Last Modified: 2011 October 9
Joe Schlobotnik / joe@amurgsval.org
URL for this frameset: http://www.slack.net/~whelan/tbrw/tbrw.cgi?1998/pairwise.980105.shtml
Let's take a run through the NCAA Tournament selection procedure and see how the NCAAs would be set up if they were held right now. Using the results from the Division I Composite Schedule on US College Hockey Online, I've calculated the selection criteria, and here are the results of the Pairwise Comparisons among the 25 Teams Under Consideration. (BTW, USCHO has a page with the current RPI, independently calculated, although since theirs is continuously updated, it won't agree with the figures here for long.)
Team PWR RPI Comparisons Won 1 Mich State 24 .589 BUNHNDMiMmYaSCPvCgWiBCCCNMPnMeNELSCrNtMDRPCkMLMT 2 Boston Univ 23 .624 NHNDMiMmYaSCPvCgWiBCCCNMPnMeNELSCrNtMDRPCkMLMT 3 New Hampshire 21 .629 NDMiMm SCPvCgWiBCCCNMPnMeNELSCrNtMDRPCkMLMT 4 North Dakota 21 .609 MiMmYaSCPvCgWiBCCCNMPnMeNELSCrNtMDRPCkMLMT 5 Michigan 20 .602 MmYaSCPvCgWiBCCCNMPnMeNELSCrNtMDRPCkMLMT 6 Miami 19 .581 YaSCPvCgWiBCCCNMPnMeNELSCrNtMDRPCkMLMT 7 Yale 19 .577 NH SCPvCgWiBCCCNMPnMeNELSCrNtMDRPCkMLMT 8 St Cloud 17 .578 PvCgWiBCCCNMPnMeNELSCrNtMDRPCkMLMT 9 Providence 16 .558 CgWiBCCCNMPnMeNELSCrNtMDRPCkMLMT 10 Colgate 15 .573 WiBCCCNMPnMeNELSCrNtMDRPCkMLMT 11 Wisconsin 14 .565 BCCCNMPnMeNELSCrNtMDRPCkMLMT 12 Boston Coll 13 .550 CCNMPnMeNELSCrNtMDRPCkMLMT 13 CO College 11 .547 NMPnMeNELSCr MDRPCkMLMT 14 Northern Mich 10 .538 PnMeNE CrNtMDRPCkMLMT 15 Princeton 10 .537 MeNELSCrNtMDRPCkMLMT 16 Maine 9 .534 NELSCrNtMDRPCkMLMT 17 Northeastern 8 .533 LSCrNtMDRPCkMLMT 18 Lake Superior 8 .530 NM CrNtMDRPCkMLMT 19 Cornell 6 .525 NtMDRPCkMLMT 20 Notre Dame 6 .548 CC MDRPCkMLMT 21 Minn-Duluth 4 .516 RPCkMLMT 22 RPI 3 .509 CkMLMT 23 Clarkson 2 .498 MLMT 24 Mass-Lowell 1 .508 MT 25 Michigan Tech 0 .476
The PWCs are remarkably transitive; there are only three cases of a team winning an individual comparison with a team with a higher PWR, and the only one of note is Yale's PWC win over New Hampshire. (But that will turn out to be very significant.) Let's assume that the regular season titles go to the teams with the best winning percentage in their respective leagues: Michigan, Yale, St. Cloud, and BU. Filling out the field is a no-brainer: UNH, Providence, Colgate and BC from the East and Michigan State, North Dakota, Miami and Wisconsin from the West. Now to assign the byes and determine which teams get shipped out, we consider the PWCs among teams in each region:
West East
1 Mich State 5 .589 NDMiMmSCWi 1 Boston Univ 5 .624 YaNHPvCgBC
2 North Dakota 4 .609 MiMmSCWi 2 Yale 4 .577 NHPvCgBC
3 Michigan 3 .602 MmSCWi 3 New Hampshire 3 .629 PvCgBC
4 Miami 2 .581 SCWi 4 Providence 2 .558 CgBC
5 St Cloud 1 .578 Wi 5 Colgate 1 .573 BC
6 Wisconsin 0 .565 6 Boston Coll 0 .550
Now the PWCs are completely transitive within each region. Note that although Yale has a lower total PWR than New Hampshire (19 vs. 21), the extra teams that UNH beats in the pairwise (North Dakota, Michigan and Miami) are all Western teams, and thus have no role in determining the Eastern bye slots. (The NCAA has said that it will not award a bye to a team from a different region except under exceptional circumstances.) So the byes are given to MSU, NoDak, BU and Yale. And the numbers indicate that we should ship St. Cloud and Wisconsin to the East and Colgate and BC to the West. (Of the two regional hosts, MSU is the top seed in the tourney and thus would be in their own region anyway, and Rensselaer does not qualify for the tournament.) Now we seed within each region:
West East
1 Mich State (C) 1 .589 ND 1 Boston Univ (H) 1 .624 Ya
2 North Dakota (W) 0 .609 2 Yale (E) 0 .577
3 Michigan (C) 3 .602 MmCgBC 3 New Hampshire (H) 3 .629 SCPvWi
4 Miami (C) 2 .581 CgBC 4 St Cloud (W) 2 .578 PvWi
5 Colgate (E) 1 .573 BC 5 Providence (H) 1 .558 Wi
6 Boston Coll (H) 0 .550 6 Wisconsin (W) 0 .565
So that's what the pairwise numbers tell us. Now it's time to look as what we've got in terms of conference matchups. Looking at the conference designations above, we see that there are no first-round conference matchups, but two potential intraconference games in the second round: Miami-Michigan State and Providence-BU. Simple arithmetic tells us that the only way to avoid two teams from a given conference being in the same three-team bracket is to have no more than two teams from one conference in the same regional. With two ECAC teams, four Hockey East teams, and three from each of the Western conferences in the field of twelve, that means we should ship out two Hockey East teams, one CCHA and one WCHA. So let's try sending Miami (the only CCHA team that can be moved) East in place of St. Cloud and Providence West instead of Colgate. Then we get
West East
1 Mich State (C) 1 .589 ND 1 Boston Univ (H) 1 .624 Ya
2 North Dakota (W) 0 .609 2 Yale (E) 0 .577
3 Michigan (C) 3 .602 SCPvBC 3 New Hampshire (H) 3 .629 MmCgWi
4 St Cloud (W) 2 .578 PvBC 4 Miami (C) 2 .581 CgWi
5 Providence (H) 1 .558 BC 5 Colgate (E) 1 .573 Wi
6 Boston Coll (H) 0 .550 6 Wisconsin (W) 0 .565
Note that if we tried to seed the six Eastern teams by their PWCs, we'd find Yale, UNH and Miami in a three-way tie with Yale beating New Hampshire, UNH beating Miami and Miami beating Yale in rock-scissors-paper fashion. The RPI would break that tie in favor of UNH, followed by Miami. However, this three-way tie is a fiction, since Miami cannot be awarded the last Eastern bye. It's a competition between Yale and New Hampshire, and the Elis win. That's why we could give them the last Eastern bye back before we started swapping teams out of their regions. (I can't say with complete certainty that this is what the committee would do, but it seems the natural outcome of the logic they used last year.)
Anyway, these seedings do indeed give a tournament with no intra-conference battles in the regionals, so let's see the brackets.
5W Providence (H) 6E Wisconsin (W)
4W St Cloud (W) 3E New Hampshire (H)
1W Mich State (C) 2E Yale (E)
2W North Dakota (W) 1E Boston Univ (H)
3W Michigan (C) 4E Miami (C)
6W Boston Coll (H) 5E Colgate (E)
From an attendance standpoint, they keep Colgate in upstate New York; the one futher change the committee might consider is swapping St. Cloud and Wisconsin to send the Badgers into Big Ten country. If they did that, here's how the rankings would look within each region:
West East
1 Mich State (C) 1 .589 ND 1 Boston Univ (H) 1 .624 Ya
2 North Dakota (W) 0 .609 2 Yale (E) 0 .577
3 Michigan (C) 3 .602 PvWiBC 3 New Hampshire (H) 3 .629 MmSCCg
4 Providence (H) 1 .558 WiBC 4 Miami (C) 2 .581 SCCg
5 Wisconsin (W) 0 .565 BC 5 St Cloud (W) 2 .578 Cg
6 Boston Coll (H) 0 .550 6 Colgate (E) 1 .573
The East now has a potential second-round game between Yale and Colgate, so we swap Colgate and St. Cloud. Ordinarily New Hampshire and Miami would also be swapped to preserve the pairings, but that would set up a possible second-round matchup between UNH and BU, so the three and four seeds are left as is. The attendance-conscious brackets are thus:
5W Wisconsin (W) 6E St Cloud (W)
4W Providence (H) 3E New Hampshire (H)
1W Mich State (C) 2E Yale (E)
2W North Dakota (W) 1E Boston Univ (H)
3W Michigan (C) 4E Miami (C)
6W Boston Coll (H) 5E Colgate (E)
If you want to see how each of the pairwise comparisons was determined, you can peruse these in-depth stats, all 160k of them.