Tag Archives: Michigan

Tournament cutlines and weekend PWR outlook

Welcome new visitors. You might want to start with my introductory post, Hello world, to see what this blog is about. It may not be for everyone.

Review of last week’s cutlines

I don’t report on the cutlines (the rankings above which teams are locks for the tournament and below which teams are unable to make the tournament at-large) weekly, because their movements are usually pretty intuitive. If I reported that a team needs to win 5 out 8 and it subsequently wins 2 games, it then needs to win 3 out of 6; the PWR curves usually look about same, just the curve labels change from “5 more wins” to “3 more wins” and so forth. To illustrate that, let’s quickly review a few of the teams that had charts in last week’s article (you may want to open its charts side-by-side for comparison if you can).

By winning 2 games, #4 Minnesota-Duluth made the old “win 0″ curve drop off and now just needs 1 or 2 more wins to stay on or above the bubble.

minnesotaduluth_endofseason

#5 Bowling Green also won 2 games, so now just needs about 4 wins to go into conference tournaments on the bubble.

bowlinggreen_endofseason

Further down the chart, #14 Minnesota shifted all of its curves with a pair of wins — the Gophers now need about 6 or 7 wins out of 10 (consistent with last week’s 8 or 9 out of 12) to climb onto the bubble before conference tournaments.

minnesota_endofseason

#30 Bemidji State, which I said last week could only afford about 2 losses, has racked up 2 losses. They would pretty much need to win out for a shot at an at-large bid.

bemidjistate_endofseason

Interesting potential movements this weekend

First, is this the week #1 Minnesota State falls out of first? It only seems possible if they get swept (which KRACH gives about a 2.6% chance of happening), and even then someone nipping at their heels (North Dakota seems the only possibility) has to do well. You can’t see the “Win 1″ curve because it’s in exactly the same place as “Win 2″—100% at 1.

mankato

The matchup of the weekend is definitely #12 Michigan vs #14 Minnesota. Neither has much upside potential, but if either sweeps the other will plummet up to 10 spots.

michigan minnesota

#15 Mass.-Lowell needs a sweep to hang on, but pair of losses could send them into the twenties.

masslowell

Remember when #16 Harvard was ranked 1st and I said that a “not particularly likely” bad 2nd half could still push them out? Two more losses this weekend could push them into the twenties.

harvard

#22 St Cloud State, mentioned last week as the lowest ranked team with a good chance of climbing into contention, can make up some ground this weekend. An unlikely sweep of #5 Minnesota-Duluth could catapult them up onto the bubble, while even a split could result in a climb of a position or two.

stcloudst

#26 Western Michigan is also poised for huge jump with an also unlikely sweep over #4 Nebraska-Omaha.

westernmichigan

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

Saturday morning update

This is a big article will in four parts:

  • Changes from yesterday
  • A new summary of the overall outlook
  • Specific scenarios that determine which of the at-large candidates make it
  • A table of all remaining PWR possibilities

As we near the end, I want to remind everyone that there’s a noticeably higher than other years chance that this information is wrong. The NCAA changed its selection process this year. While USCHO, CHN, and I have attempted to faithfully implement it and came up with identical PWR rankings, it wouldn’t be shocking if something different came out of the committee than what’s in our final PWR tables.

Changes from yesterday

Colgate is a lock
Cornell is out
Northeastern is out

Overall outlook

In

  • Minnesota
  • Boston College
  • Union
  • Ferris St
  • Wisconsin
  • Quinnipiac
  • Mass.-Lowell
  • Notre Dame
  • St Cloud (added Thursday)
  • Colgate (added Friday)

In the running at large

  • Providence (about 94%)
  • Michigan (about 17%)
  • Mankato (can also get auto bid, about 75% with loss)
  • North Dakota (about 28% with win)
  • Vermont (about 93%)

Can make it with a conference championship

  • New Hampshire
  • Ohio St
  • Denver (playing Miami)
  • Miami (playing Denver)
  • Robert Morris (playing Canisius)
  • Canisius (playing Robert Morris)

Scenarios of interest to at-large teams

North Dakota

UND makes it in about 28% of the scenarios in which it wins. UND seems to need:

UND and Mass.-Lowell win and either (Wisconsin wins) or (Canisius, Ferris St, and Miami win)

The Mass.-Lowell, Wisconsin, and Ferris St wins prevent the cut line from moving by giving auto bids to teams already above the cut. In the case of UML + Ferris, UND needs a little PWR help from the other two wins.

Minnesota State

Minnesota State is in with an auto bid with a win.

Minnesota State also makes it in about 75% of scenarios in which it loses. Those scenarios are a bit complex.

Mankato misses if:
Ferris St, Ohio State, New Hampshire win and (North Dakota, or Canisius, or Denver win)

or

Ferris St, Ohio State, Mass.-Lowell, North Dakota, Canisius, and Miami win

Michigan

Michigan makes it in about 17% of scenarios.

Michigan is in if:
Wisconsin and Mass.-Lowell win and UND either ties or loses.

Wisconsin and Mass.-Lowell wins prevent the cut-line from moving, and a UND tie should keep them below Michigan in the PWR.

Providence

Providence makes it in about 94% of scenarios.

Providence only misses if:
New Hampshire, Mankato, Colgate, and Ohio State win.

Vermont

Vermont makes it in about 93% of scenarios.

Vermont only misses if:
Ohio State, New Hampshire, Western Michigan, Ferris St, Robert Morris, and Miami win

OR

Ohio State, New Hampshire, Mankato, and Union win

Both scenarios require Ohio State and New Hampshire to move the cutline; the other games are about keeping other teams from taking all the available at-large bids.

Remaining PWR possibilities

Team PWR Possibilities
Overall By number of wins
UMN #1 100.0%
Tournament invites: 100.0%
n/a
Boston College #2 91.1%
#3 8.9%
Tournament invites: 100.0%
n/a
Union #2 8.9%
#3 91.1%
Tournament invites: 100.0%
PWR Win 0 Win 1
#2   17.7%
#3 100.0% 82.3%
Tournament invites: 100.0% 100.0%
Ferris State #4 74.0%
#5 22.4%
#6 0.0%
#7 3.6%
Tournament invites: 100.0%
PWR Win 0 Win 1
#4 47.9% 100.0%
#5 44.8%  
#6    
#7 7.3%  
Tournament invites: 100.0% 100.0%
UW #4 25.0%
#5 50.0%
#6 25.0%
Tournament invites: 100.0%
PWR Win 0 Win 1
#4   50.0%
#5 50.0% 50.0%
#6 50.0%  
Tournament invites: 100.0% 100.0%
Quinnipiac #6 75.0%
#7 25.0%
Tournament invites: 100.0%
n/a
Mass.-Lowell #4 1.0%
#5 27.6%
#6 0.0%
#7 71.4%
Tournament invites: 100.0%
PWR Win 0 Win 1
#4   2.1%
#5   55.2%
#6    
#7 100.0% 42.7%
Tournament invites: 100.0% 100.0%
Notre Dame #8 100.0%
Tournament invites: 100.0%
n/a
Providence #10 12.5%
#11 38.5%
#12 36.5%
#13 12.5%
Tournament invites: 93.8%
n/a
SCSU #9 100.0%
Tournament invites: 100.0%
n/a
Michigan #14 64.6%
#15 34.4%
#16 1.0%
Tournament invites: 16.7%
n/a
Mankato #10 50.0%
#11 0.0%
#12 2.6%
#13 45.3%
#14 2.1%
Tournament invites: 87.5%
PWR Win 0 Win 1
#10   100.0%
#11    
#12 5.2%  
#13 90.6%  
#14 4.2%  
Tournament invites: 75.0% 100.0%
UND #13 2.1%
#14 31.3%
#15 4.2%
#16 18.2%
#17 18.8%
#18 17.2%
#19 8.3%
Tournament invites: 9.4%
PWR Win 0 Win 1
#13   6.3%
#14   93.8%
#15 6.3%  
#16 27.3%  
#17 28.1%  
#18 25.8%  
#19 12.5%  
Tournament invites: 0.0% 28.1%
Vermont #11 11.5%
#12 49.5%
#13 39.1%
Tournament invites: 92.7%
n/a
Colgate #10 37.5%
#11 50.0%
#12 11.5%
#13 1.0%
Tournament invites: 100.0%
PWR Win 0 Win 1
#10 25.0% 50.0%
#11 50.0% 50.0%
#12 22.9%  
#13 2.1%  
Tournament invites: 100.0% 100.0%
Cornell #16 8.3%
#17 34.4%
#18 41.1%
#19 16.1%
Tournament invites: 0.0%
n/a
New Hampshire #14 2.1%
#15 10.9%
#16 12.0%
#17 13.5%
#18 36.5%
#19 25.0%
Tournament invites: 50.0%
PWR Win 0 Win 1
#14   4.2%
#15   21.9%
#16   24.0%
#17   27.1%
#18 50.0% 22.9%
#19 50.0%  
Tournament invites: 0.0% 100.0%
Northeastern #15 36.5%
#16 40.1%
#17 18.2%
#18 5.2%
Tournament invites: 0.0%
n/a
Western Michigan #21 66.7%
#22 33.3%
Tournament invites: 0.0%
PWR Win 0 Win 1
#21 50.0% 100.0%
#22 50.0%  
Tournament invites: 0.0% 0.0%
Ohio State #15 14.1%
#16 20.3%
#17 15.1%
#18 0.0%
#19 27.6%
#20 22.9%
Tournament invites: 50.0%
PWR Win 0 Win 1
#15   28.1%
#16   40.6%
#17   30.2%
#18    
#19 54.2% 1.0%
#20 45.8%  
Tournament invites: 0.0% 100.0%
Bowling Green #24 14.1%
#25 8.3%
#26 77.6%
Tournament invites: 0.0%
n/a
AA #27 100.0%
Tournament invites: 0.0%
n/a
Denver #23 50.0%
#24 0.0%
#25 50.0%
Tournament invites: 50.0%
PWR Win 0 Win 1
#23   100.0%
#24    
#25 100.0%  
Tournament invites: 0.0% 100.0%
Mercyhurst #32 100.0%
Tournament invites: 0.0%
n/a
Miami #29 27.6%
#30 22.4%
#31 50.0%
Tournament invites: 50.0%
PWR Win 0 Win 1
#29   55.2%
#30   44.8%
#31 100.0%  
Tournament invites: 0.0% 100.0%
Michigan State #37 18.8%
#38 81.3%
Tournament invites: 0.0%
n/a
Robert Morris #44 50.0%
#45 0.0%
#46 0.0%
#47 0.0%
#48 50.0%
Tournament invites: 50.0%
PWR Win 0 Win 1
#44   100.0%
#45    
#46    
#47    
#48 100.0%  
Tournament invites: 0.0% 100.0%
Canisius #44 7.3%
#45 21.9%
#46 14.6%
#47 6.3%
#48 50.0%
Tournament invites: 50.0%
PWR Win 0 Win 1
#44   14.6%
#45   43.8%
#46   29.2%
#47   12.5%
#48 100.0%  
Tournament invites: 0.0% 100.0%
Niagara #49 21.9%
#50 78.1%
Tournament invites: 0.0%
n/a
Penn State #51 49.5%
#52 50.5%
Tournament invites: 0.0%
n/a

Friday morning update

With the first two Big Ten games down, there are only minor changes to the overall tournament outlook.

St Cloud St now appears to be a lock for an at-large bid.

Michigan has taken on the expected “0 win” scenario from previous columns (about a 22% chance of making the tournament at-large).

Each of the bubble teams — Mankato, UND, Vermont, Colgate, and Cornell — improved their one win at-large chances by about 10% (idle Vermont’s overall chances increased by about 10%).

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%).