Ranking Systems for College hockey

© 1999-2001, Joe Schlobotnik (archives)

URL for this frameset: http://www.slack.net/~whelan/tbrw/tbrw.cgi?2001/rankings.shtml

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

See also

KRACH vs RPI

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 the past few seasons, 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 58 tournament-eligible 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. 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. (So it is a measure, not of the strength of a team's schedule, but of the contribution of that team to the strength of a schedule they appear on.) Note that this is more heavily weighted towards winning percentage than is RPI itself.

Team KRACH RPI W-L-T Pct.
Rk Rating RRWP Rk Rating Rk Strength
Mich State 1 1135 .8782 1 .6334 1 .7730 32-4-4 .8500
St Cloud 2 1113 .8764 3 .5952 3 .7164 31-8-1 .7875
North Dakota 3 789.9 .8391 5 .5843 4 .6784 27-7-9 .7326
Boston Coll 4 732.3 .8300 2 .6162 2 .7190 30-8-2 .7750
CO College 5 720.2 .8280 4 .5866 5 .6476 26-12-1 .6795
Minnesota 6 676.0 .8200 7 .5713 6 .6423 27-12-2 .6829
Wisconsin 7 515.2 .7836 9 .5560 15 .5783 21-14-4 .5897
Michigan 8 423.9 .7549 6 .5752 8 .6277 25-12-5 .6548
Denver U 9 391.8 .7428 14 .5425 21 .5501 19-15-4 .5526
Providence 10 327.1 .7140 10 .5532 11 .6007 22-12-5 .6282
Maine 11 313.2 .7068 8 .5578 12 .5910 19-11-7 .6081
New Hampshire 12 294.8 .6967 11 .5469 13 .5904 21-12-6 .6154
MSU-Mankato 13 293.6 .6959 22 .5187 27 .5150 19-18-1 .5132
Northern Mich 14 244.5 .6645 19 .5252 22 .5500 18-13-7 .5658
NE-Omaha 15 222.4 .6477 18 .5290 17 .5655 22-15-3 .5875
Western Mich 16 218.9 .6449 17 .5321 16 .5691 20-13-6 .5897
Miami 17 197.2 .6261 21 .5194 24 .5401 20-16-2 .5526
Mass-Lowell 18 188.4 .6178 20 .5217 25 .5332 19-16-3 .5395
Clarkson 19 174.1 .6033 13 .5433 10 .6073 21-11-3 .6429
St Lawrence 20 165.7 .5943 15 .5371 14 .5849 20-12-4 .6111
Boston Univ 21 161.0 .5889 30 .4994 35 .4492 14-20-3 .4189
Ohio State 22 157.1 .5844 29 .5038 31 .4843 16-18-2 .4722
Northeastern 23 146.0 .5707 34 .4886 37 .4426 13-19-4 .4167
Michigan Tech 24 135.4 .5567 42 .4570 52 .3439 8-24-4 .2778
Merrimack 25 130.5 .5498 33 .4928 36 .4479 14-20-4 .4211
Bowling Green 26 127.4 .5452 31 .4956 32 .4751 16-19-5 .4625
Harvard 27 124.7 .5412 24 .5102 29 .5140 16-15-2 .5152
AK-Anchorage 28 122.9 .5385 44 .4522 53 .3333 7-24-5 .2639
Dartmouth 29 116.5 .5285 28 .5047 26 .5205 16-14-4 .5294
Ferris State 30 116.0 .5277 36 .4770 39 .4299 12-19-5 .4028
Cornell 31 114.9 .5259 23 .5167 23 .5452 16-12-5 .5606
RPI 32 97.09 .4945 32 .4932 28 .5149 17-15-2 .5294
Yale 33 90.11 .4807 35 .4846 33 .4735 14-16-1 .4677
AK-Fairbanks 34 89.78 .4800 45 .4520 46 .3922 9-19-8 .3611
Lake Superior 35 87.28 .4748 40 .4596 50 .3737 11-23-0 .3235
Notre Dame 36 86.18 .4724 43 .4560 49 .3751 9-22-7 .3289
AL-Huntsville 37 78.73 .4558 26 .5056 18 .5654 15-10-0 .6000
Vermont 38 77.08 .4519 38 .4674 34 .4495 14-18-2 .4412
Mass-Amherst 39 76.22 .4499 46 .4449 51 .3483 8-22-4 .2941
Minn-Duluth 40 75.87 .4490 53 .4227 55 .2993 7-28-4 .2308
Princeton 41 66.10 .4241 41 .4594 42 .4231 10-16-5 .4032
Union 42 57.04 .3981 39 .4597 40 .4283 12-18-4 .4118
Colgate 43 49.16 .3725 47 .4377 47 .3823 10-20-4 .3529
Niagara 44 38.94 .3340 49 .4314 41 .4276 10-14-5 .4310
Mercyhurst 45 36.30 .3229 12 .5461 7 .6312 22-10-2 .6765
Quinnipiac 46 33.43 .3100 16 .5356 9 .6096 22-11-4 .6486
Brown 47 29.33 .2902 55 .4011 56 .2767 4-21-4 .2069
Iona 48 21.60 .2469 27 .5050 20 .5512 17-12-4 .5758
Canisius 49 20.63 .2407 25 .5089 19 .5561 16-11-4 .5806
Air Force 50 20.06 .2370 52 .4258 38 .4305 9-12-3 .4375
Sacred Heart 51 13.51 .1886 37 .4751 30 .5109 14-12-5 .5323
Connecticut 52 10.02 .1566 48 .4371 43 .4199 12-18-4 .4118
Bemidji State 53 7.986 .1348 57 .3538 58 .1889 1-22-3 .0962
Army 54 7.676 .1313 50 .4274 45 .3935 12-20-0 .3750
Fairfield 55 6.933 .1224 51 .4273 44 .4087 11-17-2 .4000
American Intl 56 6.371 .1153 54 .4192 48 .3821 10-18-1 .3621
Holy Cross 57 4.908 .0951 56 .3965 54 .3219 8-22-2 .2812
Bentley 58 2.167 .0478 58 .3452 57 .2325 4-23-2 .1724

Impact of Strength of Schedule

Although it is not usually defined this way, the KRACH rating can be thought of as a product of two factors, one quantifying a team's won-lost-tied record, the other its strength of schedule. The first factor is simply the ratio of points for (twice wins plus ties) to points against (twice losses plus ties); the "strength of schedule" factor is a weighted average of the KRACH ratings of a team's opponents. (This sounds circular at first, but under normal circumstances, there is a unique ranking which satisfies these conditions for all teams. In fact, this self-referential definition is what gives KRACH the power to ferret out the strength of teams in the presence of mostly isolated schedules.) The RPI can also be split into contributions from won-lost-tied record and strength of schedule. In this case, the two are added, 7 parts winning percentage to 13 parts strength of schedule. The strength of schedule is made up of 10 parts opponents' winning percentage and 3 parts opponents' opponents' winning percentage. (It is the average "strength" of a team's opponents, where "strength" is closely related to the last column in the table above.)

The following table lists each team's strength of schedule according to the two measures and breaks down the KRACH and RPI ratings into their contributions from W-L-T record and strength of schedule.

Team W-L-T KRACH RPI
Rk SOS Rk PF/PA Rk Rating Rk SOS Rk Pct. Rk Rating
Wisconsin 21-14-4 1 358.4 16 1.438 7 515.2 4 .5378 16 .5897 9 .5560
Michigan Tech 8-24-4 2 352.1 53 .3846 24 135.4 2 .5535 53 .2778 42 .4570
AK-Anchorage 7-24-5 3 342.8 54 .3585 28 122.9 1 .5536 54 .2639 44 .4522
CO College 26-12-1 4 339.7 6 2.120 5 720.2 6 .5366 6 .6795 4 .5866
Denver U 19-15-4 5 317.2 23 1.235 9 391.8 5 .5370 23 .5526 14 .5425
Minnesota 27-12-2 6 313.8 5 2.154 6 676.0 23 .5112 5 .6829 7 .5713
St Cloud 31-8-1 7 300.5 2 3.706 2 1113 37 .4916 2 .7875 3 .5952
North Dakota 27-7-9 8 288.4 4 2.739 3 789.9 27 .5045 4 .7326 5 .5843
MSU-Mankato 19-18-1 9 278.5 30 1.054 13 293.6 16 .5217 30 .5132 22 .5187
Minn-Duluth 7-28-4 10 252.9 55 .3000 40 75.87 14 .5261 55 .2308 53 .4227
Michigan 25-12-5 11 223.5 8 1.897 8 423.9 8 .5323 8 .6548 6 .5752
Boston Univ 14-20-3 12 223.3 38 .7209 21 161.0 3 .5427 38 .4189 30 .4994
Boston Coll 30-8-2 13 212.6 3 3.444 4 732.3 11 .5306 3 .7750 2 .6162
Northeastern 13-19-4 14 204.3 39 .7143 23 146.0 12 .5273 39 .4167 34 .4886
Maine 19-11-7 15 201.9 14 1.552 11 313.2 10 .5307 14 .6081 8 .5578
Mich State 32-4-4 16 200.2 1 5.667 1 1135 19 .5168 1 .8500 1 .6334
Providence 22-12-5 17 193.6 11 1.690 10 327.1 21 .5128 11 .6282 10 .5532
Northern Mich 18-13-7 18 187.6 21 1.303 14 244.5 28 .5034 21 .5658 19 .5252
New Hampshire 21-12-6 19 184.3 12 1.600 12 294.8 24 .5101 12 .6154 11 .5469
Mass-Amherst 8-22-4 20 182.9 51 .4167 39 76.22 13 .5261 51 .2941 46 .4449
Lake Superior 11-23-0 21 182.5 50 .4783 35 87.28 7 .5328 50 .3235 40 .4596
Merrimack 14-20-4 22 179.4 37 .7273 25 130.5 9 .5314 37 .4211 33 .4928
Notre Dame 9-22-7 23 175.8 49 .4902 36 86.18 15 .5244 49 .3289 43 .4560
Ohio State 16-18-2 24 175.6 31 .8947 22 157.1 17 .5207 31 .4722 29 .5038
Ferris State 12-19-5 25 172.0 43 .6744 30 116.0 18 .5169 43 .4028 36 .4770
Mass-Lowell 19-16-3 26 160.8 25 1.171 18 188.4 22 .5122 25 .5395 20 .5217
Miami 20-16-2 27 159.6 24 1.235 17 197.2 29 .5015 24 .5526 21 .5194
AK-Fairbanks 9-19-8 28 158.8 47 .5652 34 89.78 31 .5010 47 .3611 45 .4520
NE-Omaha 22-15-3 29 156.1 18 1.424 15 222.4 32 .4975 18 .5875 18 .5290
Western Mich 20-13-6 30 152.3 17 1.438 16 218.9 30 .5011 17 .5897 17 .5321
Bowling Green 16-19-5 31 148.0 33 .8605 26 127.4 20 .5134 33 .4625 31 .4956
Harvard 16-15-2 32 117.3 29 1.062 27 124.7 25 .5076 29 .5152 24 .5102
Brown 4-21-4 33 112.4 56 .2609 47 29.33 26 .5057 56 .2069 55 .4011
St Lawrence 20-12-4 34 105.5 13 1.571 20 165.7 33 .4973 13 .6111 15 .5371
Dartmouth 16-14-4 35 103.5 27 1.125 29 116.5 38 .4914 27 .5294 28 .5047
Yale 14-16-1 36 102.5 32 .8788 33 90.11 34 .4937 32 .4677 35 .4846
Princeton 10-16-5 37 97.83 42 .6757 41 66.10 40 .4896 42 .4032 41 .4594
Vermont 14-18-2 38 97.64 34 .7895 38 77.08 43 .4815 34 .4412 38 .4674
Clarkson 21-11-3 39 96.70 10 1.800 19 174.1 39 .4897 10 .6429 13 .5433
Colgate 10-20-4 40 90.12 48 .5455 43 49.16 42 .4834 48 .3529 47 .4377
Cornell 16-12-5 41 90.05 22 1.276 31 114.9 35 .4931 22 .5606 23 .5167
RPI 17-15-2 42 86.30 28 1.125 32 97.09 46 .4738 28 .5294 32 .4932
Union 12-18-4 43 81.48 40 .7000 42 57.04 41 .4856 40 .4118 39 .4597
Bemidji State 1-22-3 44 75.07 58 .1064 53 7.986 36 .4925 58 .0962 57 .3538
AL-Huntsville 15-10-0 45 52.49 15 1.500 37 78.73 51 .4548 15 .6000 26 .5056
Niagara 10-14-5 46 51.40 36 .7576 44 38.94 57 .4316 36 .4310 49 .4314
Air Force 9-12-3 47 25.79 35 .7778 50 20.06 58 .4196 35 .4375 52 .4258
Quinnipiac 22-11-4 48 18.11 9 1.846 46 33.43 45 .4748 9 .6486 16 .5356
Mercyhurst 22-10-2 49 17.36 7 2.091 45 36.30 44 .4759 7 .6765 12 .5461
Iona 17-12-4 50 15.91 20 1.357 48 21.60 48 .4669 20 .5758 27 .5050
Canisius 16-11-4 51 14.90 19 1.385 49 20.63 47 .4702 19 .5806 25 .5089
Connecticut 12-18-4 52 14.31 41 .7000 52 10.02 52 .4508 41 .4118 48 .4371
Army 12-20-0 53 12.79 45 .6000 54 7.676 50 .4556 45 .3750 50 .4274
Holy Cross 8-22-2 54 12.54 52 .3913 57 4.908 49 .4586 52 .2812 56 .3965
Sacred Heart 14-12-5 55 11.87 26 1.138 51 13.51 54 .4444 26 .5323 37 .4751
American Intl 10-18-1 56 11.23 46 .5676 56 6.371 53 .4500 46 .3621 54 .4192
Bentley 4-23-2 57 10.40 57 .2083 58 2.167 56 .4383 57 .1724 58 .3452
Fairfield 11-17-2 58 10.40 44 .6667 55 6.933 55 .4419 44 .4000 51 .4273

Pairwise Comparisons

The RPI is one of five selection criteria used by the NCAA to evaluate teams with non-losing records against tournament-eligible competition, known as Teams Under Consideration (TUC), performing pairwise comparisons among them. For each team, the table below 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 Mich State (C) 29 .6334 BC SC ND Mi CC Mn Me Wi Pv NH Mh Ck SL DU Qn NO Mm Ca WM ML NM Cr Mk Ha AH Da Io RP SH
2 Boston Coll (H) 28 .6162 SC ND Mi CC Mn Me Wi Pv NH Mh Ck SL DU Qn NO Mm Ca WM ML NM Cr Mk Ha AH Da Io RP SH
3 SCloud (W) 27 .5952   ND Mi CC Mn Me Wi Pv NH Mh Ck SL DU Qn NO Mm Ca WM ML NM Cr Mk Ha AH Da Io RP SH
4 North Dakota (W) 26 .5843     Mi CC Mn Me Wi Pv NH Mh Ck SL DU Qn NO Mm Ca WM ML NM Cr Mk Ha AH Da Io RP SH
5 Michigan (C) 25 .5752       CC Mn Me Wi Pv NH Mh Ck SL DU Qn NO Mm Ca WM ML NM Cr Mk Ha AH Da Io RP SH
6 CCollege (W) 24 .5866         Mn Me Wi Pv NH Mh Ck SL DU Qn NO Mm Ca WM ML NM Cr Mk Ha AH Da Io RP SH
7 Minnesota (W) 23 .5713           Me Wi Pv NH Mh Ck SL DU Qn NO Mm Ca WM ML NM Cr Mk Ha AH Da Io RP SH
8 Maine (H) 22 .5578             Wi Pv NH Mh Ck SL DU Qn NO Mm Ca WM ML NM Cr Mk Ha AH Da Io RP SH
9 Wisconsin (W) 20 .5560               Pv NH   Ck SL DU Qn NO Mm Ca WM ML NM Cr Mk Ha AH Da Io RP SH
10 Providence (H) 20 .5532                 NH Mh Ck SL DU Qn NO Mm Ca WM ML NM Cr Mk Ha AH Da Io RP SH
11 New Hampshire (H) 19 .5469                   Mh Ck SL DU Qn NO Mm Ca WM ML NM Cr Mk Ha AH Da Io RP SH
12 Mercyhurst (M) 19 .5461               Wi     Ck SL DU Qn NO Mm Ca WM ML NM Cr Mk Ha AH Da Io RP SH
13 Clarkson (E) 17 .5433                       SL DU Qn NO Mm Ca WM ML NM Cr Mk Ha AH Da Io RP SH
14 SLawrence (E) 15 .5371                           Qn NO Mm Ca WM ML NM Cr Mk Ha AH Da Io RP SH
15 Denver U (W) 14 .5425                         SL Qn   Mm   WM ML NM Cr Mk Ha AH Da Io RP SH
16 Quinnipiac (M) 14 .5356                             NO Mm Ca WM ML NM Cr Mk Ha AH Da Io RP SH
17 NE-Omaha (C) 14 .5290                           DU   Mm Ca WM ML NM Cr Mk Ha AH Da Io RP SH
18 Miami (C) 11 .5194                                 Ca WM   NM Cr Mk Ha AH Da Io RP SH
19 Canisius (M) 11 .5089                           DU       WM   NM Cr Mk Ha AH Da Io RP SH
20 Western Mich (C) 10 .5321                                     ML NM Cr Mk Ha AH Da Io RP SH
21 Mass-Lowell (H) 10 .5217                                 Mm Ca     Cr Mk Ha AH Da Io RP SH
22 Northern Mich (C) 9 .5252                                       ML Cr Mk Ha AH Da Io RP SH
23 Cornell (E) 6 .5167                                           Mk Ha AH   Io RP SH
24 MSU-Mankato (W) 5 .5187                                             Ha AH   Io RP SH
25 Harvard (E) 5 .5102                                               AH Da Io RP SH
26 AL-Huntsville (A) 4 .5056                                                 Da Io RP SH
27 Dartmouth (E) 4 .5047                                           Cr Mk       RP SH
28 Iona (M) 3 .5050                                                   Da RP SH
29 RPI (E) 1 .4932                                                       SH
30 Sacred Heart (M) 0 .4751                                                        

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 Mich State 29 .8782 SC ND BC CC Mn Wi Mi Pv DU Me NH Mk NM NO WM Mm ML Ck SL Ha Da Cr RP AH Mh Qn Io Ca SH
2 SCloud 28 .8764 ND BC CC Mn Wi Mi Pv DU Me NH Mk NM NO WM Mm ML Ck SL Ha Da Cr RP AH Mh Qn Io Ca SH
3 North Dakota 27 .8391   BC CC Mn Wi Mi Pv DU Me NH Mk NM NO WM Mm ML Ck SL Ha Da Cr RP AH Mh Qn Io Ca SH
4 Boston Coll 26 .8300     CC Mn Wi Mi Pv DU Me NH Mk NM NO WM Mm ML Ck SL Ha Da Cr RP AH Mh Qn Io Ca SH
5 CCollege 25 .8280       Mn Wi Mi Pv DU Me NH Mk NM NO WM Mm ML Ck SL Ha Da Cr RP AH Mh Qn Io Ca SH
6 Minnesota 24 .8200         Wi Mi Pv DU Me NH Mk NM NO WM Mm ML Ck SL Ha Da Cr RP AH Mh Qn Io Ca SH
7 Wisconsin 23 .7836           Mi Pv DU Me NH Mk NM NO WM Mm ML Ck SL Ha Da Cr RP AH Mh Qn Io Ca SH
8 Michigan 22 .7549             Pv DU Me NH Mk NM NO WM Mm ML Ck SL Ha Da Cr RP AH Mh Qn Io Ca SH
9 Providence 21 .7140               DU Me NH Mk NM NO WM Mm ML Ck SL Ha Da Cr RP AH Mh Qn Io Ca SH
10 Denver U 20 .7428                 Me NH Mk NM NO WM Mm ML Ck SL Ha Da Cr RP AH Mh Qn Io Ca SH
11 Maine 19 .7068                   NH Mk NM NO WM Mm ML Ck SL Ha Da Cr RP AH Mh Qn Io Ca SH
12 New Hampshire 18 .6967                     Mk NM NO WM Mm ML Ck SL Ha Da Cr RP AH Mh Qn Io Ca SH
13 MSU-Mankato 16 .6959                       NM   WM Mm ML Ck SL Ha Da Cr RP AH Mh Qn Io Ca SH
14 Northern Mich 16 .6645                         NO WM Mm ML Ck SL Ha Da Cr RP AH Mh Qn Io Ca SH
15 NE-Omaha 16 .6477                       Mk   WM Mm ML Ck SL Ha Da Cr RP AH Mh Qn Io Ca SH
16 Western Mich 13 .6449                             Mm ML   SL Ha Da Cr RP AH Mh Qn Io Ca SH
17 Miami 13 .6261                               ML Ck SL Ha Da Cr RP AH Mh Qn Io Ca SH
18 Mass-Lowell 12 .6178                                 Ck SL Ha Da Cr RP AH Mh Qn Io Ca SH
19 Clarkson 12 .6033                             WM     SL Ha Da Cr RP AH Mh Qn Io Ca SH
20 SLawrence 10 .5943                                     Ha Da Cr RP AH Mh Qn Io Ca SH
21 Harvard 9 .5412                                       Da Cr RP AH Mh Qn Io Ca SH
22 Dartmouth 8 .5285                                         Cr RP AH Mh Qn Io Ca SH
23 Cornell 7 .5259                                           RP AH Mh Qn Io Ca SH
24 RPI 6 .4945                                             AH Mh Qn Io Ca SH
25 AL-Huntsville 5 .4558                                               Mh Qn Io Ca SH
26 Mercyhurst 4 .3229                                                 Qn Io Ca SH
27 Quinnipiac 3 .3100                                                   Io Ca SH
28 Iona 2 .2469                                                     Ca SH
29 Canisius 1 .2407                                                       SH
30 Sacred Heart 0 .1886                                                        

Last Modified: 2012 March 25

Joe Schlobotnik / joe@amurgsval.org

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