Mid-February Update—What do other teams need to do to make the NCAA tournament?

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As mentioned in today’s previous article, Who’s likely to make the NCAA tournament?, most teams only have 4-6 remaining scheduled games before the playoffs, so dramatic opportunities for repositioning themselves are diminishing.

PWR Forecast (by wins)

#10 Nebraska-Omaha through #17 Penn State generally stand a chance of finishing in the top 10 if they win out, or they could fall off the bubble (#16 or below) if they earn just a win or two. Those who earn a couple wins will get jostled around on the bubble by their neighbors who do particularly well or poorly. Those teams include:
#10 Nebraska-Omaha
#11 Minnesota-Duluth
#12 North Dakota
#13 Western Michigan
#14 Michigan
#15 Northeastern
#16 Northern Michigan
#17 Penn State

The teams just below them need to approach perfection to get into position for an at-large bid. #18 Bowling Green through #24 Maine stand a chance of breaking onto the bubble at the end of the regular season (as high as about #12) if they win out. Those teams include:

#18 Bowling Green
#19 Boston University
#20 Wisconsin
#21 Boston College
#22 Union
#23 Colorado College
#24 Maine

#25 Mass.-Lowell and below appear very unlikely to climb to #12 even if they win out, meaning their only likely path to an NCAA tournament bid is success in the conference tournaments. (#27 Miami has a bit more likely path than its neighbors by virtue of having six games remaining rather than 4).

How it works

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

Mid-February update—who’s likely to make the NCAA tournament?

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It’s been just over a month since I posted the First PWR forecast of the season, and things have really settled in.

PWR Forecast (by wins)

Most teams only have 4-6 remaining scheduled games before the playoffs, so dramatic opportunities for repositioning themselves are diminishing.

Just a few weeks ago, in First look at 2018 tournament likelihoods, I noted that all but Notre Dame and Clarkson still needed to win about half their remaining games to stay well-positioned for the NCAA tournament.

Thanks to sufficient performances since then, quite a few more teams are starting to look pretty safe.

Through #6 are nearly guaranteed to stay top 12, even if they lose out, leaving them well-positioned going into the playoffs. Those teams are:

#1 St Cloud St
#2 Denver
#3 Notre Dame
#4 Cornell
#5 Mankato
#6 Ohio State

Through #9 Minnesota are almost sure to stay top 12 with even just one more win. That adds the following to the well-positioned (though not at all guaranteed!):

#7 Clarkson
#8 Providence
#9 Minnesota

How it works

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

Introducing the PWR Calculator

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I’m please to announce an exciting new tool, an interactive PWR calculator. The calculator lets you see how PWR would be affected if already played games had different outcomes, if future games turned out a certain way, or if unscheduled (fictional) games were played.

PWR Calculator

While changes to PWR over the years have stabilized it and removed some of its biggest quirks (the TUC cliff), it’s somewhat unavoidable in any ranking scheme that there will be outcomes that have a surprising or outsized impact. The tool makes it easy for you play “what if” and see how PWR would differ with different game outcomes.

Like everything on CollegeHockeyRanked, it was designed from the ground up to work well on your mobile device, your tablet, or a computer. It’s also exceptionally straightforward and easy to use—providing a point and click interface to try different results, filters to help you focus only on the games and rankings you care about, and instantaneous feedback on your scenarios with no recalculate button or form submissions.

Here are a few interesting things to look for in the calculator right now:

  • If #27 Harvard had beat #11 Minnesota in either game of its November 17-18 series (lost 2-4 and 1-2 in OT, respectively), Harvard’s PWR would currently be 19 instead of 27, an 8 rank jump! Winning both would have further catapulted the Crimson to 13.
  • #8 Nebraska-Omaha is happy to have split with #1 Notre Dame in the October 26-27 series. Had the Mavericks lost instead of a 6-4 win on October 26, they would now be #16 instead of #8.
  • Because a team’s PWR ranking is relative to other teams (it’s a comparison of each team to all other teams), results that don’t even involve a team can affect its fortunes. #11 Minnesota would instead be #8 right not if #16 Michigan had defeated #4 Clarkson.

Any questions? Did you find anything interesting yourself in the calculator?

First look at 2018 tournament likelihoods

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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

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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

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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

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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

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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

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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)

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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.