Last Modified: 2011 October 9
Joe Schlobotnik / joe@amurgsval.org
URL for this frameset: http://slack.net/~whelan/tbrw/tbrw.cgi?1999/pairwise.990321.shtml
If you want to work out some of the alternate possible interpretations of the pairwise comparisons yourself, try the interactive "You Are The Committee" script.
Another season of NCAA men's division I hockey has come to a wild finish, but before we embark upon the postseason of the NCAA tournament, there are some questions to be answered by the tournament selection procedure. First, let's start with what we know: North Dakota, Michigan State, Clarkson, New Hampshire, Denver, Michigan and Boston College will all receive automatic bids for winning their conference regular season or tournament titles. That leaves five at-large bids to be given out on the basis of pairwise comparisons among all teams which finished with Division I records of .500 or better. Running those comparisons with the final results from US College Hockey Online's Division I Composite Schedule, we obtain the following results:
Team PWR RPI Comparisons Won
1 North Dakota 21 .641 NHMSMeBCCkCCDUSLQnMiOSNMRPPnNtMkCgNiCtHCPv
2 New Hampshire 20 .629 __ MSMeBCCkCCDUSLQnMiOSNMRPPnNtMkCgNiCtHCPv
3 Mich State 19 .597 ____ MeBCCkCCDUSLQnMiOSNMRPPnNtMkCgNiCtHCPv
4 Maine 18 .609 ______ BCCkCCDUSLQnMiOSNMRPPnNtMkCgNiCtHCPv
5 Boston Coll 17 .593 ________ CkCCDUSLQnMiOSNMRPPnNtMkCgNiCtHCPv
6 Clarkson 16 .592 __________ CCDUSLQnMiOSNMRPPnNtMkCgNiCtHCPv
7 CO College 15 .583 ____________ DUSLQnMiOSNMRPPnNtMkCgNiCtHCPv
8 Denver U 14 .571 ______________ SLQnMiOSNMRPPnNtMkCgNiCtHCPv
9 St Lawrence 12 .557 ________________ Qn__OSNMRPPnNtMkCgNiCtHCPv
10 Quinnipiac 12 .536 __________________ MiOSNMRPPnNtMkCgNiCtHCPv
11 Michigan 11 .565 ________________SL__ OSNMRPPnNtMkCg__CtHCPv
12 Ohio State 8 .531 ______________________ NM____NtMkCgNiCtHCPv
13 Northern Mich 7 .543 ________________________ RPPnNtMkCg__Ct__Pv
14 RPI 7 .533 ______________________OS__ Pn__MkCg__CtHCPv
15 Princeton 7 .531 ______________________OS____ __MkCgNiCtHCPv
16 Notre Dame 6 .536 __________________________RPPn MkCg__Ct__Pv
17 MSU-Mankato 5 .525 ________________________________ CgNiCtHCPv
18 Colgate 4 .523 __________________________________ NiCtHCPv
19 Niagara 4 .480 ____________________Mi__NMRP__Nt____ ______
20 Connecticut 3 .519 ____________________________________Ni HCPv
21 Holy Cross 3 .509 ________________________NM____Nt____Ni__ __
22 Providence 2 .511 ____________________________________Ni__HC
Maine, Colorado College, and St. Lawrence all clearly qualify at-large bids since they win their pairwise comparisons with everyone else in contention for those bids. The same would appear to be true of Metro-Atlantic Athletic Conference regular season champion Quinnipiac. However, the ratings percentage index upon which the pairwise comparisons are largely based, has a weakness which is very significant this year: it does not judge a teams' strength of schedule accurately when that team's opponents have themselves played weak schedules. Since the six division I members of the new MAAC conference play 20 games each against each other, plus a few non-conference games against Division I independents, a team like Quinnipiac can rack up a high winning percentage against weak competition without the weakness of their schedule being reflected in the RPI. Anticipating this, the selection committee, as reported in the NCAA News, "noted that it reserves the right to evaluate each team based on the relative strength of their respective conference." The best way to gauge that relative strength is via the conferences' performance against the four Division I independents:
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 .523 14- 2 .875 12-0 1.000 0- 2 .000 2-0 1.000 0- 0 .---
WCHA .503 32-10 .762 0-0 .--- 0- 0 .--- 10-0 1.000 22-10 .688
CCHA .503 5- 5 .500 0-0 .--- 2- 4 .333 0-0 .--- 3- 1 .750
ECAC .495 28-10 .737 10-0 1.000 10-10 .500 2-0 1.000 6- 0 1.000
MAAC .454 8-22 .267 5-5 .500 0- 4 .000 3-5 .350 0- 8 .000
Given this poor performance against the only teams which can be used to gauge the MAAC relative to the major conferences, it seems that the NCAA's standard of competetive equity has not been reached, and therefore we can expect that the committee will decide not to award a bid to any MAAC team.
With Quinnipiac (and Connecticut and Holy Cross) out of the picture, that still leaves two at-large berths to fill, and even without worrying about the possibility of a surprise MAAC bid, there are four different ways they could reasonably be awarded. The point of confusion is that the NCAA is supposed to award at-large bids based on the pairwise comparisons among the "bubble" teams which are not obviously either in or out. The largest conceivable set of such teams is the following six:
1 Ohio State 3 .531 NiNMNt____
2 Niagara 3 .480 __ NMNtRP__
3 Northern Mich 3 .543 ____ NtRPPn
4 Notre Dame 2 .536 ______ RPPn
5 RPI 2 .533 OS______ Pn
6 Princeton 2 .531 OSNi______
With OSU, Niagara and NMU winning three of five comparisons each, and Northern losing the individual comparisons to the other two, this would seem to place Ohio State and Niagara in the tournament field. However, looking at the table of pairwise rankings above you might well ask what Niagara is doing on the bubble when they are 19th in the country in terms of total number of comparisons won. However, the total PWR is not as important to the selection committee as the individual comparisons among teams in contention for a certain spot, and if the comparisons against MAAC teams (notably Holy Cross and UConn) and recipients of automatic bids are discarded, Niagara find themselves with three comparisons won, tied with Mankato. OSU and NMU have won 6 each and Notre Dame, RPI and Princeton 5 each. If they are granted bubble status, Niagara clean up since all three of their comparison wins are against other bubble teams, even though they lose to three teams that are obviously off the bubble. If you exclude the MAAC teams and then select "automatic" on my "You Are the Committee" script, this is what happens. However, I can imagine the committee more likely than not making the cutoff for "bubbledom" above rather than below Niagara's level, so let's see what happens if they are left off the bubble. (Another issue which they will probably not consider is that Niagara benefits to a lesser extent from the weaknesses in the PWR which the MAAC is able to exploit with its weak schedule. Their records in the last 16 games and against other teams under consideration are deceptively high because these winning percentages were amassed against a weaker schedule. If strength of schedule were corrected for, they would not win the comparisons they do.)
So, supposing we look at a five-team bubble not involving Niagara:
1 Northern Mich 3 .543 NtRP__Pn
2 Notre Dame 2 .536 __ RP__Pn
3 RPI 2 .533 ____ OSPn
4 Ohio State 2 .531 NMNt__ __
5 Princeton 1 .531 ______OS
Princeton wins only one comparison out of four and NMU wins three, with the others taking two each. So if we say Northern is in and Princeton out, the other three are still tied with one comparison each. In this case, the tie breaker is RPI, which goes to Notre Dame. But it's not quite so simple. If we throw Princeton out and re-total the comparisons before doing anything about NMU (since Princeton is further from the cutoff), then Northern Michigan and Ohio State each win two out of the three remaining comparisons. (If we put Northern in before dealing with Princeton, Notre Dame again takes the last bid, since they win two out of three comparisons, including the head-to-head with RPI, who also win two.) So with a five-team bubble, we get two different answers depending in which order we prune it.
Finally, we could conceivably define the bubble to have four teams if we make an arbitrary cutoff between a total PWR of 6 and 7. Then Notre Dame is out and we find:
1 Northern Mich 2 .543 RPPn__
2 RPI 2 .533 __ PnOS
3 Princeton 1 .531 ____ OS
4 Ohio State 1 .531 NM____
Northern and Rensselaer are then the last two at-large bids. However, this option seems unlikely to me, since such a cutoff would be in the midst of the region of "non-transitive comparisons". Plus it would involve appealing to the total PWR and essentially excluding Notre Dame from the bubble for losing the suspect Holy Cross comparison.
To recap, the final two at-large bids could reasonably be given to NMU and Notre Dame or NMU and OSU, or conceivably to NMU and RPI or OSU and Niagara. What will the committee do? I cannot say for any certainty, but after the field is announced we will understand the process of identifying the bubble somewhat better than we do now.
For the sake of concreteness let's say they select Northern Michigan and Notre Dame (I think a 5-team bubble is likely, but the question of how they'd pare it down is up in the air). In that case, we have seven Western and only five Eastern teams, so we move the lowest-ranked Western team, Notre Dame, over to compensate:
West East
1 North Dakota 5 .641 MSCCDUMiNM | 1 New Hampshire 5 .629 MeBCCkSLNt
2 Mich State 4 .597 CCDUMiNM | 2 Maine 4 .609 BCCkSLNt
3 CO College 3 .583 __ DUMiNM | 3 Boston Coll 3 .593 __ CkSLNt
4 Denver U 2 .571 ____ MiNM | 4 Clarkson 2 .592 ____ SLNt
5 Michigan 1 .565 ______ NM | 5 St Lawrence 1 .557 ______ Nt
6 Northern Mich 0 .543 ________ | 6 Notre Dame 0 .536 ________
As was the case with Boston University in 1997, Clarkson receive an automatic bye for winning both the regular season and tournament championships in the ECAC. The other three regular season champions, North Dakota, Michigan State and New Hampshire, all lost in their conference playoffs, but qualify for byes on the basis of their pairwise comparisons. Now we need to ship two teams from each region into the other. In the East, it's easy to see that this will be SLU and Notre Dame; although leaving all three Hockey East teams in one regional means there will be a potential second-round intraconference matchup, attendance considerations ensure that Boston College will be left in the regional in Worcester, and Maine is too far above SLU in the comparisons to justify moving them instead. In the West, the numbers tell us to move Michigan and NMU to the East to get
West East
1 North Dakota (W) 1 .641 MS | 1 New Hampshire (H) 1 .629 Ck
2 Mich State (C) 0 .597 | 2 Clarkson (E) 0 .592
3 CO College (W) 3 .583 DUSLNt | 3 Maine (H) 3 .609 BCMiNM
4 Denver U (W) 2 .571 SLNt | 4 Boston Coll (H) 2 .593 MiNM
5 St Lawrence (E) 1 .557 __ Nt | 5 Michigan (C) 1 .565 __ NM
6 Notre Dame (C) 0 .536 ____ | 6 Northern Mich (C) 0 .543 ____
The West regional has two potential second-round matchups, but we can reduce that number to one (which is the minimum possible with seven Western teams in the NCAAs by switching the seeds of SLU and Notre Dame. Generally speaking, this also means switching CC and DU, to preserve the first-round pairings, which also has the benefit of avoiding a rematch of the WCHA final between North Dakota and Denver. The bracket that comes out is then:
5W Notre Dame (C) 6E Northern Mich (C)
4W CO College (W) 3E Maine (H)
1W North Dakota (W) --+--2E Clarkson (E)
|
2W Mich State (C) --+--1E New Hampshire (H)
3W Denver U (W) 4E Boston Coll (H)
6W St Lawrence (E) 5E Michigan (C)
However, the committee has a lot of leeway in choosing which Western teams go where, and might mix it up a little to improve attendance, for instance by moving Michigan into the regional in Madison in place of Notre Dame or Denver. Bumping Denver also heads off that WCHA tournament repeat, so to make a final guess at the brackets, let's say:
5W St Lawrence (E) 6E Northern Mich (C)
4W Michigan (C) 3E Maine (H)
1W North Dakota (W) --+--2E Clarkson (E)
|
2W Mich State (C) --+--1E New Hampshire (H)
3W CO College (W) 4E Boston Coll (H)
6W Notre Dame (C) 5E Denver U (W)
This prediction is made with very little confidence: there are several other ways to fill the field, and in each case about four plausible permutations of the Western teams. The four bye seeds are set, and I think we can say with confidence that Maine and BC will be in the East and SLU in the West. Beyond that, all we know for sure is that Michigan, Denver and Colorado College will be somewhere...
You can also see a detailed accounting of the final pairwise comparisons.