Last Modified: 2011 October 9
Joe Schlobotnik / joe@amurgsval.org
URL for this frameset: http://slack.net/~whelan/tbrw/tbrw.cgi?1999/pairwise.990215.shtml
Remember, you can go through this process interactively using the "You Are The Committee" script.
Once again, it's time to practice applying the NCAA Tournament selection procedure to the results to date from US College Hockey Online's Division I Composite Schedule. Calculating the various selection criteria and performing pairwise comparisons among the 26 tournament-eligible teams with overall records at or above .500, which are known as teams under consideration, we obtain the following results:
Team PWR RPI Comparisons Won
1 North Dakota 25 .657 MeNHMSCCCkQnBCSLDUPnMiOSNtNMPvNiCtRPMLFSCgCrAAHCIo
2 Maine 24 .633 __ NHMSCCCkQnBCSLDUPnMiOSNtNMPvNiCtRPMLFSCgCrAAHCIo
3 New Hampshire 23 .621 ____ MSCCCkQnBCSLDUPnMiOSNtNMPvNiCtRPMLFSCgCrAAHCIo
4 Mich State 22 .601 ______ CCCkQnBCSLDUPnMiOSNtNMPvNiCtRPMLFSCgCrAAHCIo
5 CO College 20 .586 ________ CkQnBCSLDU__MiOSNtNMPvNiCtRPMLFSCgCrAAHCIo
6 Clarkson 20 .576 __________ QnBCSLDUPnMiOSNtNMPvNiCtRPMLFSCgCrAAHCIo
7 Quinnipiac 18 .537 ____________ BCSL__PnMiOSNtNMPvNiCtRPMLFSCgCrAAHCIo
8 Boston Coll 16 .575 ______________ SL____MiOSNtNMPvNiCtRPMLFSCgCrAAHCIo
9 St Lawrence 16 .554 ________________ DUPn__OSNtNMPvNiCtRPMLFSCgCrAAHCIo
10 Denver U 16 .546 ____________QnBC__ Pn__OS__NMPvNiCtRPMLFSCgCrAAHCIo
11 Princeton 15 .541 ________CC____BC____ Mi____NMPvNiCtRPMLFSCgCrAAHCIo
12 Michigan 15 .558 ________________SLDU__ OSNtNMPv__CtRPMLFSCgCrAAHCIo
13 Ohio State 14 .544 ____________________Pn__ NtNMPvNiCtRPMLFSCgCrAAHCIo
14 Notre Dame 12 .552 __________________DUPn____ NMPv__CtRPMLFSCgCrAA__Io
15 Northern Mich 11 .543 ____________________________ PvNiCtRPMLFSCgCrAAHCIo
16 Providence 10 .527 ______________________________ NiCtRPMLFSCgCrAAHCIo
17 Niagara 9 .479 ______________________Mi__Nt____ Ct____FSCgCrAAHCIo
18 Connecticut 8 .521 __________________________________ RPMLFSCgCrAAHCIo
19 RPI 8 .519 ________________________________Ni__ MLFSCgCrAAHCIo
20 Mass-Lowell 7 .517 ________________________________Ni____ FSCgCrAAHCIo
21 Ferris State 5 .512 ________________________________________ CgCrAAHCIo
22 Colgate 4 .503 __________________________________________ CrAAHCIo
23 Cornell 3 .500 ____________________________________________ AAHCIo
24 AK-Anchorage 2 .462 ______________________________________________ HCIo
25 Holy Cross 2 .459 __________________________Nt____________________ Io
26 Iona 0 .423 __________________________________________________
As we did last week, we assign automatic bids to the current leaders in the four major conferences, which are North Dakota, Michigan State, Maine and St. Lawrence (who still hold the advantage over Clarkson in the ECAC Tiebreaker System) and we also exclude the four MAAC teams from the list on the basis of a lack of competative equity with the other four conferences based on the following statistics:
vs Indies vs Army vs Niagara vs AFA vs Mankato
Avg RPI PF-PA Pct PF-PA Pct PF-PA Pct PF-PA Pct PF-PA Pct
HE .528 12- 2 .857 10-0 1.000 0- 2 .000 2-0 1.000 0-0 .---
WCHA .506 28- 8 .778 0-0 .--- 0- 0 .--- 10-0 1.000 18-8 .692
CCHA .504 5- 5 .500 0-0 .--- 2- 4 .333 0-0 .--- 3-1 .750
ECAC .497 28-10 .737 10-0 1.000 10-10 .500 2-0 1.000 6-0 1.000
MAAC .446 7-19 .269 4-4 .500 0- 2 .000 3-5 .350 0-8 .000
Once again this means denying Quinnipiac a bid, but as the Braves have now supplemented a win over Army (.346, 50th out of 51 teams in the Ratings Percentage Index) with a split against Air Force (.441 and #43) as their only out-of-conference games, I think the committee will not hesitate to do that.
Now, things get tricky when it comes to assigning the at-large bids, so I want to go through that process carefully. First of all, here are the results of the comparisons among teams in contention for the eight at-large bids:
Team lPWR RPI Comps Won
1 New Hampshire 17 .621 CCCkDUPnBCMiOSNtNMPvRPNiMLFSCgCrAA
2 CO College 15 .586 CkDU__BCMiOSNtNMPvRPNiMLFSCgCrAA
3 Clarkson 15 .576 __ DUPnBCMiOSNtNMPvRPNiMLFSCgCrAA
4 Denver U 12 .546 ____ PnBC__OS__NMPvRPNiMLFSCgCrAA
5 Princeton 12 .541 CC____ BCMi____NMPvRPNiMLFSCgCrAA
6 Boston Coll 12 .575 ________ MiOSNtNMPvRPNiMLFSCgCrAA
7 Michigan 11 .558 ____DU____ OSNtNMPvRP__MLFSCgCrAA
8 Ohio State 11 .544 ______Pn____ NtNMPvRPNiMLFSCgCrAA
9 Notre Dame 10 .552 ____DUPn______ NMPvRP__MLFSCgCrAA
10 Northern Mich 8 .543 ________________ PvRPNiMLFSCgCrAA
11 Providence 7 .527 __________________ RPNiMLFSCgCrAA
12 RPI 6 .519 ____________________ NiMLFSCgCrAA
13 Niagara 6 .479 __________Mi__Nt______ __FSCgCrAA
14 Mass-Lowell 5 .517 ______________________Ni FSCgCrAA
15 Ferris State 3 .512 __________________________ CgCrAA
16 Colgate 2 .503 ____________________________ CrAA
17 Cornell 1 .500 ______________________________ AA
18 AK-Anchorage 0 .462 ________________________________
Now, it's important to realize that the committee does not simply choose the top teams based on their total number of comparisons won (which is their Pairwise Rating or PWR). Instead they give bids to teams that are "obviously" beating out the others, boot out those that are obviously losing the most comparisons, and look carefully at the comparisons among the "bubble" teams in the middle. This is a somewhat imprecise algorithm, but in past years it hasn't mattered. However, due to the unusual pattern of comparison wins for Division I Independent Niagara, who still win comparisons with several teams which beat a number of teams which in turn beat Niagara themselves, it may do so this season. So I want to describe in detail one deterministic algorithm, which is in fact the one used by my "You Are The Committee" script to choose the teams if the "automatic" button is pressed. This method involves sorting the bubble teams (initially everyone in contention for an at-large berth), removing the team or teams at the top or bottom of the bubble (whichever keeps the number of bubble teams closest to twice the number of remaining at-large bids), and re-sorting that new bubble, repeating the process until everyone is either in or out.
First of all, UNH wins comparisons with everyone left, so they're clearly in, and Ferris, Colgate, Cornell and Anchorage lose to everyone else, so they're out. That leaves 13 teams in the middle fighting for seven slots; Colorado College and Clarkson are tied for the most comparison wins among the 13, and Lowell have the fewest, so if we put CC and Clarkson in and Lowell out (which leaves five teams each above and below the cutoff), we have the following teams left on the bubble:
Team lPWR RPI Comps Won
1 Denver U 7 .546 BC__OSPn__NMPvNiRP
2 Boston Coll 7 .575 __ MiOS__NtNMPvNiRP
3 Michigan 6 .558 DU__ OS__NtNMPv__RP
4 Ohio State 6 .544 ______ PnNtNMPvNiRP
5 Princeton 6 .541 __BCMi__ __NMPvNiRP
6 Notre Dame 5 .552 DU______Pn NMPv__RP
7 Northern Mich 3 .543 ____________ PvNiRP
8 Providence 2 .527 ______________ NiRP
9 Niagara 2 .479 ____Mi____Nt____ __
10 RPI 1 .519 ________________Ni
Dropping the bottom team, Rensselaer, leaves four teams below the cutoff, and then putting DU and BC into the tournament leaves three teams above. Now the redefined bubble looks like:
Team lPWR RPI Comps Won
1 Ohio State 5 .544 Pn__NtNMNiPv
2 Princeton 4 .541 __ Mi__NMNiPv
3 Michigan 4 .558 OS__ NtNM__Pv
4 Notre Dame 3 .552 __Pn__ NM__Pv
5 Northern Mich 2 .543 ________ NiPv
6 Niagara 2 .479 ____MiNt__ __
7 Providence 1 .527 __________Ni
Dropping Providence again centers the cutoff within the bubble:
Team lPWR RPI Comps Won
1 Ohio State 4 .544 Pn__NiNtNM
2 Princeton 3 .541 __ MiNi__NM
3 Michigan 3 .558 OS__ __NtNM
4 Niagara 2 .479 ____Mi Nt__
5 Notre Dame 2 .552 __Pn____ NM
6 Northern Mich 1 .543 ______Ni__
Since there's one team at the top and one at the bottom, we again keep the cutoff centered by putting OSU in the tourney and NMU out:
Team lPWR RPI Comps Won
1 Princeton 2 .541 NiMi__
2 Niagara 2 .479 __ MiNt
3 Michigan 1 .558 ____ Nt
4 Notre Dame 1 .552 Pn____
Finally the bubble has become small enough that there is only one division left to make: the teams winning two comparisons (Princeton and Niagara) are in and those winning only one (Michigan and Notre Dame) are out. Niagara, although seemingly five spots off the pace, have managed to percolate up at each stage thanks to their comparison wins over eventual final bubble teams Michigan and Notre Dame.
I can't say if the committee will do anything like this iterative bubble redefinition, and any one-step definition and sorting of the bubble will place Michigan in the tournament in their place, but note that the individual pairwise comparison between the two indicates that Niagara stacks up better than Michigan. At any rate, since last week's "If the Season Ended Today" eschewed iterative redefinition and excluded the Purple Eagles, let's throw them into the field this time. If you haven't been keeping score, this means that at-large bids have gone to Colorado College and Denver from the WCHA, Ohio State from the CCHA, Clarkson and Princeton from the ECAC, New Hampshire and Boston College from Hockey East, and Independent Niagara. This is seven Eastern teams if we consider Niagara to come from the East. Since the Purple Eagles lose pairwise comparisons to all of the other Eastern teams (and since they may someday end up in the CCHA anyway), we consider them an honorary Western team for the purposes of seeding the tournament:
West East
1 North Dakota 5 .657 MSCCDUOSNi | 1 Maine 5 .633 NHCkBCSLPn
2 Mich State 4 .601 CCDUOSNi | 2 New Hampshire 4 .621 CkBCSLPn
3 CO College 3 .586 __ DUOSNi | 3 Clarkson 3 .576 __ BCSLPn
4 Denver U 2 .546 ____ OSNi | 4 Boston Coll 1 .575 ____ SL__
5 Ohio State 1 .544 ______ __ | 5 St Lawrence 1 .554 ______ Pn
6 Niagara 0 .479 ________ | 6 Princeton 1 .541 ____BC__
NoDak and MSU in the West, and Maine and New Hampshire in the East, earn the two bye seeds in their respective regionals by winning comparisons with all of the other teams in their regions. Now we need to swap two pairs of teams between the two regions. In the East the bottom three teams are in a classic rock-scissors-paper situation, with each winning and losing one comparison against the others. BC has the best RPI of those three, and is clearly the best team, attendance-wise, to place in the Regional in nearby Worcester, so they would almost certainly stay East along with Clarkson, although the presence of two Hockey East teams in the bye seeds means the Golden Eagles will inevitably be looking at a second-round intraconference game if they advance. In the West, Niagara and Ohio State are clearly the lowest two on the basis of comparisons, although keeping three WCHA teams in the Western Regional will also neccessitate a potential second-round conference matchup. This time I'm guessing the committee would decided Ohio State is at least as good a draw as Denver at the Madison, Wisconsin site for the regional, and ship DU East instead of OSU. This makes the regionals look like this:
West East
1 North Dakota (W) 1 .657 MS | 1 Maine (H) 1 .633 NH
2 Mich State (C) 0 .601 | 2 New Hampshire (H) 0 .621
3 CO College (W) 2 .586 SLOS__ | 3 Clarkson (E) 3 .576 DUBCNi
4 St Lawrence (E) 2 .554 __ OSPn | 4 Denver U (W) 2 .546 BCNi
5 Ohio State (C) 1 .544 ____ Pn | 5 Boston Coll (H) 1 .575 __ Ni
6 Princeton (E) 1 .541 CC____ | 6 Niagara (I) 0 .479 ____
The only first- or second-round game between teams in the same conference which results from the natural seedings is BC-Maine, and as noted before, this is inevitable if we keep Boston College in the East Regional. So the final brackets are:
5W Ohio State (C) 6E Niagara (I)
4W St Lawrence (E) 3E Clarkson (E)
1W North Dakota (W) --+--2E New Hampshire (H)
|
2W Mich State (C) --+--1E Maine (H)
3W Princeton (E) 4E Denver U (W)
6W CO College (W) 5E Boston Coll (H)
Note that Princeton and CC have switched seeds because Princeton wins individual pairwise comparison. I don't know if the committee would do things this way, but given their emphasis on pairings being more important than seedings, and the use of individual comparisons between teams, it seems reasonable.
You also can look at the detailed description of each of the pairwise comparisons, if you're so inclined.