Tag: PWR

A first look at the NCAA hockey PairWise Rankings (PWR)

January is the typical time to start paying attention to the PairWise Rankings (PWR) that mimic that NCAA’s tournament selection criteria. UND is currently ranked #7, and is poised to move this weekend with a pair of contests against arch-rival Minnesota.

North Dakota – Gophers

Both are highly ranked, Minnesota #4 and UND #7. However, the weekend’s games have only minor short term implications for Minnesota, but more significant short term implications for North Dakota if either team sweeps.

The following charts are the forecast likelihoods of each PWR ranking as of next Monday (Jan 21) for each team based on its own performance this weekend.

North Dakota’s remaining season

North Dakota seems pretty well positioned to make the tournament. Going about .500 over the rest of the regular season would likely leave UND in position for an at-large bid going into the conference tournaments.

The following chart contains the forecast likelihoods of each PWR ranking as of the end of the regular season for UND based on its own performance over the remainder of the regular season.

Minnesota’s remaining season

“Numbers” on the USCHO forum asserted that Minnesota’s 8-0-0 non-conference record particularly shores up their PWR ranking because of the Common OPponents criterion.

It seems true that running the rest of the season even under .500 would still leave Minnesota in a good position heading into the conference tournaments. Minnesota’s strength in COP does help, but once TUC is in play you still need to win one more criterion to take the comparison. Opponents’ strength held constant, going .500 would drop Minnesota’s RPI to about .555, a far more pedestrian number. Minnesota’s respectable TUC helps them in that regard, further supporting their lofty rating down the road.

TUC is coming into play

A lot of teams are just starting to hit 10 games vs. other Teams Under Consideration (TUCs), bringing that criterion into play in as-of-now PWR calculations (which, frankly, additionally reveals how absurd as-of-now calculations are; because we know most of these teams will hit 10 games vs. TUCs by the end).

The top 10 teams’ records vs TUCs are somewhat predictive:

Team Record vs TUCs
1. New Hampshire .7500
2. Boston College .6667
3. Quinnipiac .8077
4. Minnesota .6875
5. Notre Dame .6364
6. Boston University .4000
7. North Dakota .5000
8. Denver .5938
9. Yale .5000
10. Miami .6667

Indeed, Minnesota’s good TUC record is part of what helps insulate it a bit from big downward movement. But that’s true of all the top few teams.

The two most exceptional seem to be Quinnipiac, whose TUC record does seem to provide a fair amount of insurance against big downward moves; and Boston University, whose low TUC means it will take a strong effort down the stretch to maintain their current ranking.


Boston University is a particularly interesting case. Despite their dismal TUC, they’re currently #6 in the PWR on the back of the #1 strength of schedule in RPI. Looking at BU’s RPI details, it would take a noticeable increase in winning percentage (to about .800 over the remainder of the season vs. about .632 to date) to offset their upcoming decline in SOS and keep RPI constant. Short of that, expect BU’s RPI to fall and their PWR with it.

Of course, those TUC records can change not only based on teams’ own upcoming performances, but as former opponents play additional games that may add or remove them from being “under consideration”.

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.

Closing remarks

This is my first stab at firing up the PWR simulations and writing this sort of post this year. It does always seem to take me a little while to get back into the groove, so please point out any errors, questions, or points that need clarifying.

Though I started with an analysis of UND’s position, let me know if there’s anything else in particular that you’d like to see.

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UND facing #5 UMD has opportunity to climb in the PWR

UND has the potential to make a big move in the PairWise Rankings (PWR) if the Sioux can upset the struggling Bulldogs.

With tie-breakers, UND is currently #15 in the PWR. (Current PWR)

A sweep would most likely put UND in the 8-9 range (about 61% likelihood), with 7-10 probable (about 91%).

Even with a split, UND stands a fair chance of climbing a little. UND would climb to 12 or better in about 17% of scenarios, 13-14 in about 48%, stay at 15 in about 21%, and fall to 16 or lower in about 11%.

Looking ahead to the end of the regular season

UND’s regular season outlook improved slightly over its weekend off. It’s starting to look possible to lose three more before conference tournament time and still be well situated for making the NCAA tournament.

What to watch this weekend (other than UND)

Minnesota defeating Denver would be a big help to UND. UND could easily take the comparison with Denver by flipping both TUC and COP.

Alabama-Huntsville over Miami also has a big effect on UND’s ranking. Presumably this is a defensive play, preventing Miami from the taking the lead in RPI and the comparison, should UND falter this weekend.

There are a number of lesser series that seem to have RPI implications that could help UND this week:

  • Bowling Green over Northern Michigan
  • Michigan over Michigan State (only helpful if they sweep)
  • Alaska-Anchorage over Mankato (only helpful if they sweep)
  • Alaska over LSSU (only helpful if they sweep)
  • Western Michigan over Ohio State (only helpful if they sweep)
  • Ferris St over Notre Dame (only helpful if they sweep)

The only surprise in that list is AA over Mankato, since neither is nor is threatening to become a TUC. I think it’s an RPI play, AA is an opponent of UND’s while Mankato isn’t, yet. If that’s what’s happening, this is one of those outcomes that’s helpful for a week, but doesn’t matter in the long run.

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UND’s road to the NCAA tournament is getting steeper

UND’s lackluster performance since A first look at the PairWise Rankings and UND’s tournament possibilities has made the road to the NCAA tournament a little bit steeper.

That article predicted that UND could lose only 4 more of its remaining 15 regular season games to end the regular season comfortably at #13 or better in PWR. UND having gone 3-2 over the first 5 of those games, the new forecast shouldn’t be surprising.

It looks like UND needs 8 wins in the remaining 10 games to stand a good shot of finishing in the top 13. Also remember that this prediction is for the end of the regular season, UND could easily finish in the mid teens and still climb to the high teens during the WCHA tournament.

UND this week

The current PWR table shows UND in sole possession of 19th. The opportunities for movement this week are pretty big:

  • A sweep leads to the most indeterminate outcome — UND most likely (75% chance) would land in the 15-18 range, though a bit higher or lower are distinctly possible.
  • A split would likely leave UND in the 19-20 range.
  • Getting swept would most likely land UND in the 22-25 range.

It’s also a big week for UND’s opponent, also fighting for a playoff spot, the Wisconsin Badgers. They’re looking forward to a likely PWR of anywhere from #18 to #28, depending on their performance this weekend.

On the cliff’s edge this week — Mass.-Lowell

Minnesota’s big drop last week was exactly as forecast, which got me looking for this week’s “Minnesota”. The team sitting on the edge of a cliff this week is definitely Mass.-Lowell. Currently #3 in the PWR, they would need to win all three games in the coming week to be likely to finish #2 or #3 (84% chance). Get swept? #14-15 are most likely, with #16 or #17 a real possibility.

Series of the week — Northern Michigan vs. Miami

There’s really only other series this week that could lead to even more PWR movement than the UND/UW series — Northern Michigan (#10) vs. Miami (#15). Northern Michigan’s likely outcomes range from #3 to #17, while Miami’s range from #6-#19.

A few technical notes

The PWR rankings on USCHO have been different from all other source (CHN, TBRW, SiouxSports) today. That’s because USCHO currently isn’t dropping “harmful wins” from its RPI calculation. I haven’t heard of any such change in the calculation, so will assume that USCHO just made a mistake and that the calculations here are right.

This week’s projections are as of Monday Jan. 30, including any games on Sunday but not on Monday. It’s getting tricky to pick an “as of” date when there are college hockey games most days of the week in the coming two weeks.

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A first look at the PairWise Rankings and UND’s tournament possibilities

UND fans accustomed to slow starts might be tempted to brush off this season’s slow start as inconsequential, but should they?

January is the typical time to start paying attention to the PairWise Rankings (PWR) that mimic that NCAA’s tournament selection criteria. UND’s current PWR ranking is #19, which would not be sufficient to make the NCAA tournament, but the season isn’t over, so how much does that matter?

Some humorously early bracketology discussions in recent years led me to write an essay a couple years ago, When to start looking at PWR. In short, PWR is so volatile as to be almost meaningless before January; also, PWR doesn’t become a very good predictor of the end-of-season PWR (the only one that matters) until March. So, rather than write much more about today’s PWR ranking, I’ll spend the rest of this article focusing on where UND’s PWR could be in March.

UND’s 2011-12 PWR vs. past performances

UND’s current PWR ranking of 19 is the second worst for a Hakstol-era UND team at this time of year.

2008 – non-TUC (climbed to #5 at the end of the WCHA play-in round with a 15-2-3 run, fell to #8 after getting swept out of the WCHA tournament)
2006 – #18 (climbed to #10 at the end of the WCHA play-in round with a 12-2-4 run, to #7 with a win and a loss in the WCHA tournament)

Each of those teams made the NCAA tournament, but only after a phenomenal second half run.

Where will UND finish?

Mathematically, UND can still finish the regular season #1 overall even if they lose one more game.

The above graph is the distribution of rankings, given how many of its remaining games wins.  So, for example, the gray “Win 11” curve shows that UND is quite likely to have a PWR ranking of 10-13 at the end of the regular season if they win 11 of their remaining games.

Making the NCAA tournament is a distinct possibility. If you guess at a PWR ranking of 13 as the cutoff for making it at large (it depends how many lower-ranked teams get autobids, thus taking one of the 16 slots), winning 8 or 9 of the remaining 15 games could be sufficient with a decent WCHA tournament run.

Technical note on PWR (change in COP)

For students of PWR, you should note one change in the way PWR is calculated this year.

Rather than the common opponents (COP) criterion simply being a sum of each teams’ records vs all common opponents, it’s the average of each teams’ record vs each common opponent. That’s a subtle distinction, so I’ll try to illustrate it with a hypothetical example which highlights the reason they made this change.

Suppose these outcomes:

UND vs Sacred Heart: 5-0-0
UND vs Ohio State: 0-1-0

Minnesota vs Sacred Heart: 1-0-0
Minnesota vs Ohio State: 3-2-0

Old COP would be: UND 5-1-0 (.8333) / Minnesota (.6667)
New COP would be: UND .500 (average of 100% and 0%) / Minnesota .800 (average of 100% and 60%)

In short, the old formula rewarded UND for having more games against the easier opponent, despite having been winless vs the other common opponent. The new formula gives Minnesota the COP comparison for having winning records vs. both opponents.

I just stumbled on this, how is PWR being predicted?

I simulate the outcomes of the remaining games in the season a million or so times, using KRACH to predict the likelihood of each team winning in each iteration. That’s enough simulations to ensure that even the most unlikely possibilities occur at least once. For each simulated season I calculate what PWR would result from that set of outcomes. I then use the aggregate results of those simulations to assign a likelihood to a particular outcome, that is, if UND finishes #3 in PWR in 370,000 of 1,000,000 simulations, I say that UND has about a 37% chance of finishing #3.

Closing remarks

This is my first stab at firing up the PWR simulations and writing this sort of post this year. It does always seem to take me a little while to get back into the groove, so please point out any errors, questions, or points that need clarifying.

Though I started with an analysis of UND’s position, let me know if there’s anything else in particular that you’d like to see.

Resources