Tag: monte carlo

UND closes in on NCAA tournament berth

#6 UND has moved much closer to clinching a tournament berth. Winning at least 2 of the remaining 6 would have UND more likely than not in the top 13 in PWR going into the conference tournaments. Even if UND won only 0 or 1 of its remaining games, an at large berth would still be within reach with a good showing in the conference tournament.

Given the above, UND faces a somewhat predictable situation this week of being able to make a small gain with a sweep over Denver, stay pretty much the same with a split, or fall a bit more if swept.

The final weeks of the regular season

Only three teams can’t fall from being a TUC by the end of the regular season: #1 Quinnipiac, #2 Minnesota, and #3 Miami.

Quinnipiac (PWR Details) is particularly safe, even a catastrophe seems to only drop them 3 spots. Winning only 2 of their remaining 4 would leave them with only about a 10% chance of falling from the #1 spot. Their .7778 vs. TUCs is unassailable, and .5828 RPI is miles ahead of #2 Minnesota .5658. To put that RPI into perspective, if Minnesota swept its final 6 games their RPI would only rise to about .5738 (Minnesota RPI details).

#2 Minnesota and #3 Miami each also have good RPI leads over the teams chasing them, coming in at .5658 and .5529 respectively, with #4 New Hampshire at .5477.

However, #2 Minnesota and #3 Miami aren’t alone in vying for the #2 PWR ranking at the end of the regular season. A staggering 9 teams could claim that position: #2 Minnesota, #3 Miami, #4 New Hampshire, #5 Boston College, #6 North Dakota, #7 MSU-Mankato, #9 St. Cloud St, #11 Denver, and #14 Mass.-Lowell.

Interestingly, the list of teams that can finish top 4 isn’t much longer, add only #8 Western Michigan and #10 Niagara to the list.

The team with the most upside potential for the remaining regular season is #29 Providence, which can climb to #8. That’s mostly just because big upward moves are possible from that low a rank (#28 Colgate and #30 Colorado College could each rise to #14).

The team with the most downside potential for the remaining regular season is #13 Boston University (BU PWR details), which could fall to not being a TUC. #13 BU is only #20 in RPI, and is already losing most of its common opponents comparisons.

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.

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Small rankings moves likely for UND in bye week

Idle #6 North Dakota could make some small moves in the Pairwise Rankings (PWR) this week, with anything between 5 and 8 being reasonably likely.

Key games for UND

Matchups that most affect UND’s PWR
Matchup Number
of wins		 Effect on
UND’s PWR
Ohio State over Western Michigan (1 of 2) 1.13
Ohio State over Western Michigan (2 of 2) 1.05

The reason those games (and others) are important can be deduced by studying the PWR comparison details for UND.

UND’s downside potential

Western Michigan is clearly the bigggest threat this week, with UND currently winning the comparison on the back of a very narrow .5470 to .5454 RPI lead.

Niagara is similarly knocking on the door, losing the comparison to UND only on the basis of Niagara’s RPI of .5381.

Finally, Yale could take the comparison with UND by defeating both Union and Rensselaer, thus raising their TUC record to .5667 (vs. UND’s .5470).

UND’s upside potential

Though New Hampshire is winning the comparison to UND 3-0, two of those criteria would flip to UND if New Hampshire got swept. UND could take both RPI and TUC.

Other interesting teams this week

Smallest range of outcomes — #1 Quinnipiac (#1-#1). Sorry Gopher fans, not this week.

Of the teams that have a two comparison or less deficit with Quinnipiac [Quinnipiac PWR comparisons] (only North Dakota, MSU-Mankato, Niagara, Wisconsin, Providence, Holy Cross, and Robert Morris), none can hope to catch their RPI of .5885 any time soon.

Largest range of outcomes — #23 Rensselaer (#13-#32), #25 Colgate (#13-#32), and #20 Merrimack (#12-#31)

Looking at Rensselaer PWR comparisons, Colgate PWR comparisons, and Merrimack PWR comparisons, all have fairly middling RPIs in the .5100s and quite a few comparisons being decided by RPI. That creates a lot of opportunity for both upward and downward movement from that part of the comparison table.

Most upside potential — #31 Robert Morris (#16–non-TUC)

Robert Morris’s story is simple (Robert Morris PWR comparisons): The TUC criterion hasn’t come into play for them yet because they don’t have 10 games and a sweep this weekend (at least a win seems necessary to stay a TUC) would give them an impressive .700 record vs. TUCs. That would immediately flip a lot of the 1-1 comparisons, and some of the 0-2’s vs teams that Robert Morris can overtake on RPI.

Most downside potential — #14 Dartmouth (#9-#27), #18 Nebraska-Omaha (#17-#31)

Dartmouth is tricky; just looking at Dartmouth’s PWR comparisons, it’s not immediately obvious why #14 Dartmouth has so much more downside potential than #15 Alaska [Alaska PWR comparisons], as RPIs and TUCs are similar. Fortunately, the simulations keep track of which games have the biggest effects on each teams, and there’s a valuable clue there:

Matchups that most affect Dartmouth’s PWR
Matchup Number
of wins		 Effect on
Dartmouth’s PWR
Dartmouth over Colgate   5.55
Dartmouth over Cornell   3.94
Brown over Rensselaer   1.56
Brown over Union   1.52
Miami over Notre Dame (2 of 2) 0.98
Lake Superior over Alaska (2 of 2) 0.84
Minnesota over Wisconsin (2 of 2) 0.80
Minnesota over Wisconsin (1 of 2) 0.61
Massachusetts over Mass.-Lowell (1 of 2) 0.58
Lake Superior over Alaska (1 of 2) 0.52
Robert Morris over Niagara (2 of 2) 0.51

The first thing that jumps out is how much Dartmouth wants Brown to win. It turns out that Brown is in danger of not being a TUC, and Dartmouth has 3 wins vs. Brown. Losing those wins would drop Dartmouth’s TUC record from .5333 to .4167. That gives Dartmouth significantly more downside potential with a couple losses than similarly ranked teams with similar RPIs.

Nebraska-Omaha [PWR comparisons], on the other hand, just has a miserable TUC of .3824. Alaska-Anchorage is a weak enough opponent that getting swept would push UNOs RPI from .5196 to about .5086. That would be enough on today’s RPI chart to drop UNO from #17 to #27 in RPI, certainly flipping a lot of comparisons given the poor TUC record. UNO seems to need a sweep not to fall.

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.

Resources

UND has opportunity to rise in rankings

#10 UND has fallen to a much more natural position in the Pairwise Rankings (PWR) than its lofty perch of the last couple weeks. If UND wins, its ranking goes up; it UND loses, its ranking goes down.

Follow up on last week’s predictions

In last week’s Weekly rankings analysis column I observed (and the outcomes were) that:

  • UND had more downside than upside and was likely to slump with anything less than a sweep. (Another one point weekend later, UND indeed fell from #6 to #10, right between the predicted win 1 and win 0 curves).
  • Mass.-Lowell similarly had more downside than upside, with only the comparison with UND as a possible gain and six comparisons as possible losses. (Mass.-Lowell took 3 of 4 points for the weekend and stayed #7 by taking the comparison with UND but losing the comparison with Miami).
  • Ferris St had big movement potential from #21 with a sweep or being swept (Ferris St split the weekend and dropped just one spot to #22).
  • Alaska had big movement potential from #18 (Alaska swept the weekend and climbed to #12, a much higher PWR than RPI).
  • Cornell had big movement potential from #22 (Cornell lost two and dropped to #27).
  • Dartmouth had the most downside potential from #9 (Dartmouth split the weekend and dropped to #15).

Bottom-line: this stuff works and reveals useful information that would be difficult to uncover browsing the comparison tables. But enough back-patting.

Whither UND?

In my first PWR post two weeks ago, I noted that UND was artificially high at #7 and needed to win about 6 of 14 remaining regular season games to finish in the at-large bid range of 13-15. UND has since gone 0-2-2 (.250) but dropped only to #10 in PWR.

UND still has a ton of downside potential if they continue to lose, but things are evening up a little with some upside potential for a sweep.

In the longer run view, the rough equivalent of 1 win has left UND needing about 5 wins in the remaining 10 games to be most likely to finish the regular season in the at-large bid range. Remember, though, that big moves can occur with a winning streak in the conference tournament.

Outcomes that most affect UND’s PWR this week
Outcome Average effect
on UND’s PWR
UND over Wisconsin (2 of 2) 11.57
UND over Wisconsin (1 of 2) 6.84
Holy Cross over Canisius (2 of 2) 1.74
Holy Cross over Canisius (1 of 2) 1.59
Minnesota-Duluth over Denver (2 of 2) 1.30
Michigan Tech over Nebraska-Omaha (2 of 2) 1.10
Minnesota-Duluth over Denver (1 of 2) 1.04
Michigan Tech over Nebraska-Omaha (1 of 2) 0.89
Bentley over Niagara (2 of 2) 0.76
Ferris St over Western Michigan (2 of 2) 0.71
Bentley over Niagara (1 of 2) 0.56
Rensselaer over Dartmouth 0.56

A lot of those are obvious with a quick glance at UND’s PWR comparisons.

  • Holy Cross is in danger of not being a TUC, but UND needs its 2 wins over the Crusaders to contribute to its mediocre record vs. TUCs (currently .500).
  • Denver could pass UND in RPI with a better weekend than North Dakota. Also, Duluth becoming a TUC seems to give UND a little juice (probably due to UND’s 1-0-1 record vs the Bulldogs, better than UND’s record vs current TUCs).
  • Nebraska-Omaha’s RPI could climb to about .539 with a sweep this weekend, which could allow them to take the comparison if UND also drops.
  • Similarly, Niagara and Dartmouth could take their comparisons with UND with a climb in RPI and a drop by UND.
  • Finally, UND barely loses the comparison with Western Michigan on the basis of RPI. Outperforming the Broncos this weekend would probably flip that.

Teams to watch

Biggest potential outcome (likelihood greater than 1%) spread of the week goes to UND (likely to come out between #5 and #23) and Dartmouth (likely to come out between #6 and #24).

Biggest upside potential goes to Nebraska-Omaha, which could climb a staggering 13 slots from #21 to #8 if everything went their way. This is mostly due to their reasonably strong RPI for a #21 team.

Biggest downside potential goes to Mass.-Lowell, which could drop 14 slots from #7 to #21 if everything went wrong. The looming disaster for Mass.-Lowell is clearly their miserable .250 TUC record coming into play when they hit 10 games vs. teams under consideration. It won’t happen this week without a little movement on the cliff (Maine isn’t a TUC), but it will eventually if they don’t gain some wins vs. TUCs.

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.

Resources

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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