[I'm going to put the references at the beginning of this
analysis, since people who are unfamiliar with the information in them
will be totally lost by the end of the current message.]
USCHO's Explanation of the PWR:
http://www.uscollegehockey.com/news/1998/01/26_pwr.html
Adam Wodon's interview with Selection Committee chair Joe Marsh:
http://www.uscollegehockey.com/tournament/032097.html
My description of the NCAA Selection Procedure:
http://www.cc.utah.edu/~jtw16960/pwframe.html
[Note that what USCHO refers to as a "comparison point" I call
a "criterion", and what they call a "PWR point" I refer to as a
"pairwise comparison" (PWC). I'm trying to avoid using the word
"point" for clarity's sake, but I have at times used it to refer to a
criterion within a comparison.]
Although the NCAA Selection Committee no longer uses the
Ratings Percentage Index exclusively to seed the national tournament,
it still has special status in the current pairwise comparison scheme.
It is one of the five criteria used when comparing each pair of teams
(along with common opponents, record vs the top 20, record vs teams
under consideration and head-to-head wins), but it is also used to
resolve a comparison if if each team wins the same number of criteria.
This means RPI effectively counts as one and a half criteria. (It
should be pointed out that each head to head win contributes to the
comparison, so head-to-head record can be worth as much as six
"ordinary" criteria if a WCHA team sweeps a four-game RS series and a
two-game playoff series with another TUC.) On top of this, after the
comparisons have been determined, the RPI is also used as an ultimate
tiebreaker if an odd number of teams cannot be separated in the
seeding process on the basis of their comparisons.
One way to reduce the dominance of RPI in the selection
process would be to use it only as a tiebreaker and not count it as an
individual criterion in a pairwise comparison. (In this case, RPI
would effectively count as half a criterion, rather than one and a
half.) I calculated the pairwise comparisons from the current results
<http://www.uscollegehockey.com/schedules/confsched.cgi?19971998+ncaa+d1>
first using the current method, and then without including RPI as a
criterion, and here are the results:
Real Pairwise Comparisons:
Team PWR RPI Comparisons Won
1 North Dakota 22 .624 MiNHMSBUYaBCMmSCWiCgOSCkNMNECCCrMDPnLSRPPvDa
2 Michigan 21 .606 NHMSBUYaBCMmSCWiCgOSCkNMNECCCrMDPnLSRPPvDa
3 New Hampshire 20 .616 __ MSBUYaBCMmSCWiCgOSCkNMNECCCrMDPnLSRPPvDa
4 Mich State 19 .600 ____ BUYaBCMmSCWiCgOSCkNMNECCCrMDPnLSRPPvDa
5 Boston Univ 18 .615 ______ YaBCMmSCWiCgOSCkNMNECCCrMDPnLSRPPvDa
6 Yale 17 .584 ________ BCMmSCWiCgOSCkNMNECCCrMDPnLSRPPvDa
7 Boston Coll 16 .565 __________ MmSCWiCgOSCkNMNECCCrMDPnLSRPPvDa
8 Miami 15 .569 ____________ SCWiCgOSCkNMNECCCrMDPnLSRPPvDa
9 St Cloud 14 .561 ______________ WiCgOSCkNMNECCCrMDPnLSRPPvDa
10 Wisconsin 13 .553 ________________ CgOSCkNMNECCCrMDPnLSRPPvDa
11 Colgate 12 .545 __________________ OSCkNMNECCCrMDPnLSRPPvDa
12 Ohio State 11 .544 ____________________ CkNMNECCCrMDPnLSRPPvDa
13 Clarkson 9 .529 ______________________ NMNECCCr__PnLSRPPvDa
14 Northern Mich 7 .527 ________________________ NECCCr____LSRPPvDa
15 Northeastern 7 .513 __________________________ CC__MDPnLSRPPvDa
16 CO College 7 .520 ____________________________ CrMDPnLSRPPvDa
17 Cornell 6 .519 __________________________NE__ MDPnLS__PvDa
18 Minn-Duluth 6 .509 ______________________CkNM______ __LSRPPvDa
19 Princeton 5 .509 ________________________NM______MD __RPPvDa
20 Lake Superior 4 .501 __________________________________Pn RPPvDa
21 Rensselaer 3 .493 ______________________________Cr______ PvDa
22 Providence 1 .495 ________________________________________ Da
23 Dartmouth 0 .469 __________________________________________
Modified Comparisons without RPI criterion:
Team PWR RPI Comparisons Won
1 Mich State 22 .600 NDMiNHYaBUWiBCSCOSCgMmCkNEMDLSPnCCNMRPCrPvDa
2 North Dakota 21 .624 MiNHYaBUWiBCSCOSCgMmCkNEMDLSPnCCNMRPCrPvDa
3 Michigan 20 .606 __ NHYaBUWiBCSCOSCgMmCkNEMDLSPnCCNMRPCrPvDa
4 New Hampshire 19 .616 ____ YaBUWiBCSCOSCgMmCkNEMDLSPnCCNMRPCrPvDa
5 Yale 18 .584 ______ BUWiBCSCOSCgMmCkNEMDLSPnCCNMRPCrPvDa
6 Boston Univ 17 .615 ________ WiBCSCOSCgMmCkNEMDLSPnCCNMRPCrPvDa
7 Wisconsin 14 .553 __________ BCSC__CgMmCk__MDLSPnCCNMRPCrPvDa
8 Boston Coll 13 .565 ____________ SC__CgMm__NEMDLSPnCCNMRPCrPvDa
9 St Cloud 13 .561 ______________ OSCg__CkNEMDLSPnCCNMRPCrPvDa
10 Ohio State 13 .544 __________WiBC__ ____CkNEMDLSPnCCNMRPCrPvDa
11 Colgate 12 .545 ________________OS Mm__NEMDLSPnCCNMRPCrPvDa
12 Miami 12 .569 ______________SCOS__ __NEMDLSPnCCNMRPCrPvDa
13 Clarkson 11 .529 ____________BC____CgMm NE____PnCCNMRPCrPvDa
14 Northeastern 7 .513 __________Wi____________ MDLSPnCC______PvDa
15 Minn-Duluth 7 .509 ______________________Ck__ LS____NMRPCrPvDa
16 Lake Superior 7 .501 ______________________Ck____ PnCC__RPCrPvDa
17 Princeton 6 .509 __________________________MD__ __NMRPCrPvDa
18 CO College 5 .520 __________________________MD__Pn NMRPCr____
19 Northern Mich 5 .527 ________________________NE__LS____ RP__PvDa
20 Rensselaer 4 .493 ________________________NE__________ CrPvDa
21 Cornell 4 .519 ________________________NE________NM__ PvDa
22 Providence 2 .495 ________________________________CC______ Da
23 Dartmouth 1 .469 ________________________________CC________
One thing that leaps out immediately is that the comparisons
are much less transitive without RPI as a criterion (i.e., if team A
beats team B and team B beats team C, team A is less likely to beat
team C). Out of 252 comparisons, 20 are won by the team with the
lower PWR[*], as opposed to only 7 in the current scheme. (For
[*] When I talk about ranking teams by their PWR, that includes
breaking ties with individual comparisons, or if that's unresolved,
with the RPI. Thus no teams are considered to be tied in the PWR,
even if they've won the same number of overall comparisons.
reference, the modified scheme has 35 comparisons won by the team with
the lower RPI, compared to 11 in the actual one.) This doesn't cause
too much trouble for seeding small numbers of teams, but it actually
makes deciding the field of twelve for the NCAAs very tricky. The
field is supposed to be determined by pairwise comparisons among the
"bubble" teams, but who makes it in depends on how big the bubble is
taken to be. For instance, if we compare Colgate, Miami and Clarkson,
Clarkson and Colgate are in and Miami out.
If we also add BC, St. Cloud and Ohio State to the bubble, and
look at comparisons among those six teams, BC, SCSU and Clarkson each
win three comparisons, Colgate, Miami and Ohio State two. Ohio State
loses pairwise comparisons to both Colgate and Miami and so in that
case, they'd be the odd team out.
If we expand our definition of the bubble to include teams
ranked 8 through 16 in the overall PWR, we get a "local PWR" that
looks like
Team lPWR RPI Comparisons Won
8 Boston Coll 6 .565 SCCgMm____NEMDLS
9 St Cloud 6 .561 __ Cg__OSCkNEMDLS
10 Colgate 5 .545 ____ MmOS__NEMDLS
11 Miami 5 .569 __SC__ OS__NEMDLS
12 Ohio State 5 .544 BC______ CkNEMDLS
13 Clarkson 4 .529 BC__CgMm__ NE____
14 Northeastern 2 .513 ____________ MDLS
15 Minn-Duluth 2 .509 __________Ck__ LS
16 Lake Superior 1 .501 __________Ck____
That's hardly decisive, so I'd say BC and St. Cloud are in and Lake
State is out, and look at the comparisons among the remaining teams:
Team lPWR RPI Comparisons Won
10 Colgate 4 .545 MmOS__NEMD
11 Miami 3 .569 __ OS__NEMD
12 Ohio State 3 .544 ____ CkNEMD
13 Clarkson 3 .529 CgMm__ NE__
14 Northeastern 1 .513 ________ MD
15 Minn-Duluth 1 .509 ______Ck__
this then tells us to consider Miami, and Clarkson, each of which has
won a comparison with only one of the others, and when this tie is
resolved based on the Ratings Percentage Index, Miami and Ohio State
are in and Clarkson is out, leading to the same field we'd get if we
used the *real* PWCs.
If we use the most methodical method, ranking the teams by
total PWR, throwing out the teams at the very top or bottom (whichever
comes closer to leaving the same number of teams above and below the
cutoff, and both if they're the same), recalculating the number of
comparisons won among those teams, and repeating the process, we'd
once again get down to Clarkson, Miami and Ohio State, and get the
same field as before.
Once the field is chosen, the seedings would also come out
different with the modified PWCs; with the existing criteria BU and
Michigan get byes that would go to Yale and Michigan State if the RPI
were removed as a criterion. But then the ordering of the top three
teams within each region has been changing from week to week anyway,
so it's not surprising that tweaking the criteria changes them.
What's the moral? Well, I'm trying to avoid injecting my own
opinion here, but is seems that if this modification were made to the
criteria for pairwise comparisons, the algorithm for picking the field
of twelve would need to be clarified a bit beyond "look at the
comparisons among the bubble teams". With RPI included as a
criterion, the comparisons are only slightly non-transitive, so any
definition of "the bubble" is likely to give the same results. Not so
if it were removed.
John Whelan, Cornell '91
Official Scorer/PA Announcer
U of Utah Ice Hockey Club
<[log in to unmask]>
<http://www.cc.utah.edu/~jtw16960/joe.html>
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