Ranking Systems for College Hockey in 1999-2000

© 1999, 2000, Joe Schlobotnik (archives)

URL for this frameset: http://slack.net/~whelan/tbrw/tbrw.cgi?2000/rankings.shtml

Game results taken from US College Hockey Online's Division I composite schedule

See also

KRACH vs RPI (and PWR)

The NCAA assigns at-large bids and seeds for its Division I Men's Ice Hockey Tournament based primarily on the system of pairwise comparisons, an important component of which is the Ratings Percentage Index. However, as was demonstrated by the case of MAAC regular season champions Quinnipiac last season, the RPI can overestimate the strength of a team's schedule if their opponents also played predominantly weak schedules. A rating system which seems, both in theory and in practice, to be immune to this defect, while only considering the factors used in producing the RPI (won-lost-tied records between pairs of teams, without regard to factors such as score or home-ice advantage) is the Bradley-Terry or KRACH rating system. The table below lists the 54 Division I teams by their KRACH ratings (The RRWP column lists the expected winning percentage a team would have, according to the Bradley-Terry ratings, if they played each other team in the country an equal number of times), along with their ratings and rankings according to RPI and PWR, the latter being the number of pairwise comparisons won with other teams with overall records of .500 or above. The "Strength" column under RPI gives the combination (10/13 winning percentage and 3/13 opponents winning percentage) which is the effective measure of the strength of an opponent in the RPI calculations. Finally, the columns labelled KPWR provide the rankings and number of comparisons won according to a proposed modification of the pairwise comparison system, described below.

Team KRACH RPI W-L-T Pct. PWR KPWR
Rk Rating RRWP Rk Rating Rk Strength Rk Rating Rk Rating
Wisconsin 1 863.4 .8577 1 .6095 1 .7237 31-8-1 .7875 1 25 1 25
North Dakota 2 652.0 .8234 3 .5982 5 .6845 26-8-5 .7308 3 23 3 23
Maine 3 615.7 .8157 2 .6082 2 .7001 26-7-5 .7500 2 24 2 24
New Hampshire 4 503.9 .7876 4 .5921 7 .6641 23-8-6 .7027 7 19 4 21
Boston Coll 5 490.5 .7836 6 .5835 10 .6563 26-11-1 .6974 8 18 5 21
Boston Univ 6 435.4 .7655 7 .5830 12 .6506 24-9-7 .6875 9 18 7 20
St Lawrence 7 432.8 .7646 5 .5886 3 .6971 24-7-2 .7576 4 22 6 20
St Cloud 8 360.1 .7351 13 .5459 14 .5855 21-13-3 .6081 13 12 8 18
Michigan 9 323.1 .7170 10 .5680 8 .6638 26-9-4 .7179 12 14 9 16
Colgate 10 312.5 .7113 9 .5701 6 .6702 23-8-2 .7273 6 19 10 16
Mich State 11 308.4 .7091 12 .5631 11 .6508 26-10-4 .7000 11 16 11 16
Minnesota 12 305.6 .7075 14 .5439 22 .5268 20-19-2 .5122 17 7 13 13
MSU-Mankato 13 283.7 .6946 16 .5250 16 .5621 19-13-3 .5857 14 12 12 14
CO College 14 238.3 .6634 17 .5240 25 .5101 18-18-3 .5000 16 8 15 11
RPI 15 194.8 .6263 15 .5427 13 .5940 22-13-2 .6216 15 11 17 9
Providence 16 184.5 .6161 22 .5078 26 .5020 18-18-2 .5000 25 3 14 12
Northern Mich 17 178.4 .6098 20 .5125 15 .5755 22-13-4 .6154 24 4 18 6
Niagara 18 175.9 .6072 8 .5723 9 .6579 18-7-2 .7037 5 20 16 10
Ferris State 19 163.1 .5929 19 .5181 20 .5337 19-16-2 .5405 21 5 19 6
AK-Anchorage 20 159.4 .5885 30 .4816 30 .4653 15-18-3 .4583
Clarkson 21 150.9 .5781 18 .5205 21 .5284 16-14-3 .5303 18 7 20 6
Northeastern 22 147.8 .5742 26 .4913 34 .4354 12-19-5 .4028
Cornell 23 142.0 .5666 21 .5099 23 .5235 16-14-2 .5312 19 6 21 6
Lake Superior 24 136.1 .5585 25 .4949 24 .5147 18-16-2 .5278 20 6 22 6
Merrimack 25 133.3 .5545 27 .4901 36 .4266 11-19-6 .3889
Denver U 26 129.9 .5496 36 .4704 37 .4246 15-23-2 .4000
Minn-Duluth 27 129.9 .5495 43 .4614 44 .4024 13-22-0 .3714
NE-Omaha 28 117.1 .5298 28 .4886 29 .4738 16-19-7 .4643
Notre Dame 29 113.6 .5241 31 .4790 27 .4760 16-18-8 .4762
Mass-Amherst 30 107.5 .5136 33 .4753 41 .4115 11-20-5 .3750
Bowling Green 31 101.5 .5027 32 .4756 32 .4544 15-19-1 .4429
Miami 32 98.35 .4969 35 .4714 35 .4281 13-20-3 .4028
Vermont 33 87.42 .4749 38 .4637 42 .4113 5-9-3 .3824
Harvard 34 87.05 .4741 42 .4618 38 .4211 11-17-2 .4000
Princeton 35 84.79 .4693 41 .4623 33 .4390 10-14-4 .4286
Ohio State 36 83.84 .4672 40 .4626 40 .4117 11-19-4 .3824
Western Mich 37 80.18 .4590 39 .4633 43 .4080 12-21-3 .3750
Mass-Lowell 38 76.97 .4515 45 .4563 47 .3624 9-22-3 .3088
Dartmouth 39 69.93 .4342 46 .4476 45 .3946 9-17-4 .3667
Yale 40 66.74 .4259 37 .4667 39 .4143 9-16-5 .3833
Brown 41 44.82 .3583 48 .4203 50 .3219 6-19-3 .2679
Union 42 38.01 .3324 49 .4082 51 .3103 8-24-1 .2576
AK-Fairbanks 43 31.54 .3046 52 .3829 52 .2567 5-25-2 .1875
Quinnipiac 44 30.43 .2994 11 .5657 4 .6958 20-5-3 .7679 10 16 23 3
Michigan Tech 45 25.71 .2761 53 .3761 53 .2029 4-34-0 .1053
Air Force 46 21.32 .2517 34 .4736 28 .4739 9-10-1 .4750
Canisius 47 8.550 .1556 23 .5068 17 .5547 14-10-1 .5800 26 1 24 2
Iona 48 7.986 .1497 24 .4954 18 .5430 15-11-3 .5690 22 5 26 0
Sacred Heart 49 7.535 .1449 29 .4860 19 .5416 14-10-3 .5741 23 4 25 1
Army 50 6.360 .1314 47 .4222 46 .3937 7-12-2 .3810
Connecticut 51 5.448 .1200 44 .4607 31 .4637 13-15-1 .4655
Holy Cross 52 2.405 .0711 50 .4033 48 .3343 7-18-2 .2963
American Intl 53 1.803 .0580 51 .3917 49 .3289 5-14-3 .2955
Fairfield 54 .4275 .0156 54 .3180 54 .1588 1-25-2 .0714

Pairwise Comparisons

What follows is a table listing the teams with non-losing records against tournament-eligible competition, known as Teams Under Consideration (TUC). For each team, the table lists the number of comparisons they win with other TUCs (PWR), their RPI, and the teams with which they win comparisons. Each entry in the table corresponding to a comparison is a link to a breakdown of the criteria in that comparison. Additionally, each team's name in the table is a link to a list of the games contributing to their RPI as well as to their record vs TUCs and in the last 16 games.

Pairwise Comparisons
Rk Team PWR RPI Comparisons Won
1 Wisconsin (W) 25 .6095 Me ND SL Ni Cg NH BC BU Qn MS Mi SC Mk RP CC Mn Ck Cr LS FS Io SH NM Pv Ca
2 Maine (H) 24 .6082 ND SL Ni Cg NH BC BU Qn MS Mi SC Mk RP CC Mn Ck Cr LS FS Io SH NM Pv Ca
3 North Dakota (W) 23 .5982   SL Ni Cg NH BC BU Qn MS Mi SC Mk RP CC Mn Ck Cr LS FS Io SH NM Pv Ca
4 St Lawrence (E) 22 .5886     Ni Cg NH BC BU Qn MS Mi SC Mk RP CC Mn Ck Cr LS FS Io SH NM Pv Ca
5 Niagara (A) 20 .5723       Cg   BC BU Qn MS Mi SC Mk RP CC Mn Ck Cr LS FS Io SH NM Pv Ca
6 Colgate (E) 19 .5701         NH BC   Qn MS Mi SC Mk RP CC Mn Ck Cr LS FS Io SH NM Pv Ca
7 New Hampshire (H) 19 .5921       Ni   BC   Qn MS Mi SC Mk RP CC Mn Ck Cr LS FS Io SH NM Pv Ca
8 Boston Coll (H) 18 .5835             BU Qn MS Mi SC Mk RP CC Mn Ck Cr LS FS Io SH NM Pv Ca
9 Boston Univ (H) 18 .5830         Cg NH   Qn   Mi SC Mk RP CC Mn Ck Cr LS FS Io SH NM Pv Ca
10 Quinnipiac (M) 16 .5657                 MS Mi SC Mk RP CC Mn Ck Cr LS FS Io SH NM Pv Ca
11 Mich State (C) 16 .5631               BU   Mi SC Mk RP CC Mn Ck Cr LS FS Io SH NM Pv Ca
12 Michigan (C) 14 .5680                     SC Mk RP CC Mn Ck Cr LS FS Io SH NM Pv Ca
13 St Cloud (W) 12 .5459                       Mk RP CC Mn Ck Cr   FS Io SH NM Pv Ca
14 MSU-Mankato (W) 12 .5250                         RP CC Mn Ck Cr LS FS Io SH NM Pv Ca
15 RPI (E) 11 .5427                           CC Mn Ck Cr LS FS Io SH NM Pv Ca
16 CO College (W) 8 .5240                               Ck Cr LS FS Io SH   Pv Ca
17 Minnesota (W) 7 .5439                             CC Ck   LS FS     NM Pv Ca
18 Clarkson (E) 7 .5205                                 Cr LS   Io SH NM Pv Ca
19 Cornell (E) 6 .5099                               Mn   LS     SH NM Pv Ca
20 Lake Superior (C) 6 .4949                       SC             FS Io SH NM   Ca
21 Ferris State (C) 5 .5181                                 Ck Cr   Io     Pv Ca
22 Iona (M) 5 .4954                               Mn   Cr     SH NM   Ca
23 Sacred Heart (M) 4 .4860                               Mn       FS   NM Pv  
24 Northern Mich (C) 4 .5125                             CC         FS     Pv Ca
25 Providence (H) 3 .5078                                     LS   Io     Ca
26 Canisius (M) 1 .5068                                           SH    

Bradley-Terry Modified Pairwise Comparisons

In addition to the potential use of KRACH or RRWP as a replacement for RPI, the other criteria in the NCAA's pairwise comparison system can also be improved with the use of Bradley-Terry methods. A modification to the pairwise comparison system has been proposed which replaces RPI as a criterion and tiebreaker with RRWP, and replaces the three criteria which compare the two teams' winning percentages in subsets of their games (record vs TUCs, in the last 16 games and against common opponents) with a comparison of the Bradley-Terry ratings they would need in order to compile the observed set of results in those games. Modifying the criteria in this way corrects for possible differences in the strength of the opposition being considered; if two teams have for example played the same set of TUCs the same number of times, comparing these effective Bradley-Terry ratings will produce the same results as comparing the won-lost-tied records against TUCs.

The table below lists the results of these modified pairwise comparisons, analogously to the table above. Once again, each comparison result is linked to a breakdown of which team won which criterion in the modified system, and each team's name is a link to the breakdown of the team's overall KRACH rating plus the criterion-specific ones for "vs TUCs" and "Last 16".

Bradley-Terry Modified Pairwise Comparisons
Rk Team KPWR RRWP Comparisons Won
1 Wisconsin 25 .8577 Me ND NH BC SL BU SC Mi Cg MS Mk Mn Pv CC Ni RP NM FS Ck Cr LS Qn Ca SH Io
2 Maine 24 .8157 ND NH BC SL BU SC Mi Cg MS Mk Mn Pv CC Ni RP NM FS Ck Cr LS Qn Ca SH Io
3 North Dakota 23 .8234   NH BC SL BU SC Mi Cg MS Mk Mn Pv CC Ni RP NM FS Ck Cr LS Qn Ca SH Io
4 New Hampshire 21 .7876     BC SL   SC Mi Cg MS Mk Mn Pv CC Ni RP NM FS Ck Cr LS Qn Ca SH Io
5 Boston Coll 21 .7836       SL BU SC Mi Cg MS Mk Mn Pv CC Ni RP NM FS Ck Cr LS Qn Ca SH Io
6 St Lawrence 20 .7646         BU SC Mi Cg MS Mk Mn Pv CC Ni RP NM FS Ck Cr LS Qn Ca SH Io
7 Boston Univ 20 .7655     NH     SC Mi Cg MS Mk Mn Pv CC Ni RP NM FS Ck Cr LS Qn Ca SH Io
8 St Cloud 18 .7351             Mi Cg MS Mk Mn Pv CC Ni RP NM FS Ck Cr LS Qn Ca SH Io
9 Michigan 16 .7170               Cg   Mk Mn Pv CC Ni RP NM FS Ck Cr LS Qn Ca SH Io
10 Colgate 16 .7113                 MS Mk Mn Pv CC Ni RP NM FS Ck Cr LS Qn Ca SH Io
11 Mich State 16 .7091               Mi   Mk Mn Pv CC Ni RP NM FS Ck Cr LS Qn Ca SH Io
12 MSU-Mankato 14 .6946                     Mn Pv CC Ni RP NM FS Ck Cr LS Qn Ca SH Io
13 Minnesota 13 .7075                       Pv CC Ni RP NM FS Ck Cr LS Qn Ca SH Io
14 Providence 12 .6161                         CC Ni RP NM FS Ck Cr LS Qn Ca SH Io
15 CO College 11 .6634                           Ni RP NM FS Ck Cr LS Qn Ca SH Io
16 Niagara 10 .6072                             RP NM FS Ck Cr LS Qn Ca SH Io
17 RPI 9 .6263                               NM FS Ck Cr LS Qn Ca SH Io
18 Northern Mich 6 .6098                                 FS Ck     Qn Ca SH Io
19 Ferris State 6 .5929                                   Ck Cr   Qn Ca SH Io
20 Clarkson 6 .5781                                     Cr LS Qn Ca SH Io
21 Cornell 6 .5666                                 NM     LS Qn Ca SH Io
22 Lake Superior 6 .5585                                 NM FS     Qn Ca SH Io
23 Quinnipiac 3 .2994                                           Ca SH Io
24 Canisius 2 .1556                                             SH Io
25 Sacred Heart 1 .1449                                               Io
26 Iona 0 .1497                                                

Last Modified: 2012 March 25

Joe Schlobotnik / joe@amurgsval.org

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