just enough of an RPI edge; note also that the top 4 in that example end up within .0003 in RPI).

This is pretty unlikely, occurring only in about 1 of 940 scenarios in which Boston College wins its conference championship.

Quinnipiac missing a 1 seed

An example:

Even with a win, it’s possible for Quinnipiac to fall to 5th and miss out on a 1 seed. Success by other teams eligible for #1 is a key, in this case Boston College, Denver, and St Cloud St. Note how unusual this scenario is, with a 3-way tie in pairwise comparisons and the RPI tie-breaker settled by just .001 between the three teams.

This is pretty unlikely, occurring in only about 1 of 1900 scenarios in which Quinnipiac wins one, or 1 in 210 scenarios in which Quinnipiac loses its first game.

These teams should really try to win this weekend

Need to win

These teams clearly need to win this weekend. A pair of losses could plummet any of them into the 20s and out of reach of an at-large bid.

#13 Minnesota-Duluth
#14 Michigan Tech
#15 Nebraska-Omaha
#16 Cornell
#17 Minnesota
#18 Penn St
#19 Northeastern
#20 Clarkson
#22 Rensselaer

On the flip side, a pair of wins could propel any of them onto the 11-13 bubble in preparation for next weekend. Even with a pair of wins, 13 is a bit of a longshot for Clarkson and Rensselaer, while Minnesota will struggle to hit 14.

Minnesota-Duluth is the team most likely to survive a sweep, as the Bulldogs face a huge range of possible outcomes if swept—from 14 to 22 being somewhat likely, though 16-20 is most likely. Where they fall in the range will be determined by how the other teams on the list above perform — the more that lose, the better for Minnesota-Duluth.


Michigan Tech and Nebraska-Omaha seem most likely to fall to 15 or below if they don’t emerge from the weekend victorious, so would face an uphill battle to get an at-large bid with no additional games to play.



Cornell could land in the 13-14 range with a single win this weekend (though 15 is more likely), which would leave them alive but with no control.


Minnesota and Penn State would each have an additional shot to climb in the Big Ten tournament, even if swept this weekend. But, each would also be in a pretty deep hold without a win. Even with a sweep, Minnesota won’t climb much, with 15-18 the most likely outcome. The Gophers would need an additional conference tournament win to gain confidence in an at-large bid. Penn State fares a bit better with either a single win or a pair of wins, being able to climb to the top of the bubble with the latter.



Though Northeastern could climb to the 12-13 range with a pair of wins, 14-15 is much more likely. Clarkson and Rensselaer face a broad range of possible outcomes with a sweep, being able to reach 13-14, but with 15-18 more likely, and even 19-21 realistic. All three need to win, plan to win next weekend, and get some help from others.




Mathematically possible?

These teams are long shots for at-large bids. Even with a sweep this weekend it would take a lot of luck to come out ranked #15. A subsequent win and a loss in the conference tournament shouldn’t move either much, so it would take some PWR luck and some cutline luck to get in at-large. Better just plan to win the conference tournament.

#21 Robert Morris
#23 Miami



Win the conference tournament

These teams could give their fans some false hope by cracking the teens with a pair of wins this weekend. Unfortunately, it’s pretty unlikely to climb from there to above the cutline with a win and a loss.

#24 Minnesota St
#25 St. Lawrence
#27 Dartmouth




Other teams not yet mentioned don’t even seem likely to be able to crack the teens this weekend. It would take an extremely unusual confluence of events for any of them to move into position for an at-large bid.

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

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

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

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





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

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

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

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

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



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

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

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

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






Almost had it—Michigan

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


The new “next one”—Denver

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


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

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


This weekend’s big PWR movers

Sorry for the lateness and any errors, had to crank this one out in a hurry…

More upside than you might expect

Not this week. Usually a team or two in the mid-20s have the opportunities for jumps approaching 10 spots. Plenty of teams in that range have the chance to jump about 5 spots, maybe even 6 if all goes well, but anything approaching a 10 spot jump from a team of any consequence is very unlikely.

More downside than you might expect

The high teens is a tough place to be this time of year.

#14 Penn State, idle last weekend but on the list of potential big drops two weeks ago, is in familiar territory — win 2 to stay in place, or be prepared to fall. A 10 spot drop to #24 is possible.


#15 Minnesota-Duluth, which jumped 10 spots (as predicted) with an impressive pair of wins last weekend, doesn’t have much upside potential but stands to give back its ground if it doesn’t keep up its winning streak. An 11 spot drop to #26 is possible.


#16 Minnesota, which was also on last week’s potential big drop list, finds itself there again. Two wins won’t do much for the Gophers, but losses could result in up to a 9 spot drop to #25.


#17 Michigan Tech, #18 Miami, and #20 Cornell also face potentially significant drops of up to 7-8 positions if they lose 2. They each, however, face more normal upside potential with success.




Weekend PWR watch — first conference tournament round

Watching the top

#2 North Dakota used a pair of wins over #13 Nebraska-Omaha to climb past #3 St Cloud, which dropped a pair of games to desperate #15 Minnesota-Duluth. That leaves UND as the only team capable of taking over #1 from idle Quinnipiac this weekend.


In last week’s outlook I predicted that the top 12 were generally safe, with no one likely to drop below 14. Though there was some minor shuffling within the group, only Nebraska-Omaha fell out of the top 12, landing at #13 following a pair of losses to North Dakota.


Safe this weekend

This week’s top 12 look similarly safe for another week, with no one likely to come out of the weekend below #13. Note that quite a few of these teams, including #9 Notre Dame, #11 Harvard, and #12 Mass.-Lowell, are insulated against much movement by being idle this weekend. Teams likely safe in the top 13 include:

#1 Quinnipiac
#2 North Dakota
#3 St Cloud St
#4 Providence
#5 Boston College
#6 Michigan
#7 Denver
#8 Yale
#9 Notre Dame
#10 Boston University
#11 Harvard
#12 Mass.-Lowell


Around the bubble

Most teams from #13 Nebraska-Omaha down to #21 Minnesota State could end up on either side of the bubble—at #14 or higher after this weekend, or below 14. The notable exceptions are #16 Minnesota will struggle to climb above #15 and idle #19 Robert Morris isn’t likely to climb beyond #17.

#13 Nebraska-Omaha
#14 Penn State
#15 Minnesota Duluth
#17 Michigan Tech
#18 Miami
#20 Cornell
#21 Minnesota St



Need to climb

A handful of teams can’t quite make it into position for an at-large bid (which we’re currently calling #14 and better), but can come out of the weekend in the teens, preserving hope for an at-large bid with additional conference tournament success. Those include:
#16 Minnesota
#19 Robert Morris
#22 Northeastern
#23 Clarkson
#25 Rensselaer






Need to win their conference tournaments

Idle #24 St Lawrence, and #26 Bowling Green and below are unlikely to come out of the weekend in the teens, and thus face a steep climb to gain an at-large bid.



A couple data notes

The Eastern teams are already in conference tournaments, and thus playing best of three series this weekend. Their “win 2” curves include both the 2-0 and 2-1 scenarios. They are generally double-topped, and the 2-0 scenario is the better outcome.

There seems to be some confusion about whether the Feb. 20 Denver vs CC matchup was a neutral site game. As of now, USCHO, CHN, and the Denver site all list it as a home game for Denver; while and the CC site list it is a neutral site game. This has a minor effect on RPI which does not affect any of the above outcomes; though these calculations assume it was a neutral site.

This weekend’s big PWR movers

Looking up!

As mentioned in yesterday’s PWR outlook article, all the teams from #20 St. Lawrence to #26 Clarkson have the potential to climb into the teens this weekend. But, #25 Minnesota-Duluth and #26 Clarkson, in particular, have the potential to make huge jumps.

The #25 Bulldogs could find themselves as high as #14, a jump of 11 spots, with a sweep of #2 St. Cloud St. Most likely with a sweep is a still unusual climb of 8-9 positions to #16-17.


#26 Clarkson could find itself as high as 16 with wins over Dartmouth and Harvard, though #19-21 are more likely. The likely outcomes for Clarkson with two wins cover a surprising #16-#23 span. Clarkson’s outcome with two wins would rest a lot on other games, with the Golden Knights cheering for sweeps from Alaska Anchorage over Minnesota St, St. Cloud St over Minnesota-Duluth, Maine over Northeastern, Alaska over Michigan Tech, and Canisius over Robert Morris.


Going down?

Every team in the #14-22 range, except idle #15 Penn State, could fall more than five positions with a pair of losses. #14 Cornell, #17 Miami, #18 Michigan Tech, and #16 Minnesota are facing particularly steep falls.

Cornell could see itself fall as low as #24 with losses to Rensselaer and Union, though the spread of likely outcomes stretches a huge span of 17-24.


Miami faces a steep drop to as low as #29 if swept by Colorado College, with a still significant drop to 26-27 most likely.


Michigan Tech could find itself as low as #28 if they drop a pair to Alaska, though #24-26 are more likely.


If Minnesota gets swept by Michigan, it will face a broad range of potential outcomes that stretches as low as #25. #19-23 are all reasonably likely in that scenario.


Last full weekend of the regular season PWR outlook

Half the conferences end regular season play this weekend, so I’ll mostly be taking a short-term focus for a couple weeks as we transition from the regular season to conference tournaments. I will, however, comment on the long-term implications when possible1.

Who’s in?

The top 5 are starting to look like locks for the NCAA tournament. It would take catastrophic results, really bad luck, and a lot of conference tournaments being won by low PWR teams for any of #1 Quinnipiac, #2 St Cloud St, #3 Boston College, #4 North Dakota, or #5 Providence to miss out on an at-large bid. #6 Michigan is just too close and has too many games remaining to make the call yet.







A new #1 this weekend?

Despite winning only half its games in 2016, Quinnipiac has stayed atop the PairWise Rankings throughout. If they drop a game this weekend against Brown or Yale, St. Cloud St and North Dakota remain positioned to take over if they can secure their own wins. Despite sneaking ahead of North Dakota by the slimmest of RPI margins, Boston College is not a threat to take #1 this weekend.


Who’s safe this weekend?

The top 12 are generally secure this weekend, with no one particularly likely to fall below #14, regardless of the weekend’s results. Those include:
#1 Quinnipiac
#2 St. Cloud St
#3 Boston College
#4 North Dakota
#5 Providence
#6 Michigan
#7 Yale
#8 Denver
#9 Notre Dame
#10 Boston University
#11 Nebraska-Omaha
#12 Harvard


Action on the bubble

#13 Mass.-Lowell through #19 Rensselaer, #21 Dartmouth, and #25 Minnesota-Duluth are all in play to come out of the weekend on either side of 14 (though climbing to 14 is mathematically possible for #20 St. Lawrence, it would take some luck). Those include:
#13 Mass.-Lowell
#14 Cornell
#15 Penn State
#16 Minnesota
#17 Miami
#18 Michigan Tech
#19 Rensselaer
#21 Dartmouth
#25 Minnesota-Duluth





The long shots

Teams between #20 St. Lawrence through #26 Clarkson (except those mentioned above) are fighting to break into the teens this weekend, positioning themselves for a climb to the bubble in coming weeks. Those include:
#20 St. Lawrence
#22 Northeastern
#23 Robert Morris
#24 Minnesota St
#26 Clarkson



Who’s out?

It will be difficult for teams at #27 Bowling Green and below to move into position for an at-large bid.



Forecasts include the results of games played through Sunday of this week.

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.


1Technical note—I can’t reliably use simulations to forecast across the line between regular season games, of which there are 87 remaining, and conference playoffs, which feature 31 best of 3 series with reseeding and 21 regular games. The total 1.5*10^51 scenarios is too many outcomes to exhaustively search, and sampling via monte carlos doesn’t work particularly well when the games’ participants aren’t known across the reseedings and elimination games.

This weekend’s big PWR movers

As the weekend game results come in during the final few weeks of conference play, college hockey fans start watching the PairWise Rankings tables for big moves that might push teams into, or out of, position for an at-large bid. Here are the teams most likely to be cited on forums and in tweets this weekend for “surprisingly” large moves.

Don’t look down

#14 Penn State is unlikely to benefit much from a pair of wins over #40 Ohio State, but would likely plummet to about #20 (as low as #24 is realistically possible) if swept.


Surprise! #15 St. Lawrence could climb just a little with a pair of wins over #10 Yale and #53 Brown, but is facing steep decline to the #22-24 range with a pair of losses (or a more modest decline with a single loss).


#17 Rensselaer won’t move much if they defeat #1 Quinnipiac and #55 Princeton, but face a steep decline of about 9 ranking positions if they drop both.


Going up?

#23 Minnesota Duluth, which I already noted is facing significant upside potential with a visit to #3 North Dakota, could surge to the #14-16 range if they hand the Fighting Hawks a second consecutive conference sweep. Even a single win would likely result in a noticeable climb.


#25 Robert Morris could excite fans with a likely move into the teens with a pair of wins over #30 Air Force. But remember, they’d need a repeat performance against Canisius next weekend to avoid giving that ground right back.


The mathematical long shots for at-large NCAA bids

While #24 Minnesota St is pretty unlikely to climb to an at-large position by the end of the regular season, with a perfect run they could get close enough that an at-large bid wouldn’t be out of the question with some additional success in the conference tournament and a little luck.

The same is true, with decreasing likelihood with the lower ranks, down to about #29 Ferris St.

#24 Minnesota State
#25 Robert Morris
#26 Northeastern
#27 Bowling Green
#29 Ferris State

(Note that #28 Union getting into position for an at-large bid is particularly unlikely — that doesn’t mean mathematically impossible, it just didn’t come up enough in the simulations to be noticeable).