Tag Archives: Cornell

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.

What to watch for in PWR this weekend

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This article looks at the most interesting outcomes of games this weekend, with a focus on what PWR might look like next Monday. If you want a more general analysis of the remaining regular season and NCAA tournament likelihood, check out the article, NCAA tournament outlook as conferences enter final regular season weekend, and the table, Wins needed to likely end regular season at PWR rank.

Biggest upside potential

#20 Wisconsin, visiting the red hot #4 Gophers in Minneapolis, has an opportunity to surge. The Badgers could climb to the 9-11 range with a sweep (as high as 7 is realistic), but will likely just stay put if swept. Of course, in the long run staying put is not good enough for the Badgers who needs 3-4 wins in their final 6 games to climb to the bubble (see NCAA tournament outlook).

#18 Boston College has a similar opportunity facing #8 Mass.-Lowell for a home-and-home series. Sweeping would provide a broad range of possible outcomes, from #8-#15 quite possible. Getting swept would likely result in a modest decline to the 19-20 range.

Biggest downside potential

As past readers of these articles know, just as teams around #20 usually have the most upside potential, teams around #10 usually have the most potential to fall.

#10 Cornell faces the most downside potential, with ranks 15-21 possible if swept by Rensselaer and Union. Given that these are the last two games of the regular season for Cornell, that would put the Big Red firmly on the bubble.

#9 Providence faces a similar outlook, with ranks 15-20 possible with a pair of losses to Massachusetts.

All of #8 Mass.-Lowell, #11 Penn State, #12 St Cloud St, #13 Ohio St, and #14 North Dakota face similar chances of a slightly more modest plunge with a pair of losses. Only Mass.-Lowell’s regular season ends this weekend, so others would have some opportunity to recover.

Top seeds?

#1 Denver and #2 Minnesota-Duluth each look unlikely to leave the weekend outside of the 1-3 range, regardless of outcome, and one of the two is almost certain to come out #1. Denver doesn’t quite control its own destiny, as Minnesota-Duluth stands about a 10% chance of sneaking into #1 even if both sweep. Other teams fighting for spots in the top 4 this weekend are #3 Harvard, #4 Minnesota, #5 Western Michigan, and #6 Boston University.

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

Current PWR Rankings
Current RPI Rankings
CHN PWR Rankings (CollegeHockeyNews.com)
USCHO PWR Rankings (USCHO.com)
Explanation of how PWR mimics NCAA tournament selection (CollegeHockeyNews.com)

How Cornell can make the NCAA tournament

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Background

You may want to read the Background on how PWR matters for tournament selection and How the “can make it at-large teams” can make it sections of NCAA tournament possibilities (with less math), if you haven’t already.

How Cornell can make it

Idle Cornell is currently sitting at #16 in the PWR, but has the possibility of landing anywhere between #13-#19. Because the Atlantic Hockey conference tournament winner will come from outside the top 16, only teams that finish in the top 15 stand any chance of an at-large bid.

So, Cornell is looking for some combination of climbing to the 13-15 range and having 3 to 5 of the conference tournaments won by teams ranked ahead of them.

Climbing in RPI ranking

Because Cornell is idle, their two levers to move their RPI ranking are to have their opponents’ (and opponents’ opponents’) win percentage rise to increase their own RPI, and to have teams that are just ahead of them (and still playing) stumble and drop below them in RPI.

Looking at Cornell’s weighted games played against teams that are still playing, Cornell has the largest potential RPI boost from Quinnipiac, Dartmouth, Harvard, and St. Lawrence winning. Of course, those teams all play each other, so it’s best to go with Quinnipiac as the champ and Harvard as runner up to get the most upward bounce. Providence winning its conference is also common in Cornell’s successful scenarios. Cornell’s weighted games played vs teams that are still playing are the following:
Quinnipiac 5
Dartmouth 2.4
Harvard 2.2
St. Lawrence 1.6
Providence 1
Ohio State 1

The other way Cornell can pass teams in PWR is to have teams immediately ahead of them have their own RPI fall enough to be passed. All of #13 Minnesota-Duluth, #14 Northeastern, and #15 Michigan Tech are active, so each losing can clear the way for Cornell to rise.

Conference tournaments won by high ranked teams

In addition to winning more PWR comparisons, Cornell needs conference tournaments won by teams ranked ahead of them. We learned above that Quinnipiac and Providence wins are key to raising Cornell’s RPI, so those two winning their conference tournaments are the cornerstone of most successful scenarios for Cornell. That leaves the following additional possibilities for the necessary 3-5 high-ranked conference tournament champions:
Big Ten – Michigan
NCHC – North Dakota, St Cloud St, Denver
WCHA – Michigan Tech

Remember, how many of those Cornell needs to happen depends on how many teams Cornell can pass in PWR.

Summary

Needing both to increase their PWR ranking (through a combination of raising their own RPI and others’ falling) and to have top teams win most conference tournaments makes this a pretty long short for Cornell, with the Big Red advancing in only about 1% of possible scenarios. Those scenarios generally include:

Increasing Cornell’s RPI (e.g. wins by Quinnipiac, Harvard, and Providence)
and/or decreasing RPI of teams directly ahead of Cornell (e.g. Minnesota-Duluth, Michigan Tech, and/or Northeastern losing)
and having enough top teams win their conference tournaments that Cornell’s final PWR rank is included at-large (e.g. Quinnipiac, Providence, and Michigan as winners)

Example of Cornell making it from #15
http://pwp.uscho.com/rankings/pairwise-predictor/?uniq=pwp_56e7130347abe

Example of Cornell making it from #13
http://pwp.uscho.com/rankings/pairwise-predictor/?uniq=pwp_56e71e9410e14

Edit – original version stated that Northeastern was idle, updated to reflect that they’re still playing.

This weekend’s big PWR movers

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Sorry for the lateness and any errors, had to crank this one out in a hurry…

More upside than you might expect

Not this week. Usually a team or two in the mid-20s have the opportunities for jumps approaching 10 spots. Plenty of teams in that range have the chance to jump about 5 spots, maybe even 6 if all goes well, but anything approaching a 10 spot jump from a team of any consequence is very unlikely.

More downside than you might expect

The high teens is a tough place to be this time of year.

#14 Penn State, idle last weekend but on the list of potential big drops two weeks ago, is in familiar territory — win 2 to stay in place, or be prepared to fall. A 10 spot drop to #24 is possible.

#15 Minnesota-Duluth, which jumped 10 spots (as predicted) with an impressive pair of wins last weekend, doesn’t have much upside potential but stands to give back its ground if it doesn’t keep up its winning streak. An 11 spot drop to #26 is possible.

#16 Minnesota, which was also on last week’s potential big drop list, finds itself there again. Two wins won’t do much for the Gophers, but losses could result in up to a 9 spot drop to #25.

#17 Michigan Tech, #18 Miami, and #20 Cornell also face potentially significant drops of up to 7-8 positions if they lose 2. They each, however, face more normal upside potential with success.

This weekend’s big PWR movers

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Looking up!

As mentioned in yesterday’s PWR outlook article, all the teams from #20 St. Lawrence to #26 Clarkson have the potential to climb into the teens this weekend. But, #25 Minnesota-Duluth and #26 Clarkson, in particular, have the potential to make huge jumps.

The #25 Bulldogs could find themselves as high as #14, a jump of 11 spots, with a sweep of #2 St. Cloud St. Most likely with a sweep is a still unusual climb of 8-9 positions to #16-17.

#26 Clarkson could find itself as high as 16 with wins over Dartmouth and Harvard, though #19-21 are more likely. The likely outcomes for Clarkson with two wins cover a surprising #16-#23 span. Clarkson’s outcome with two wins would rest a lot on other games, with the Golden Knights cheering for sweeps from Alaska Anchorage over Minnesota St, St. Cloud St over Minnesota-Duluth, Maine over Northeastern, Alaska over Michigan Tech, and Canisius over Robert Morris.

Going down?

Every team in the #14-22 range, except idle #15 Penn State, could fall more than five positions with a pair of losses. #14 Cornell, #17 Miami, #18 Michigan Tech, and #16 Minnesota are facing particularly steep falls.

Cornell could see itself fall as low as #24 with losses to Rensselaer and Union, though the spread of likely outcomes stretches a huge span of 17-24.

Miami faces a steep drop to as low as #29 if swept by Colorado College, with a still significant drop to 26-27 most likely.

Michigan Tech could find itself as low as #28 if they drop a pair to Alaska, though #24-26 are more likely.

If Minnesota gets swept by Michigan, it will face a broad range of potential outcomes that stretches as low as #25. #19-23 are all reasonably likely in that scenario.

With two weeks until conference tournaments begin, teams on the bubble need to get hot

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Picking up where I left off yesterday, in A few top teams are starting to look like locks for the NCAA tournament, those teams currently ranked #10 and below in the PWR need to do some work to ensure being positioned for an NCAA tournament bid.

If #10 Yale and below lose more than they win, they risk going into conference tournaments in the teens and having to glue themselves to this blog. #11 Boston University and #12 Harvard have very similar outlooks to Yale, each with 4 scheduled regular season games remaining, and each wanting two wins to maintain their current position.

#13 Mass.-Lowell can also maintain its current position, or slip slightly, with a pair of wins. But, that would leave them squarely on the bubble going into conference tournament play.

Because the Big Ten regular season extends later into March, #14 Penn State has 6 games remaining. But, the Nittany Lions need 4 wins to make maintaining their #14 ranking the most likely outcome.

#15 St. Lawrence has kept me in business this year, with a wild ride from #10 in my inaugural January article, down to as low as #27 at the end of January. I noted back in January that they would need to win about 9 of their last 10 to go into the conference tournament on the bubble. After a 5-0-1 run, the Saints are still positioned for a #13-14 ranking with no more losses, or a #15-16 ranking with one loss.

The #16 Minnesota Gophers have 6 games remaining, and most likely need 5 wins just to maintain that ranking going into the conference tournament.

That should be no surprise, as all the way back on January 6, I published a chart on Minnesota that suggested Minnesota needed to win about 12 of its remaining 16 to end up ranked #15-16. Including two additional tournament games, Minnesota has gone 8-4 over that period, leaving them little room for additional losses.

#17 Rensselaer, #18 Cornell, #19 Michigan Tech, #20 Miami, #21 Dartmouth, and #22 Clarkson all need to win out to be most likely to end the regular season in the #13-14 range.

#23 Minnesota-Duluth has a bit more wiggle room, with a finish in the #14-16 range likely with even just 4 wins in its remaining 6 games. The Bulldogs have the notable RPI improvement possibility, and challenge, of playing #2 St. Cloud and #3 North Dakota on the road.

In late January, I suggested that the Bulldogs would need to win 8/9 out of their final 11 to end up in the 14-16 range. In the interim, they’ve delivered a 3-2 performance, so it’s a modest upside surprise that they might be able to afford two more losses.

Playoff cutline movers

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It’s been three weeks since my first look at the 2016 cutlines, in which I identified five different tranches of teams. With most teams having played about 6 games and having about 10 remaining, some have managed to noticeably shift their fates.

The article noted that no one was safe (which is still true), but that 1-11 would be fine as long as they didn’t slump with performances approaching .500.

#9 Nebraska-Omaha (then #3) is demonstrating just such a swing, with a 1-5 run since that article. They now need to win about 5 of the remaining 10 to stay on or above the bubble going into conference playoffs.

#14 Cornell (then #7) is also teetering on the edge following a 2-3-1 run. The Big Red need to take at least 6 of the remaining 10 for a chance to stay on the bubble at the end of the regular season.

#26 St. Lawrence (then #10) has plummeted with a 1-6 run, and now needs an improbable 9 out of 10 wins to get back into at-large position.

The article also observed that the 12-19 teams were very much alive, and generally needed to win 60-80% of their games to stay positioned for an at-large bid. A 3-0-3 run has treated #7 Boston College well (rising from #16). An 0-3-2 run has treated #29 Union (formerly #18) poorly.

In the 20-26 block, which I noted is the lowest from which a team usually manages to break out for an at-large bid, #13 Denver has thus far delivered with a 5-0-1 run. The Pioneers need to keep up that success and win about 6 of the remaining 10 scheduled regular season games to go into the conference tournament on the bubble.

I noted that 27-45 weren’t mathematically eliminated, but needed a near perfect season for a shot (and that those near the top were in much better shape than those near the bottom). Of that group, #22 Miami (then #28) has come the closest with a 3-1-1 performance that still leaves them needing near perfection for a shot at the bubble.

From the 46-60 block, which I predicted needed to win the conference tournament for a bid, #27 Northeastern (formerly #49) has made the most noise with an unexpected 6-0 run (the Huskies were 3-12-4 until that run). However, even if they improbably maintain perfection over the remaining 9 scheduled games, the bubble still seems just on the edge of their reach.

Methodology

Forecasts include the results of games played through Sunday of this week, unless otherwise noted.

Resources

Current PWR Rankings (SiouxSports.com)
Current RPI Rankings (SiouxSports.com)
CHN PWR Rankings (CollegeHockeyNews.com)
USCHO PWR Rankings (USCHO.com)
Explanation of how PWR mimics NCAA tournament selection (CollegeHockeyNews.com)

Friday morning update

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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

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In previous columns this week I presented what tournament selection outcomes are most likely, every possible tournament selection outcome, and what determines the fate of teams with the most uncertainty as to outcome. Today, I’ll dive into the nooks and crannies of the most unlikely outcomes to explain how they could come about.

How Union could climb to #2 and Boston College could fall to #3

The key to swapping #2 Boston College (idle) and #3 Union is for Union to overcome BC’s current RPI advantage. That would change the comparison, currently 2-0 in BC’s favor, to 1-1 with the RPI tie-breaker going to Union. Though the current RPI gap is only .5892 for BC to .5810 for Union, it’s difficult for Union to overcome because BC isn’t playing so can’t move down much.

Obviously, the best thing Union can do to improve its own RPI is win two games. To further maximize the benefit, Union prefers to play #6 in RPI Quinnipiac over #16 in RPI Colgate (though Colgate’s better opponent win% somewhat offsets Quinnipiac’s better win%, the quality win bonus for defeating Quinnipiac tips the scales).

The next most important thing for Union’s RPI is to further improve its quality win bonus by having teams it has defeated climb in the RPI ranks. New Hampshire is the most obvious candidate, capable of climbing from its current #18 in RPI to as high as #12. In addition to the benefit it would receive from two wins, New Hampshire would be helped by losses from teams immediately above it such as #15 Colgate, #16 Cornell, #13 North Dakota, #12 Mankato, and #11 Michigan.

Finally, Union can pick up a few other quality win bonus points by having Bowling Green become a contender.

Here’s an example of one such scenario:
http://goo.gl/qs5CXO

When such factors all come together Union can climb to #2 in about .5% of remaining possible outcomes, or about 2% of the scenarios in which Union wins its conference tournament.

How Providence could miss the NCAA tournament

The two keys to Providence missing the NCAA tournament are for Providence to fall in the PWR and for conference autobids to go to teams that wouldn’t make it at large. Combined, the two can push Providence down and move the line for an at-large bid up enough such that Providence doesn’t make the tournament.

For Providence’s PWR to fall sufficiently, Providence must exit winless by losing its first game. Second, a combination of teams below Providence must rise sufficiently to further push Providence down.

Here’s one such example in which #16 Cornell, #10 St Cloud St, and #14 Vermont pass Providence, pushing it to #12. This scenario additionally features 5 of the 6 conference autobids going to teams below the cutoff, thus denying #12 Providence an at-large bid.

http://goo.gl/uevH6G

Similar factors come together for Providence to miss the NCAA tournament in about 1.3% of remaining outcomes, or about 2.6% of scenarios in which Providence loses its first game.

How St. Cloud State could miss the NCAA tournament

The principles for St. Cloud State missing are the same as for Providence — St. Cloud St’s PWR must fall and conference autobids must go to teams that wouldn’t make it at large.

Because SCSU is idle, it’s a little harder to move their PWR. The biggest lever available to do so is the quality win bonus. St. Cloud St currently enjoys QWB’s from wins over #3 RPI Union, #12 RPI Minnesota State, #13 RPI North Dakota, #16 RPI Colgate, and #19 RPI Western Michigan. Poor performances from those teams, and resulting drops in SCSU’s QWB, are key to St. Cloud St missing.

Here’s one such scenario in which each of the above loses as many as possible, pushing SCSU down to #12. This scenario additionally features 5 of the 6 conference autobids going to teams below the cutoff, thus denying #12 St Cloud St an at-large bid.

http://goo.gl/slBcnQ

Similar factors come together for SCSU to miss the NCAA tournament in only 80 of the 3,145,728 remaining possible scenarios (about .003%).

How North Dakota makes the NCAA tournament without any more wins

A quirk of this year’s revised conference tournaments is that only the NCHC has a consolation game, thus an opportunity for a team to go winless across two conference tournament games.

For North Dakota to make the tournament without any additional wins, the principles are familiar — maximize UND’s PWR ranking while having as many conference autobids as possible go to teams that would otherwise make the tournament at large.

Another quirk of consolation games is that they can end in ties. To maximize UND’s PWR without a win, North Dakota needs a loss in the opening game but a tie in the consolation game. Even with a loss and a tie, UND’s PWR is almost certain to fall, so the key is for teams around UND to perform poorly enough that UND’s fall is minimal.

There are a few ways that could happen, but here’s one such scenario in which only two teams (#18 Northeastern and #14 Vermont) rise above UND but only one (#11 Michigan) falls below, resulting in a net loss of only one position to #14. This is dependent on poor performance by #15 Colgate, #16 Cornell, and #17 New Hampshire. This scenario additionally features only two conference tournaments going to non-autobid teams, thus allowing #14 UND to get an at-large bid despite no additional wins.

http://goo.gl/HS0PSQ

Similar factors come together for UND to make the NCAA tournament in about .5% of outcomes in which UND loses the first game, or about 1.5% of outcomes in which UND loses the first game then ties the consolation game.

How Colgate makes the NCAA tournament without any more wins

The principles for Colgate making the NCAA tournament without another win are similar to those for North Dakota — maximize Colgate’s PWR and have as many conference autobids as possible go to teams that would otherwise make the tournament at large.

Because we’ve already stipulated that Colgate must lose a game, maximizing its PWR relies primarily on poor performance from the teams around it and an improvement in its quality win bonus.

There are a few ways to do that, but here’s one such scenario in which #15 Colgate passes two teams (#12 Mankato and #13 North Dakota) while being passed by only one (#17 Northeastern) resulting in a rise to #14. While this is dependent on poor performances by North Dakota and Northeastern, it is also helped by a poor performance from Cornell and a mixed performance from New Hampshire to prevent those teams from overtaking Colgate. Colgate’s PWR is also helped in this scenario by a modest rise in its quality win bonus from good performances by Ferris State, Quinnipiac, and Union. This scenario additionally features only two conference tournaments going to non-autobid teams, thus allowing #14 Colgate to get an at-large bid despite no additional wins.

http://goo.gl/WjT4bM

Similar factors come together for Colgate to make the NCAA tournament in about 2.1% of scenarios in which it loses its lone conference tournament game.

How Cornell makes the NCAA tournament without any more wins

The principles for Cornell making the NCAA tournament without winning are the same as for North Dakota and Colgate — maximize Cornell’s PWR and have as many conference autobids as possible go to teams that would otherwise make the tournament at large.

Because we’ve already stipulated that Cornell must lose a game, maximizing its PWR relies primarily on poor performance from the teams around it and an improvement in its quality win bonus.

Though #16 Cornell has a slight RPI edge on #15 Colgate (Cornell is currently one PWR rank lower because it loses the comparison between the two because of their H2H results), it has a much tougher time improving its PWR this weekend because it doesn’t have the wins versus Ferris State and Union that give Colgate the opportunity to improve its quality win bonus. While wins by Quinnipiac help a bit, Cornell’s RPI seems doomed to fall.

So, to actually rise in the PWR (#16 won’t make it at large because the AHA autobid will go to someone not in the top 16), Cornell needs more teams above it to fall than teams below it rise. Here’s a scenario in which only one team (#15 Colgate) dips below Cornell while no teams below Cornell rise, resulting in Cornell taking the #15 spot. To make the tournament from #15, this scenario also features only one team outside the top 15 winning its conference tournament.

http://goo.gl/GJlLTr

Such a set of outcomes useful to Cornell is quite unusual, occurring in only 182 of the 1,572,864 scenarios in which Cornell loses its lone game (about .01%).

A more in-depth look at the at-large chances for teams on the bubble

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With this year’s simplification of PWR (primarily moving the good wins bonus into RPI), there are far fewer fluky outcomes that push teams up or down. Teams trying to make the tournament from the #12-16 range are looking for two things:

maximizing the number of teams that make the tournament on the basis of PWR
maximizing their own PWR

The first is accomplished by minimizing the number of autobids that go to teams with lower PWRs.

Because of the new PWR’s simplicity, the second is usually accomplished by teams with rankings near the team in question is losing. If the team in question wins, it is helped by teams around it losing to clear a path. If the team in question loses, it is mostly focused on teams below it also losing so as not to be overtaken.

PWR Rankings (SiouxSports.com)

Autobids to high ranking teams

If you think of the tournament as having 6 autobids (for conference tournament winners) and 10 at-large bids, then each autobid that goes a team that would have made it at-large essentially frees up the at-large bid for the next lower ranked team.

So, if four autobids go to teams that otherwise would have made the tournament, then #14 in PWR will get a bid. If only two autobids go to teams that otherwise would have made the tournament, then only through #12 in PWR will get a bid.

So, the teams on the at-large bubble of #12-#16 want as many conferences tournaments as possible to be won by teams that were going to make the tournament regardless. Those are:

Big Ten

#1 Minnesota
#5 Wisconsin

ECAC

#3 Union
#6 Quinnipiac

WCHA

#4 Ferris State

Hockey East

#7 Mass.-Lowell
#8 Notre Dame
#9 Providence

#2 Boston College and #10 St Cloud St are idle.

As teams like #11 Michigan and the teams featured in this article advance to the point that they’re pretty much guaranteed a tournament spot, it may similarly benefit the featured teams for those teams to continue to succeed and claim conference championships. However, the Atlantic Hockey tournament autobid guarantees that at most the top 15 in PWR will make it, so teams featured in this article have to be cheering for at least some of the others to lose.

Minnesota State

#12 Minnesota State makes the tournament in 54% of scenarios in which it wins 1 game and 6.4% of scenarios in which it has no wins.

Minnesota State is most helped by #16 Cornell, #17 New Hampshire, #13 North Dakota, and #15 Colgate losing (note that #14 Vermont is not playing).

Minnesota State, like all teams featured in this article, is also helped by autobids going to highly ranked teams as described above.

North Dakota

#13 UND makes the tournament in 42% of scenarios in which it wins 1 game and .5% of scenarios in which it has no wins (a tie in the consolation game seems to be required).

Because the NCHC has a consolation game, UND could exit the tournament with one win either by winning then losing, or by losing then winning. The two have slightly different outlooks.

If UND wins its first game, it makes the tournament in about 46% of scenarios in which it loses the championship game. Most useful to UND in this situation seems to be #12 Minnesota State, #16 Cornell, #15 Colgate, and #11 Michigan losing (note that #14 Vermont is not playing).

If UND loses its first game, it makes the tournament in about .5% of scenarios in which it ties the consolation game or about 36% of scenarios in which it wins the consolation game. Most useful to UND in this situation seems to be #17 New Hampshire, #21 Ohio State, #16 Cornell, and #15 Colgate losing (note again that #14 Vermont is not playing).

North Dakota, like all teams featured in this article, is also helped by autobids going to highly ranked teams as described above.

Vermont

#14 Vermont has no opportunity for an auto bid but makes the tournament at large in 69% of scenarios.

Because Vermont is idle, it’s counting on others to clear it a path. Its own PWR is most helped by losses from #11 Michigan, #15 Colgate, #16 Cornell, #12 Mankato, and #13 North Dakota.

Vermont, like all teams featured in this article, is also helped by autobids going to highly ranked teams as described above.

Colgate

#15 Colgate makes the tournament in 77% of scenarios in which it wins a game, but only 2% of scenarios in which it has no wins.

Colgate is most helped by #12 Minnesota State, #16 Cornell, #13 North Dakota, and #17 New Hampshire losing (remember that #14 Vermont is idle).

Colgate, like all teams featured in this article, is also helped by autobids going to highly ranked teams as described above.

Cornell

#16 Cornell makes the tournament in 85% of scenarios in which it wins a game, but under 1% of scenarios in which it has no wins.

Cornell is most helped by #15 Colgate and #13 North Dakota losing (remember that #14 Vermont is idle).

Cornell, like all teams featured in this article, is also helped by autobids going to highly ranked teams as described above.