First look at 2018 tournament likelihoods

This week’s PWR by wins forecast is now available. See last week’s post, First 2018 PWR forecasts available, for an explanation of the forecasts and how to interpret the results.

For those who would rather just know the bottom line, this post will go into deeper detail interpreting the forecast table.

Is anyone safe yet?

No one is completely, mathematically, guaranteed a tournament appearance yet.

Neither #1 Notre Dame nor #2 Clarkson fell below #12 in any of the simulations (and thus would almost be guaranteed an at-large bid). But, note that in those same simulations neither team ever dipped down to 0-1 wins, so falling to the bubble is mathematically possible, but would take a highly improbable collapse.

Ok, then who’s likely to make the tournament?

#1 Notre Dame, #2 Clarkson, #3 St Cloud St, #4 Cornell, #5 Ohio St, and #6 Denver are all most likely to finish in the top 12 if they win at least half their remaining games.

Is anyone out?

Much like the at the top, very little is completely mathematically settled at this point. But, by looking at the near perfect seasons some lower ranked teams would require to get an at-large bid, you can guess at the low likelihood of that outcome.

From #35 Mercyhurst down need a near perfect remaining season to get in position for an at-large bid. Those teams include the following:

#35 Mercyhurst
#36 Merrimack
#37 Air Force
#38 Army
#39 New Hampshire
#40 Holy Cross
#41 Niagara
#42 Princeton
#43 Robert Morris
#44 Quinnipiac
#45 Bentley
#46 RIT

Getting an at-large bid, even with a perfect remainder of the season, seems very unlikely for #47 Ferris St and down.

#47 Ferris State
#48 Arizona State
#49 Dartmouth
#50 Connecticut
#51 American Internationl
#52 Brown
#53 Alaska
#54 Alabama-Huntsville
#55 Rensselaer
#56 St. Lawrence
#57 Sacred Heart
#58 Lake Superior
#59 Vermont
#60 Alaska Anchorage

What next?

I’ll keep updating the forecasts weekly, 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 2018 PWR forecasts available

With the regular season about half over, it’s a good time to start paying attention to PWR. Remember that PWR is a ranking whose calculation mimics the NCAA’s tournament selection process, so the final PWR ranking perfectly predicts the teams that will be selected for the NCAA tournament. The 2014 article, When to start looking at PWR (revisited), examines how today’s PWR is reasonably predictive of the final PWR.

Current PWR Ranking

But, if what we’re really interested in is knowing what PWR is going to be at the end of the regular season, can we do better than a table of the PWR as if the season ends today? In last year’s article, New forecast presentation—PWR by wins, I introduced a new tool that can be used to answer questions such as:

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

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

The table on the PWR By Wins page shows you how many wins each team needs to likely finish at each PWR ranking. If you want more detail on a specific team, you can click a team name to see the probability curves of how likely that team is to end the regular season with each PWR ranking with a given number of wins in its remaining scheduled games.

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

How it works

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

Each forecast is based on at least one million monte carlo simulations of the games in the described period. For each simulation, the PairWise Ranking (PWR) is calculated and the results tallied. The probabilities presented in the forecasts are the share of simulations in which a particular outcome occurred.

The outcome of each game in each simulation is determined by random draw, with the probability of victory for each team set by their relative KRACH ratings. So, if the simulation set included a contest between team A with KRACH 300 and team B with KRACH 100, team A will win the game in very close to 75% of the simulations. I don’t simulate ties or home ice advantage.

Saturday morning possibilities

The NCAA tournament field is almost set and the scenarios for which teams can still make it are among the most straightforward in recent memory.

In for sure

The following 12 teams are in for sure:

Denver
Minnesota Duluth
Harvard
Western Michigan
Minnesota
Boston University
Union
Mass.-Lowell
Cornell
Notre Dame
North Dakota
Penn State

In with a win

The winners of the WCHA tournament and Atlantic Hockey tournament will be in with their conferences’ autobids, but none can make it at-large. So, two more slots will be taken with two of the following teams:

Robert Morris or Air Force
Bowling Green or Michigan Tech

At-large hopes

With 14 slots taken, only 2 remain. The two teams eligible for at-large bids are:
Providence
Ohio State

Their fates come down to the two conference championships that feature one team that’s in for sure and one that isn’t. If a team that isn’t otherwise in takes one of those conference championships, they will take a slot and deny one of the at-large teams.

If Mass.-Lowell and Penn State win, both Providence and Ohio State are in
If only one of Mass.-Lowell or Penn State win, Providence is in but Ohio State is out
If Mass.-Lowell and Penn State both lose, both Providence and Ohio State are out

How Cornell, Notre Dame, North Dakota, or Providence could miss the NCAAs

For each of Cornell, Notre Dame, North Dakota, and Providence, missing the tournament requires a poor PWR ranking because of the success of the others.

All but idle Providence control their own fates, being able to guarantee an at-large bid with a single semi-final win.

With no additional wins, each is likely to land somewhere in the 9-16 range in PWR. To miss the NCAA tournament requires landing at the bottom of that range, requiring other teams in that range to do well. In addition to the other teams in this list doing well, Penn State, Ohio State, Air Force, and Boston College all have opportunities to move ahead of one of these teams that remains winless.

How Cornell misses

Cornell misses in about 6% of the scenarios in which they lose their semifinal game.

Here’s a scenario that pushes Cornell down to #16, so out of contention:
https://goo.gl/hFduxl

In this scenario, Cornell’s RPI falls enough and teams just below Cornell are successful enough that they pass Cornell in RPI and take the PWR comparison. Notre Dame, North Dakota, Providence, Penn State, Ohio State, Air Force, and Boston College each take the comparison, moving Cornell from 51 comparisons won to 44, enough to fall to #16 and out of contention.

Note that in that scenario, only the WCHA is won by a team that doesn’t finish in the top 15 in PWR. If only some of those teams pass Cornell, such that Cornell lands somewhere in the #12-15 range, enough conferences would need to be won by teams outside the top 15 for Cornell to still miss it.

How North Dakota misses

North Dakota misses in about 11% of the scenarios in which they lose their semifinal game.

Here’s a scenario that pushes North Dakota down to #16, so out of contention:
https://goo.gl/o7E4Pz

In that scenario, North Dakota’s RPI falls enough and teams just below the Hawks are successful enough that they pass North Dakota in RPI and take the PWR comparison. Providence, Penn State, Ohio State, Air Force, and Boston College each take the comparison, moving North Dakota from 49 comparisons won to 44, enough to fall to #16 and out of contention.

Note that in that scenario, only the WCHA is won by a team that doesn’t finish in the top 15 in PWR. If only some of those teams pass North Dakota, such that UND lands somewhere in the #12-15 range, enough conferences would need to be won by teams outside the top 15 for North Dakota to still miss it.

How Notre Dame misses

Notre Dame misses in about 4% of the scenarios in which they lose their semifinal game.

Here’s a scenario that pushes Notre Dame down to #16, so out of contention:
https://goo.gl/cUZqLw

In that scenario, Notre Dame’s RPI falls enough and teams just below the Irish are successful enough that they pass Notre Dame in RPI and the PWR comparison. North Dakota, Providence, Penn State, Ohio State, Air Force, and Boston College each take the comparison, moving Notre Dame from 50 comparisons won to 45, enough to fall to #16 (due to losing the RPI tie-breaker w/Providence) and out of contention.

Note that in that scenario, only the WCHA is won by a team that doesn’t finish in the top 15 in PWR. If only some of those teams pass Notre Dame, such that Notre Dame lands somewhere in the #12-15 range, enough conferences would need to be won by teams outside the top 15 for Notre Dame to still miss it.

How Providence misses

Providence is the only idle team with a shot at an at-large bid, though its scenario highly resembles those of Cornell, North Dakota, and Notre Dame with a semifinal loss. Providence misses the NCAA tournament in about 4% of possible scenarios.

Here’s a scenario that pushes Providence down to #16, so out of contention:
https://goo.gl/NVhyEE

In that scenario, Providence’s RPI actually rises a bit but teams just below Providence are successful enough that they pass Providence in RPI and take the PWR comparison. Penn State, Ohio State, and Air Force each take the comparison, moving Providence from 47 comparisons won to 44, enough to fall to #16 and out of contention. (Note that Providence already loses the comparison to BC, but BC moves ahead of Providence in PWR ranking in this scenario on the basis of Providence’s decline in comparisons won).

Note that in that scenario, only the WCHA is won by a team that doesn’t finish in the top 15 in PWR. If only some of those teams pass Providence, such that Providence lands somewhere in the #12-15 range, enough conferences would need to be won by teams outside the top 15 for Providence to still miss it.

How Harvard can reach #1 overall

You might want to follow along with a sample scenario – https://goo.gl/Zc38am (CHN You are the Committee)

Harvard getting to #1 overall is possible, though not very likely. The Crimson only advance to #1 in about 2% of the scenarios in which they win the ECAC tournament.

Poor performance by Minnesota-Duluth and Denver is obviously required for Harvard to be able to overtake each in RPI. Each needs to lose their opener, but they then would meet in a consolation game in which both can’t lose. Duluth must defeat Denver in that game to knock Denver’s RPI just a hair below Harvard’s, while not allowing Duluth to climb enough to overtake Harvard.

Even if Duluth and Denver both lose their semifinal games and the Bulldogs lose the consolation game, Harvard still only advances to #1 in about 11% of those scenarios. Other tournament outcomes then need to push Harvard’s RPI up enough to catch Denver, but there’s no single linchpin team or game that would do it, it will take a lucky combination of outcomes. I’ll post updates throughout the tournament as the odds change.

How BC can lose and still make the NCAA tournament

You might want to follow along on a sample scenario –
https://goo.gl/KBMK04 (CHN You Are The Committee)

With a single loss the weekend, the highest Boston College can climb in the PWR is #15 (see College Hockey Tournament Possibilities). That happens in about 10% of the scenarios in which BC loses its semifinal. However, even with that ranking, BC would additionally need the conference tournament winners to be such that #15 gets an at-large spot.

The key to BC’s PWR ranking in this scenario is idle Providence falling from #12 to #16, allowing BC to rise to #15. In this example, Air Force, Penn State, and Ohio State all do well enough to take the comparison w/Providence (on the basis of RPI), pushing Providence from 47 comparisons won to 44. BC, staying at 45 comparisons won, climbs to #15 overall.

The other necessary ingredient for BC to advance in this scenario is for the #15 team to advance, which requires only one conference tournament be won by a team outside the top 15. Because the WCHA winner must come from outside the top 15, every other conference must be won by a team that ends in the top 15. Those possibilities include:

Big Ten – Minnesota, Penn State, or Ohio State
ECAC – Harvard, Union, or Cornell
Hockey East – any
NCHC – any
Atlantic Hockey – Air Force

NCAA tournament conference participation possibilities (2017 edition)

Conference representation in NCAA tournament by share of possible scenarios
1 2 3 4 5
Atlantic Hockey 91% 9%
Big Ten 3% 46% 50%
ECAC 1% 77% 23%
Hockey East 1% 73% 26%
NCHC 4% 96%
WCHA 100%

Atlantic Hockey

Only the auto-qualifying winner of the conference tournament is in for sure, from #15 Air Force, #25 Canisius, #26 Robert Morris, and #34 Army. Air Force could also sneak in at-large even if they don’t win the conference tournament.

Big Ten

#5 Minnesota is in for sure, but the Big Ten is very unlikely to have the Gophers as their only representative. 5 other teams (#13 Penn State, #14 Ohio State, #18 Wisconsin, #36 Michigan, and #47 Michigan State) are also still vying for the conference tournament championship and its automatic bid. Of those, Penn State and Ohio State each stand a decent chance of making it at-large, particularly if they win a game or two.

ECAC

#3 Harvard and #7 Union are in for sure, but the ECAC is also quite likely to have additional representation. #9 Cornell and #20 Quinnipiac are also vying for the conference tournament championship and its automatic bid. Cornell stands a very good chance of getting an at-large bid.

Hockey East

#6 Boston University and #8 Mass.-Lowell are in for sure. Idle #12 Providence is also very likely (about 96% of remaining scenarios) to make the NCAA tournament at-large. #10 Notre Dame and #16 Boston College are also vying for the conference tournament championship and its automatic bid. Notre Dame stands a very good chance of getting an at-large bid, while Boston College stands a slim chance even if they don’t win the conference tournament.

NCHC

#1 Denver, #2 Minnesota-Duluth, and #4 Western Michigan are in for sure. The only other NCHC team vying for the conference tournament championship is #11 North Dakota, which is quite likely to make the NCAAs regardless of conference tournament outcome.

WCHA

The WCHA will only send the winner of its conference tournament, either #28 Michigan Tech or #37 Bowling Green.

February forecast follow-up

In February I published an article, How many teams will each conference put in the playoffs? (2017 edition) that used simulations to predict how many teams each conference would put in the top 14 of PWR (on the assumption that two conferences would go to autobids not otherwise in the top 14). That forecast has held up very well, confirming that February PWR is a pretty good predictor of March PWR and that KRACH-based simulations have some forecasting value.

2017 NCAA tournament possibilities

This article will summarize the possible outcomes for each team, as displayed in the College Hockey Tournament Possibilities page.

Background on how PWR matters for tournament selection

Because we get lots of new readers during the tournament season, here’s some background information that my posts generally assume you know:

  • The PWR rankings are not a poll or computer model, but are instead an implementation of the same process the NCAA uses to select its tournament participants. They have correctly predicted the NCAA tournament participants for a decade or two.
  • Each conference gets to send one tournament winner to the NCAA tournament. So, we don’t need to look at the PWR of a team that wins its conference tournament.
  • The remaining 10 slots are given to top teams as ranked by the process implemented in PWR. So, PWR ranks 1-10 are in for sure; but, for 11-16 to make it requires some of the autobids to have gone to teams ranked above them (e.g. if an autobid goes to the team ranked #3, then an extra slot is open for the team ranked #11, and so on).
  • Because of that structure, we think of teams that are going to finish in the 12-15 range as “on the bubble”. Teams’ prospects are dependent not only on their final ranking, but also on how many lower ranked teams wins conference tournaments. Bubble teams’ chances for an at-large bid increase as slots are freed up by more conference tournaments being won by teams that would have made the NCAA tournament at-large.

These teams are in

The top 8 are in, no matter what happens.

#1 Denver
#2 Minnesota-Duluth
#3 Harvard
#4 Western Michigan
#5 Minnesota
#6 Boston University
#7 Union
#8 Mass.-Lowell

Of those, the top 3 are set as Denver, Minnesota-Duluth, and Harvard; each could finish 1-3. Denver can clinch #1 by winning its conference tournament.

Fighting for the final top seed in the #4 position are Western Michigan, Minnesota, Boston University, Union, and Mass.-Lowell. Western Michigan can clinch #4 by winning its conference tournament.

These teams control their own destinies

#9 Cornell through #11 are all guaranteed an NCAA tournament appearance with a single win.

#9 Cornell (100% with 1 win, 94% with 0 wins)
#10 Notre Dame (100% with 1 win, 96% with 0 wins)
#11 North Dakota (100% with 1 win, 89% with 0 wins)

Watching from the sidelines

#12 Providence is the only idle team with a chance to make the tournament at-large. It does so in about 96% of scenarios, which largely come down to how many lower ranked teams win their conference tournaments.

Can make it at-large

#13 Penn State through #16 Boston College not only can all make it at-large, but all stand a chance even with no additional wins (though admittedly a slim chance for Air Force and Boston College).

#13 Penn State (97% chance with 2 wins, 72% chance with 1 win, 26% chance with 0 wins)
#14 Ohio State (85% chance with 2 wins, 50% chance with 1 win, 13% chance with 0 wins)
#15 Air Force (29% chance with 1 win, 4% chance with 0 wins)
#16 Boston College (22% chance with 1 win, <1% chance with 0 wins)

Need the conference tournament

The remaining teams that are still alive can only make the NCAA tournament by winning their conference tournaments.

#18 Wisconsin
#20 Quinnipiac
#25 Canisius
#26 Robert Morris
#28 Michigan Tech
#34 Army
#36 Michigan
#47 Michigan State
#37 Bowling Green

How the at-large teams make it

The winner of the WCHA will be a team that would not get an at-large bid, taking away one spot. That leaves at most 15 spots for top PWR teams.

For each conference tournament won by a top PWR team, an additional at-large team can make it. So, the at-large group wants the conference tournaments to be won by the following:

Big Ten – Minnesota
ECAC – Harvard or Union
Hockey East – Mass.-Lowell or Boston University
NCHC – Denver, Minnesota-Duluth, or Western Michigan

The at-large group are also competing with each other for ranking position, so generally want other at-large candidates to lose.

Penultimate weekend PWR/NCAA tournament outlook

Stability at the top

#1 Denver and #2 Minnesota-Duluth are again duking it out for #1 this weekend, with neither likely to drop below #3.

Only #3 Harvard is also safely in the top 10, and thus a near certainty for the NCAA tournament (Harvard is very unlikely to fall below #5 this weekend, even with a pair of losses which would preclude any additional games and much opportunity to fall further).

#4 Western Michigan is pretty safe, with a pair of losses dropping them to the 6-10 range. But, with some bad luck of falling to #10, some additional bad luck while idle, and some additional bad luck on the cutline, it’s possible for the Broncos to miss the tournament.

#5 Minnesota appears at first to be in a similar situation to Western Michigan, but because the Big Ten season hasn’t ended, the Gophers’ worst case scenario is tacking an additional loss next weekend on a pair of losses this weekend, which could push them into the teens.

#6 Mass.-Lowell, #7 Boston University, and #8 Union are likely to end up in the top 12 after this weekend even with a pair of losses. While certainly more vulnerable than Denver through Minnesota, all three are likely in barring unlikely PWR movement while idle and a harsh cutline.

Bubble teams

#9 Penn State could easily fall to the bubble with a pair of losses and then would still have another game in the Big Ten tournament, which could result in a further decline.

#10 Cornell through #21 Northeastern are all fighting for their lives. Wins improve their chances, losses hurt them. From about #12 North Dakota to about #15 Vermont, a pair of wins this weekend is required to be comfortably in bubble position. From about #16 Air Force down, it seems almost impossible to make the tournament without a pair of wins this weekend.

#10 Cornell
#11 Providence
#12 North Dakota
#13 Wisconsin
#14 Notre Dame
#15 Vermont
#16 Air Force
#17 Ohio State
#18 St Cloud St
#19 Boston College
#20 Nebraska-Omaha
#21 Northeastern

Mathematical long shots

#22 St. Lawrence and #23 Quinnipiac are mathematical long shots for at-large bids. Each could conceivably move into the teens with a pair of wins, from which position it would still take another win and a lot of luck to get an at-large bid.

Need to win their conference tournaments

#24 Clarkson and below really need to focus on winning their conference tournaments if they want to see the NCAA tournament.

#24 Clarkson
#25 Mankato
#26 Canisius
#27 Bemidji St
#28 Michigan Tech
#29 Robert Morris
#30 Merrimack
#31 Princeton
#32 Miami
#33 Yale
#34 Army
#35 Connecticut
#36 Colorado College
#37 New Hampshire
#38 Bowling Green
#39 Michigan
#40 Holy Cross
#41 Bentley
#42 Sacred Heart
#43 Dartmouth
#44 Arizona State
#45 Mercyhurst
#46 Maine
#47 Northern Michigan
#48 Michigan State
#49 Colgate
#50 Ferris State
#51 RIT
#52 Alaska
#53 Lake Superior
#54 American Int’l
#55 Rensselaer
#56 Alabama-Huntsville
#57 Alaska Anchorage
#58 Massachusetts
#59 Brown
#60 Niagara

A data note

All conferences except the Big Ten are 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. A 2-0 scenario is almost always preferable to a 2-1.

Methodology

Forecasts include the results of games played through Tuesday 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.

Resources

Weekend PWR outlook – first playoff weekend

Watching the top

#1 Denver, #2 Minnesota-Duluth, and #3 Harvard will probably keep the top 3 spots among themselves after this weekend, with the ordering of the three dependent on their outcomes. Duluth is capable of taking #1 from Denver, even if Denver gets a pair of wins. Idle Harvard isn’t moving much, most likely staying at #3 with a slim chance of climbing to #2 if a team above them stumbles and some other lucky breaks occur.

With much of the top 8 idle, little movement is likely.

#4 Minnesota, #5 Western Michigan, #6 Mass.-Lowell (idle), #7 Boston University (idle), and #8 Union (idle) are all near locks to stay in the top 10, and thus firmly in control of their own destiny.

Note that the Big Ten teams, including #4 Minnesota, have another weekend of regular season play remaining after this one. With a bad enough string of losses, Minnesota could find itself on the bubble going into the Big Ten tournament.

Watching the bubble

This is where the action is this time of year. #9 Penn State to #19 Vermont could land somewhere on the bubble this weekend, and most are playing this weekend, so have significant control over their own fate.

#9 Penn State
#10 Cornell (idle)
#11 Notre Dame (idle)
#12 Providence
#13 Wisconsin
#14 St Cloud St
#15 Ohio St
#16 North Dakota
#17 Nebraska-Omaha
#18 Air Force (idle)
#19 Vermont

Need conference tournament success

No team #20 or below seems likely to climb to at least 16 this weekend. However, teams down to about the mid-20s in PWR have slim possibilities of an at-large bid with some success in their conference tournaments.

#20 Boston College (idle)
#21 St Lawrence
#22 Quinnipiac
#23 Northeastern
#24 Bemidji St
#25 Canisius (idle)
#26 Clarkson
#27 Mankato
#28 Merrimack
#29 Miami
#30 Robert Morris
#31 Michigan Tech
#32 Princeton
#33 Connecticut
#34 Army (idle)
#35 Yale
#36 Colorado College
#37 New Hampshire
#38 Holy Cross
#39 Bowling Green
#40 Michigan
#41 Dartmouth
#42 Bentley
#43 Sacred Heart
#44 Maine
#45 Arizona St (idle)
#46 RIT
#47 Ferris St
#48 Mercyhurst
#49 Northern Michigan
#50 Colgate
#51 Alaska
#52 Lake Superior
#53 Michigan St
#54 American Int’l
#55 Rensselaer
#56 Alabama-Huntsville (idle)
#57 Alaska Anchorage (idle)
#58 Massachusetts
#59 Brown
#60 Niagra

A data note

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.