## Weekend’s Pairwise Ranking outlook

Last week I wrote an update on the break lines for NCAA tournament chances. Because it targeted the end of the regular season, its predictions still hold. So, this week I’ll take a shorter term look at what’s likely to happen this weekend.

## What the forecasts really mean (there is some math)

These forecasts are not yet to the precision of completely mathematically eliminating outcomes. The number of possible outcomes is still so large that it wouldn’t be as useful to (and I can’t!) go into the detail of what’s mathematically possible and not until the conference tournaments.

Instead, I’ll refer to outcomes with at least a 10% probability as “likely”, and outcomes with a 1% probability as something that “could happen”. That suggests that one time out of ten, you’re going to see a “could happen” outcome instead of a “likely” one. It also suggests that one time out of a hundred you’re going to see an outcome outside what I even declared “could happen”.

The probabilities of possible outcomes do have a bell-shaped distribution, as you’ll see in the graphs, so when I say “a range of #10-#13 is likely” it’s usually most likely (over a 50% chance) of being in the middle of the range, #11-#12 in this case.

## Who could fall to the bubble

#7 Quinnipiac and #8 Mass.-Lowell seem relatively safe, neither being likely to drop below #13 even if swept (though drops as low as #14 could happen for each).

#9 Northeastern is the highest ranked team with an obvious chance to fall to the bubble, with a drop to #13-#16 likely if swept.

#10 UND (#12-#14 likely and #16 could happen), #11 Cornell (#17-#19 likely and #21 could happen), and #12 Vermont (#16-#19 likely and #20 could happen) face similar downsides to the bubble if swept.

## What will the bubble teams do?

Now it gets interesting. While the bubble teams can all fall off the bubble if swept or shore up their position with a sweep, those on the upper part of the bubble seem to face more downside while those on the lower part of the bubble seem to face more upside.

#13 Colgate is likely to fall to #18-#20 if swept (as low as #21 could happen), rise to #10-#13 with a sweep (as high as #9 could happen), or stay about the same or fall slightly with a split.

Similarly, #14 Michigan is likely to fall to #18-#20 if swept (as low as #22 could happen), rise to #10-#12 with a sweep (as high as #9 could happen), or stay about the same or fall slightly with a split.

#15 Notre Dame only plays one game this weekend. A win would result in a likely climb to #10-#13 (as high as #9 could happen), while a loss would result in a likely fall to #15-#17 (as low as #18 could happen).

#16 Providence would likely climb to #10-#13 with a sweep (as high as #9 could happen), but is also likely to rise modestly to #13-#15 with a split.

## Teams that could climb onto the bubble

#17 Maine would likely climb to #11-#14 with a sweep (as high as #10 could happen).

#18 Yale would likely climb to #13-#16 with a sweep (as high as #12 could happen). But, for Yale a split is likely to result in a modest drop to #18-#20.

#19 Minnesota State and #20 New Hampshire can just reach the bottom of the bubble, with rankings ranging from #15-#17 and #16-#18 respectively likely with a sweep (#13 and #14 could happen for each respectively).

## 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.

## Update on each team’s tournament chances

As the regular season pushes into its final month, I’ll do more frequent updates on who’s a lock for an at-large bid and who’s out of the running.

## Calculation details

The way I judge that is by forecasting each team’s Pairwise Ranking, and determining how likely the team is to finish in the top 12.

Readers may recall previous controversy about the PWR rankings, which was apparently resolved last weekend when USCHO adopted the formula CHN has been using. This site continues to use that same formula as the basis for its predictions.

## End of regular season outlook

Last week I stated that #8 Mass.-Lowell was the last lock, which remains true this week. Their chance of falling to #13 or below by the end of the regular season has fallen to about 2.5%. Just below them, #9 Northeastern is the highest ranked team with a serious chance of dropping out, with about a 24% chance of falling to #13 or lower.

The dividing line for controlling their own destiny appears to around #19 at first glance, in that #19 Mankato can clearly make it while #20 New Hampshire is in trouble.

But, at this level and point in the season, the different number of games remaining is starting to matter. #21 Yale and #22 Denver both stand noticeably better chances than Yale.

Finally, the “remote mathematical chance of making it if they close out the season perfectly” line has climbed to about #27 Alaska Anchorage. #28 Nebraska-Omaha and below need conference tournament success to make the NCAAs.

## 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.

## PWR formula uncertainty resolved

The previously dueling PWR implementations (see Uncertainty around PWR calculation) seem to have been resolved for now. This weekend, USCHO changed the formula it uses to calculate PWR so its tables now match those on CHN and SiouxSports. Previously, USCHO had weighted only the win% component while the others had weighted all components (win%, opponents win%, and opponents opponents win%).

As of right now, all three tables are identical:

Reading USCHO’s change as a sign that they received confirmation that their previous method was incorrect, this is great news for college hockey fans as it lifts the uncertainty that was previously hanging over the dueling implementations.

## One month outlook for the end of the regular season

With conference tournaments just a month or so away, this week I’ll take another look toward the end of the regular season — who’s a lock for an at-large bid, and who’s out of the running.

## PWR calculation details

Readers of this blog probably already know that the RPI and PWR formulas for hockey changed this year. As I mentioned in a previous column—Dueling PWRs—there are currently two different interpretations of the new formulas. USCHO and CollegeHockeyNews implement the home/away weightings for RPI a bit differently.

From this post forward, unless otherwise stated the calculations referred to on this blog match the CHN implementation. Though I think that the more correct implementation, I will continue to monitor the situation.

## End of regular season outlook

#1 Boston College and #2 Minnesota are likely duking it out for the top two rankings, unless one has a serious slump.

#8 Mass.-Lowell is the highest ranked team with a reasonable chance (about 7%) of falling to #13 or lower, so the top 8 can feel reasonably secure that they’ll be going into the conference tournaments in place for an at-large bid.

From #8 Mass-Lowell to about #19 Yale, the teams control their own destinies. Winning puts them in position for an at-large bid, losing does not.

#20 Clarkson through #29 Nebraska-Omaha have outside chances of climbing into the top 14 or so with stellar performances. They’re not mathematically eliminated, but would need nearly flawless runs to climb into position for an at-large bid.

#30 Brown and below are extremely unlikely to be in position to make the NCAA tournament at large going into the conference tournaments, so their best hopes for a bid would be winning their conference tournaments.

## Methodology

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.

## Pairwise Ranking outlook for this weekend

Quite a few teams have an opportunity to make big moves this weekend.

Before I jump into the weekend’s forecast, be warned that some dispute has arisen in the college hockey online media world over the proper implementation of the NCAA’s 2014 revisions to the tournament selection process (see Uncertainty around PWR calculation). These forecasts currently assume the USCHO PWR formula.

## Review of last week’s forecasts

Last week I highlighted the teams poised to make the biggest moves with extraordinary performances (both positive and negative).

Of Yale, Clarkson, Michigan, Minnesota-Duluth, New Hampshire, Western Michigan, and Michigan State, only New Hampshire delivered the necessary extraordinary performance. As predicted, the then #22 Wildcats experienced a significant move up, landing at #14 going into this weekend.

## Poised to climb

A few teams in the 20s face particularly lopsided upside opportunities this weekend.

#23 Ohio State is most likely to jump to 15-18 with a sweep (though as high as 13 is plausible)
#26 Brown is most likely to jump to 17-18 with two wins (though as high as 14 is plausible)
#20 Yale is most likely to jump to 12-14 with two wins (though as high as 11 is plausible)

## Poised to fall

Just inside the bubble seems to be a bad place to be, as a few teams in the teens face particularly lopsided downside opportunities this weekend.

#13 Minnesota-Duluth is most likely to fall to 19-20 if swept (though as low as 23 is plausible)
#14 New Hampshire is most likely to fall to 21-22 if swept (though as low as 25 is plausible)
#15 North Dakota is most likely to fall to 22-23 if swept (though as low as 26 is plausible)
#16 Notre Dame is most likely to fall to 23-24 if swept (though as low as 27 is plausible)

## Could go either way

The #11 Wisconsin Badgers face the biggest combined upside/downside. Though their most likely outcomes are climbing up to 7-8 with a sweep or falling to 18-20 if swept, as high as #4 or as low as #23 after this weekend are plausible.

## Methodology

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.

## Uncertainty around PWR calculation

Some uncertainty apparently still persists around the NCAA’s new tournament selection criteria for men’s hockey.

CollegeHockeyNews unveiled its first Pairwise Rankings for the season (CHN PWR), and their implementation is a bit different from USCHO’s (USCHO PWR).

The differences aren’t just discrepancies in the underlying game data (e.g. neutral ice vs. not), but instead seem to be modest differences in the way the game weights are applied. CHN acknowledged that:

“But while the committee was transparent in how the weightings and Bonus were supposed to be done in general, it didn’t completely explain how the numbers were supposed to be applied against the existing RPI. There are different ways to do it.

Therefore, different sites are showing slightly different results. And we’ve been fielding constant questions as to why ours doesn’t match what’s being shown elsewhere.”

This PWR on this site has mimicked what USCHO has been publishing, though I’ll certainly keep an eye on developments.

Hopefully people in the know can help everyone converge on a common understanding of the new criteria, or there could be some surprises come tournament time for the first time in many years!