Category Archives: forecasts


How Boston University can make the NCAAs without winning Hockey East

An example of Boston University making the NCAA tournament at-large (that is, without winning the Hockey East tournament) follows:
https://goo.gl/UJMXKt

Generalizing that individual scenario, two things need to happen for Boston University to make the NCAAs at-large:

  1. Game outcomes need to be such that BU gets pushed up to #14 PWR, despite a loss
  2. Only two conference tournaments can be won by low PWR teams, so the #14 PWR team gets selected at-large

Getting BU to #14

One mandatory outcome for the Terriers to advance without winning the conference tournament seems to be North Dakota losing two games. Any win or tie by the Hawks, even if it doesn’t result in UND getting a bid, eliminates any chance of BU getting an at-large bid.

Beyond that, it takes one of a few particular combinations of outcomes to land BU at #14. There are 41 such combinations in the 12,288 possible outcomes in which Boston University wins the opening game versus Boston College but loses the Hockey East championship.

Getting #14 into the tournament

Even if Boston University gets to #14 in the PWR, as described above, only two conference tournaments can be won by teams ranked #15 or lower for the #14 team to get an at-large bid.

Because the WCHA (#17 Northern Michigan vs #24 Michigan Tech) and Atlantic Hockey (#20 Mercyhurst, #43 Robert Morris, #30 Air Force, and #34 Canisius) can only be won by teams that will finish #14 or lower, all other conference tournaments must be won by teams that finish in the top 14.

That’s guaranteed in the Big Ten, where only #2 Notre Dame and #4 Ohio State are vying for the championship. Also in a Hockey East tournament in which BU doesn’t win, a winner from among #15 Boston College, #9 Providence, and #7 Northeastern is guaranteed to be in the top 14.

So, from the ECAC, #3 Cornell or #11 Clarkson must take the championship rather than #22 Princeton or #26 Harvard. And, in the NCHC, #1 St Cloud St, #5 Denver, or #8 Minnesota Duluth must win (though #14 North Dakota losing is already a mandatory condition to get BU to #14, as stated above).

Summary

To get to #14 but not win the Hockey East championship, Boston University needs to win vs. Boston College but lose the championship game. The Terriers also need some help from North Dakota, which must lose in both the semifinal and consolation games.

Also, for the #14 team to advance to the NCAA tournament, the above must hold and Cornell or Clarkson must win the ECAC tournament.

  • BU wins 1 game, loses championship
  • North Dakota loses two games
  • Cornell or Clarkson wins ECAC tournament

Those conditions leave 1024 remaining possible scenarios, in which 41 of them see BU hold onto the #14 slot and get an NCAA bid.

NCAA tournament possibilities

This article describes what teams might make the NCAA hockey tournament based on the data in the College Hockey Tournament Possibilities table:
College Hockey Tournament Possibilities

Because of a new conference tournament schedule this year, there are only 15 games remaining and thus only 49,152 possible outcomes remaining (the NCHC consolation game can end in a tie). That’s a dramatic simplification from past years, and there are thus few surprises in the possible outcomes.

16 teams make the tournament. The winner of each conference tournament is selected with what I sometimes call an “autobid”, then the remaining slots are filled in order of final PWR rank. Thus, teams that don’t make the tournament with an autobid but end up in “bubble” PWR ranks of 12-15 want conference tournaments won by high ranking teams so there are still slots available for them to get selected at-large. Teams that can’t finish in the top 16 of PWR can only be selected for the NCAA tournament by winning their conference tournaments and getting an autobid.

In

9 teams are guaranteed to make the NCAA tournament regardless of outcome next weekend.

#1 St Cloud St
#2 Notre Dame
#3 Cornell
#4 Ohio St
#5 Denver
#6 Mankato (idle)
#7 Northeastern
#9 Providence
#10 Michigan (idle)

A lock with a win

Minnesota-Duluth and Clarkson both stand a good chance to make the NCAA tournament regardless of outcome (in 89% of scenarios in which they go 0-2 for Duluth and 73% of scenarios in which they lose for Clarkson), but can lock up at-large bids with a single win. If either should lose, they just need enough of the teams above to advance to leave at-large spots available for them.

#8 Duluth
#11 Clarkson

At-large possible

Much like Duluth and Clarkson, these teams hoping for an at-large bid want conference tournaments to be won by teams that have already locked up a bid (above). If a team that wouldn’t otherwise make the tournament wins a conference tournament and gains an autobid, that would leave one fewer at-large slot for these teams.

Penn State is quite likely to advance, in 98% of remaining scenarios. Minnesota faces a more perilous 76% of scenarios remaining that allow the Gophers to advance.

Of course, the 3 teams that are still playing have varying amounts of control over their own destinies:

  • North Dakota gets selected in 14% of scenarios in which they’re winless, 25% of scenarios in which they win 1, and can get an autobid.
  • Boston College faces less favorable 3% and 9% chances with zero or one wins.
  • Boston University can’t make it without a win, and even with 1 win faces a tiny chance of being selected at-large (under 1% of scenarios in which they win just 1 game).

#12 Penn St (idle)
#13 Minnesota (idle)
#14 North Dakota
#15 Boston College
#18 Boston University

Need to win the conference tournament

#17 Northern Michigan
#20 Mercyhurst
#22 Princeton
#24 Michigan Tech
#26 Harvard
#30 Air Force
#34 Canisius
#43 Robert Morris

March 9-11 weekend PWR outlook

This article discusses who is likely to make the NCAA tournament based on potential outcomes this weekend. It’s largely based on the following forecast:
Wins needed to emerge at PWR rank

Now that we’re in conference tournament play, note that the forecast is for one week.

Near locks for the NCAA tournament

It would take highly unlikely (though not mathematically impossible!) bad luck for any of the current top 6 to miss the NCAA tournament.

#1 St Cloud through #6 Denver should emerge from the weekend in the top 8, even if they fail to advance. It would be exceedingly unlikely for any of them to then fall to #12 or below while idle AND have conference tournaments won by enough low ranked teams that teams in the #12 range fail to make the NCAA tournament at-large.

#1 St Cloud St
#2 Nore Dame
#3 Cornell
#4 Ohio St
#5 Minnesota St
#6 Denver

Almost a lock?

A similar case can be made for #7 Michigan, who should fall between #7-#12 if they lose. But, it’s just possible enough to hit #12 (or below) and miss that I don’t yet dare call the Wolverines a lock.

#7 Michigan

Control their own destiny

#8 Clarkson through #12 Providence can drop to the bubble with loss(es), or position themselves well with win(s). None of these teams would be outright eliminated if they fail to advance this weekend, but would become dependent on others’ performances and some luck.

#8 Clarkson
#9 Minnesota-Duluth
#10 Northeastern
#11 Penn St
#12 Providence

Watching from the sidelines

#13 Minnesota has already been eliminated from the Big Ten tournament, so is not playing this weekend, and is likely to emerge from the weekend between #10-14. Nothing is likely to change for the Gophers this weekend–they’re not yet eliminated, but will be dependent on others’ performances and some luck.

#13 Minnesota

Need to win

It’s tough to imagine #14 Nebraska-Omaha or below making the NCAA tournament unless they advance this weekend. The Mavericks show some chance of emerging #15, with a slim remaining chance of an at-large bid, from a winless weekend; but even that hope doesn’t seem to extend to #15 North Dakota and below.

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

Conference tournament play-in weekend outlook

With all conferences except the NCHC in the opening round of conference playoffs, many teams have the weekend off while others play in a best-of-3 play-in series.

Here’s where teams could end up after this weekend’s play:
PWR Forecast By Wins

View from the top

#1 St Cloud St isn’t going anywhere. Even though the Huskies play a pair of games, #2 Notre Dame and #3 Cornell are idle so can’t do enough to overtake St Cloud. They’re also both nearly guaranteed to stay in the top 4.

#4 Minnesota St, #5 Denver, and #6 Ohio St are all playing and all vying to fill spots 4-6.

Above the bubble

Idle teams #7 Clarkson, #11 Northeastern, and #12 Providence should all stay at 13 or above.

#8 Minnesota-Duluth, #9 Minnesota, and #10 Michigan can stay top 10 with a pair of wins (though even with a pair of wins Michigan could stumble out of the top 10, most likely in the condition that they also get a loss in the best of 3 series).

On the bubble

#13 Penn State, #14 North Dakota, ad #15 Nebraska-Omaha all have the potential to climb into the single digits with a pair of wins, or fall to 16 or below with no wins on the weekend.

Of other teams, only #17 Northern Michigan and #18 Bowling Green stand a significant chance of climbing to 13 with a pair of wins.

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

Weekend outlook for February 23-25

First, let’s review last weekend’s prognostications.

#1 St Cloud St didn’t need to sweep to hold onto the #1 spot because #2 Notre Dame stumbled with a pair of losses. Nonetheless, the Irish held onto #2 as predicted (#5 Denver could have overtaken them with a strong performance, but the Pioneers split on the weekend).

Those stumbles allowed #4 Mankato to climb into the top 4, as was noted could happen in that scenario.

None of the potential big movers came to fruition, as none pulled off the required sweeps.

Now, let’s look ahead to the coming weekend.

Potential 1 seeds

Because of stumbles by both St Cloud and Notre Dame last weekend, there are now 4 teams vying to emerge #1 from this weekend. In addition to the Huskies and Irish, #3 Cornell and #5 Denver stand a change of emerging from the weekend #1.

St Cloud is pretty much guaranteed to hold the #1 spot with a sweep of Denver. But, the same series gives Denver the best opportunity to take over the #1 spot if the Pioneers manage to pull off the sweep.

Above the bubble

Only the top 8 teams are pretty certain to emerge from the weekend in the top 12. Including those mentioned above, those teams are:

#1 St Cloud
#2 Notre Dame
#3 Cornell
#4 Minnesota State
#5 Denver
#6 Ohio State
#7 Clarkson
#8 Minnesota

It’s too early to call them all locks for the NCAA tournament (disaster in conference tournament play could easily push one of the bottom few onto the bubble), but they’ll be well positioned heading into the conference tournaments.

On the bubble

Almost all teams through #24 Wisconsin have a chance to emerge from the weekend in the top 14, thus on the bubble for an at-large bid for the NCAA tournament.

Those include:

#14 Nebraska-Omaha
#15 Western Michigan
#16 Northern Michigan
#17 Penn State
#18 Bowling Green
#20 Union
#21 Boston College
#22 Harvard
#23 Colorado College
#24 Wisconsin

#19 Boston University is the one exception. Hosting a pair of games against #47 Vermont just doesn’t give the Terriers much upside, with #16 looking like the best likely weekend outcome (and even that isn’t very likely).

On the outside, looking in

#25 Maine and below just aren’t very likely to climb onto the bubble, regardless of their performance this weekend. Those teams will be looking for success in their conference tournaments to gain access to the NCAA tournament.

Other interesting potential moves

#11 Michigan is the highest ranking team facing a precipitous cliff. Getting swept by #55 Arizona St could push the Wolverines as low as #22, with the #17-19 range most likely. A sweep isn’t particularly helpful, with a #10-11 ranking the most likely outcome of a sweep.

Perhaps more likely, #14 Nebraska-Omaha faces similar downside in a pair of games against #23 Colorado College. Getting swept could push the Mavericks as low as #24, though #19-21 are most likely. UNO, however, faces some upside potential from a sweep, with a climb to #11-12 most likely.

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

Interesting potential PWR movements the weekend of Feb. 16

Will there be a new #1?

#1 St Cloud State is almost, but not quite, guaranteed to hold onto #1 with a sweep (the Huskies stay #1 in about 98% of scenarios in which they sweep), but with a single loss would become vulnerable to #2 Notre Dame overtaking them if the Irish can pull off a sweep. Neither has an easy matchup, with St Cloud State facing #12 Western Michigan and Notre Dame facing #15 Michigan.

Who’s vying for a 1-seed position?

In addition to St Cloud St and Notre Dame, the rest of the top 6 are also likely to be vying for top 4 slots this weekend.

#3 Cornell is unlikely to climb, but is hoping not to fall as low as #7.

#4 Denver could climb to #2 with stumbles by those ahead of them, but could also fall as low as #7 with a poor performance.

#5 Mankato could climb to #3, but could fall as low as #8.

#6 Ohio State could climb as high as #3, or slip a little to #7.

Biggest upside potential of the weekend

#24 Colorado College is the big upside team of the week. If the Tigers sweep and all goes well, they could climb as high as #12 and firmly onto the bubble. The #14-16 range is more likely with a sweep, but even that would represent a tremendous one week climb.

Biggest downside potential of the weekend

As often seems to be the case this time of year, around the #10-12 range can be precarious. These teams face a lot of downside potential if swept, and usually not much upside potential with a sweep. They generally need to win just to hang on, or rely on significant losses above them to climb.

#8 Providence could fall as low as #16 if swept, though #13-14 is a bit more likely.

#10 Nebraksa-Omaha could fall as low as #18 if swept, though #14-15 is more likely.

#11 Minnesota-Duluth could fall as low as #19 if swept, though #16-17 are a bit more likely.

Biggest range of outcomes for the weekend

This usually comes from the 30s, where win-loss records and RPI are both in the .500 range and there’s lots of potential to climb or fall out of the pack.

This week’s biggest potential mover is #30 Yale. The Bulldogs could climb as high as about #21 with two wins or fall as low as #39 with two losses, a range of 18 positions of likely outcomes!

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—What do other teams need to do to make the NCAA tournament?

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?

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

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.