Category Archives: forecasts

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

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

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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

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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.

Resources

Final regular season Pairwise forecast

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One last week of mixed games — five conferences are in best-of-three quarterfinals, while one is playing its last week of the regular season.

About these forecasts

I’m again going to look just one week ahead because of the mix of games, though we’re starting to get a pretty good idea where the break lines are of teams that are locks for the NCAA tournament and those that can only make it by winning their conference tournaments. There are quite a few teams in the middle still capable of winning their way to an at-large bid.

If you didn’t read Feb. 26’s article, I’d urge you to check out the part that explains what I mean by a particular outcome being “likely”.

Teams that could fall to the bubble if swept

Every conference except the Big Ten is a best-of-three playoff round, meaning that any non-Big Ten team that loses two games this weekend won’t play any more games before the NCAA tournament selection. While teams’ PWR rankings can move a bit when idle, they’re pretty unlikely to make big moves. So, to determine teams’ worst case outcomes if swept we look at their likely PWR rankings following such an outcome this weekend and assume they’ll go into NCAA tournament selection with PWRs in the same neighborhoods.

#7 Quinnipiac is the highest ranked team with a noticeable chance of falling to the bubble (about a 16% chance of falling to #13 or lower if swept this weekend).

For #8 Mass.-Lowell, that jumps to about 29% chance of falling to #13 or lower if swept this weekend. For #9 Notre Dame, about 39% chance of falling to #13 or lower if swept.

Note that it’s also possible for a team that emerges victorious this weekend to end up with a lower PWR ranking going into NCAA selection due to a subsequent loss in a conference tournament.

Teams that could fall out of contention if swept

#10 North Dakota is the highest ranked team with a significant chance of falling out of contention if swept this weekend, with a ranking of #15-#18 most likely following such a result. It may prove to be possible to climb a couple spots while idle or even make the tournament from #15, but it’s not most likely.

#11 Providence and #12 Vermont face similar outlooks.

Teams that probably need to win this round

#13 Cornell is the highest ranked team with very little chance of staying in contention if swept this weekend, with a ranking of #18-#20 most likely if swept or #16-#19 most likely with a single win. Winning the round would keep Cornell in contention, most likely landing between #10-#15 (the broad range is attributable to two wins being achievable with either zero or one losses).

#14 Michigan will fall to the bottom of the bubble if swept this weekend, but has not yet entered its conference tournament so would get one more chance to make up ground next weekend.

#15 Northeastern is likely to fall out of contention if swept, or (unlike Cornell) move above the bubble with two wins.

#16 Colgate, #17 Mankato, and #18 Yale also fall out of contention if swept. Colgate and Minnesota State climb just to the bottom of the bubble with two wins (#13-#17 and #13-#16 most likely, respectively), while Yale is more likely to climb above the bubble with two wins (#10-#14 most likely).

Teams that can barely make the bubble with two wins

#19 Minnesota Duluth has only a 1% chance of making #13 or above with two wins this weekend, or a 15% chance of making #15 or above. #20 New Hampshire and #21 Western Michigan face similarly daunting outlooks.

Remember that after winning this weekend, three more wins would get any of these teams a conference tournament victory and auto-bid, so the chances for an at-large bid are really only interesting if you assume the conference tournament is going to end in a loss. It’s possible for one of these teams to get into position for an at-large bid with a sweep this weekend and then one or two wins followed by a loss, but not most likely.

#22 Maine fares slightly better, looking at about a 6% chance of landing at #13 or higher with two wins or a 31% chance of making #15 or above.

Teams that probably need to win their conference tournaments

#23 Ohio State can’t quite get to the bubble (no higher than #17 likely) even with two wins this weekend. Following such an outcome with two wins and a loss at the Big Ten conference tournament could be enough to get OSU onto the bubble, but it would take some luck.

#24 Clarkson and below aren’t even likely to break #20 with two wins this weekend. It’s hard to imagine one or two wins and a loss being enough to push any of them into place for an at-large bid.

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)

Transition week rankings outlook

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It’s an interesting week as one conference has two remaining weekends of regular season contests, two enter their final weekends, two begin best of three rounds in their conference tournaments, and one has a single elimination round.

Review of last week’s results

To keep me honest, we’ll first have a very quick review of last week’s forecasts. I’ll focus on the extraordinary results rather than recap the entire column.

#9 Northeastern was designated the highest ranked team that could fall to the bubble (#13-#16 most likely) if swept. After two losses, they fell to #15.

#15 Notre Dame was designated a bubble team that could climb off the bubble (#10-#13 most likely) with a win. The Fighting Irish pulled off the upset and climbed to #10.

#16 Providence was also designated a team that could climb off the bubble (most likely #10-#13) with a sweep. The Friars swept Maine and climbed to #11.

Of teams just below the bubble, only #19 Minnesota State pulled off the required sweep and climbed to #17—the lower end of the likely #15-#17 from the forecast.

About these forecasts

I’m again going to look just one week out because of the unusual mix of games.

If you didn’t read last week’s forecasts, I’d urge you to check out the part that explains what I mean by a particular outcome being “likely”.

Who could fall to the bubble this weekend

#9 remains the break point of being likely to fall to the bubble with a bad performance. This week it’s North Dakota (#14-#16 most likely if swept).

#10 Notre Dame has a pretty broad spread as to how far it could fall with a loss in its single game this weekend, with #12-#16 most likely. Note that the Hockey East tournament has begun and ND is in a single elimination game, so a loss would place them firmly on the bubble and out of control of their destiny.

With no games this weekend, #11 Providence can’t quite fall to the bubble.

#12 Michigan is facing down a cliff, likely to fall onto the bubble with a split (#12-#17 likely) or below the bubble if swept (#17-#19 most likely).

Quiet weekend on the bubble

#13 Cornell, #15 Northeastern, and #16 Colgate don’t play this weekend, but could still move a little in either direction.

#14 Vermont climbs a bit higher (#12-#14 most likely) with a win in its single game this weekend, or falls off (#16-#18 most likely) with a loss. Vermont is also in a single elimination game in the HE tournament, so this game weighs heavily on their fate.

Few teams can climb onto the bubble

A sweep would likely land #17 Minnesota State between #12-#15.

#18 Minnesota-Duluth can barely climb onto the bubble, with #14-#16 most likely with a sweep.

#22 Ohio State is an honorable mention, with a likely climb to #16-#19 with an unlikely sweep of #1 Minnesota.

Teams facing possible elimination this weekend

A few teams playing in conference tournaments this weekend only have hope for an at-large bid with a few wins:

#19 Yale is most likely to climb to #17-#19 with two wins this weekend

A win in its single elimination game this weekend doesn’t move #21 Maine much, with a #20-#22 range the most likely outcome. But hope would remain for an at large bid.

#24 Clarkson wouldn’t budge much even with two wins this weekend, likely to #22-#25. That’s not very promising.

Teams playing this weekend that not only need to win this weekend, but probably also their conference tournaments, to see the NCAA tournament:

#31 St Lawrence
#36 Brown
#37 Harvard
#44 Boston University
#45 Dartmouth
#46 Massachusetts
#47 Merrimack
#49 Robert Morris
#52 Niagara
#51 Holy Cross
#53 Canisius
#54 RIT
#55 Sacred Heart
#56 Princeton
#57 American International
#59 Army

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)

Weekend’s Pairwise Ranking outlook

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Last week I wrote an update on the break lines for NCAA tournament chances. Because it targeted the end of the regular season, its predictions still hold. So, this week I’ll take a shorter term look at what’s likely to happen this weekend.

What the forecasts really mean (there is some math)

These forecasts are not yet to the precision of completely mathematically eliminating outcomes. The number of possible outcomes is still so large that it wouldn’t be as useful to (and I can’t!) go into the detail of what’s mathematically possible and not until the conference tournaments.

Instead, I’ll refer to outcomes with at least a 10% probability as “likely”, and outcomes with a 1% probability as something that “could happen”. That suggests that one time out of ten, you’re going to see a “could happen” outcome instead of a “likely” one. It also suggests that one time out of a hundred you’re going to see an outcome outside what I even declared “could happen”.

The probabilities of possible outcomes do have a bell-shaped distribution, as you’ll see in the graphs, so when I say “a range of #10-#13 is likely” it’s usually most likely (over a 50% chance) of being in the middle of the range, #11-#12 in this case.

Who could fall to the bubble

#7 Quinnipiac and #8 Mass.-Lowell seem relatively safe, neither being likely to drop below #13 even if swept (though drops as low as #14 could happen for each).

#9 Northeastern is the highest ranked team with an obvious chance to fall to the bubble, with a drop to #13-#16 likely if swept.

#10 UND (#12-#14 likely and #16 could happen), #11 Cornell (#17-#19 likely and #21 could happen), and #12 Vermont (#16-#19 likely and #20 could happen) face similar downsides to the bubble if swept.

What will the bubble teams do?

Now it gets interesting. While the bubble teams can all fall off the bubble if swept or shore up their position with a sweep, those on the upper part of the bubble seem to face more downside while those on the lower part of the bubble seem to face more upside.

#13 Colgate is likely to fall to #18-#20 if swept (as low as #21 could happen), rise to #10-#13 with a sweep (as high as #9 could happen), or stay about the same or fall slightly with a split.

Similarly, #14 Michigan is likely to fall to #18-#20 if swept (as low as #22 could happen), rise to #10-#12 with a sweep (as high as #9 could happen), or stay about the same or fall slightly with a split.

#15 Notre Dame only plays one game this weekend. A win would result in a likely climb to #10-#13 (as high as #9 could happen), while a loss would result in a likely fall to #15-#17 (as low as #18 could happen).

#16 Providence would likely climb to #10-#13 with a sweep (as high as #9 could happen), but is also likely to rise modestly to #13-#15 with a split.

Teams that could climb onto the bubble

#17 Maine would likely climb to #11-#14 with a sweep (as high as #10 could happen).

#18 Yale would likely climb to #13-#16 with a sweep (as high as #12 could happen). But, for Yale a split is likely to result in a modest drop to #18-#20.

#19 Minnesota State and #20 New Hampshire can just reach the bottom of the bubble, with rankings ranging from #15-#17 and #16-#18 respectively likely with a sweep (#13 and #14 could happen for each respectively).

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)

Update on each team’s tournament chances

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As the regular season pushes into its final month, I’ll do more frequent updates on who’s a lock for an at-large bid and who’s out of the running.

Calculation details

The way I judge that is by forecasting each team’s Pairwise Ranking, and determining how likely the team is to finish in the top 12.

Readers may recall previous controversy about the PWR rankings, which was apparently resolved last weekend when USCHO adopted the formula CHN has been using. This site continues to use that same formula as the basis for its predictions.

End of regular season outlook

Last week I stated that #8 Mass.-Lowell was the last lock, which remains true this week. Their chance of falling to #13 or below by the end of the regular season has fallen to about 2.5%. Just below them, #9 Northeastern is the highest ranked team with a serious chance of dropping out, with about a 24% chance of falling to #13 or lower.

The dividing line for controlling their own destiny appears to around #19 at first glance, in that #19 Mankato can clearly make it while #20 New Hampshire is in trouble.

But, at this level and point in the season, the different number of games remaining is starting to matter. #21 Yale and #22 Denver both stand noticeably better chances than Yale.

Finally, the “remote mathematical chance of making it if they close out the season perfectly” line has climbed to about #27 Alaska Anchorage. #28 Nebraska-Omaha and below need conference tournament success to make the NCAAs.

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)

One month outlook for the end of the regular season

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With conference tournaments just a month or so away, this week I’ll take another look toward the end of the regular season — who’s a lock for an at-large bid, and who’s out of the running.

PWR calculation details

Readers of this blog probably already know that the RPI and PWR formulas for hockey changed this year. As I mentioned in a previous column—Dueling PWRs—there are currently two different interpretations of the new formulas. USCHO and CollegeHockeyNews implement the home/away weightings for RPI a bit differently.

From this post forward, unless otherwise stated the calculations referred to on this blog match the CHN implementation. Though I think that the more correct implementation, I will continue to monitor the situation.

End of regular season outlook

#1 Boston College and #2 Minnesota are likely duking it out for the top two rankings, unless one has a serious slump.

#8 Mass.-Lowell is the highest ranked team with a reasonable chance (about 7%) of falling to #13 or lower, so the top 8 can feel reasonably secure that they’ll be going into the conference tournaments in place for an at-large bid.

From #8 Mass-Lowell to about #19 Yale, the teams control their own destinies. Winning puts them in position for an at-large bid, losing does not.

#20 Clarkson through #29 Nebraska-Omaha have outside chances of climbing into the top 14 or so with stellar performances. They’re not mathematically eliminated, but would need nearly flawless runs to climb into position for an at-large bid.

#30 Brown and below are extremely unlikely to be in position to make the NCAA tournament at large going into the conference tournaments, so their best hopes for a bid would be winning their conference tournaments.

Methodology

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)

Pairwise Ranking outlook for this weekend

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Quite a few teams have an opportunity to make big moves this weekend.

Before I jump into the weekend’s forecast, be warned that some dispute has arisen in the college hockey online media world over the proper implementation of the NCAA’s 2014 revisions to the tournament selection process (see Uncertainty around PWR calculation). These forecasts currently assume the USCHO PWR formula.

Review of last week’s forecasts

Last week I highlighted the teams poised to make the biggest moves with extraordinary performances (both positive and negative).

Of Yale, Clarkson, Michigan, Minnesota-Duluth, New Hampshire, Western Michigan, and Michigan State, only New Hampshire delivered the necessary extraordinary performance. As predicted, the then #22 Wildcats experienced a significant move up, landing at #14 going into this weekend.

Poised to climb

A few teams in the 20s face particularly lopsided upside opportunities this weekend.

#23 Ohio State is most likely to jump to 15-18 with a sweep (though as high as 13 is plausible)
#26 Brown is most likely to jump to 17-18 with two wins (though as high as 14 is plausible)
#20 Yale is most likely to jump to 12-14 with two wins (though as high as 11 is plausible)

Poised to fall

Just inside the bubble seems to be a bad place to be, as a few teams in the teens face particularly lopsided downside opportunities this weekend.

#13 Minnesota-Duluth is most likely to fall to 19-20 if swept (though as low as 23 is plausible)
#14 New Hampshire is most likely to fall to 21-22 if swept (though as low as 25 is plausible)
#15 North Dakota is most likely to fall to 22-23 if swept (though as low as 26 is plausible)
#16 Notre Dame is most likely to fall to 23-24 if swept (though as low as 27 is plausible)

Could go either way

The #11 Wisconsin Badgers face the biggest combined upside/downside. Though their most likely outcomes are climbing up to 7-8 with a sweep or falling to 18-20 if swept, as high as #4 or as low as #23 after this weekend are plausible.

Methodology

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)