Ratings Percentage Index for D1 College Hockey (2009-2010)

© 1999-2009, Joe Schlobotnik (archives)

URL for this frameset: http://slack.net/~whelan/tbrw/tbrw.cgi?2010/rpi.shtml

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

Today's RPI (including games of 2010 March 20)

Team RPI Record RPIRecord Sched Strength Opp Pct Opp Opp Pct RPIStr
Rk Rating Rk W-L-T Pct Rk W-L-T Pct Rk SOS Rk OPct Rk OOPct Rk Rating
Miami 1 .5793 1 27-7-7 .7439 1 25-7-7 .7308 5 .5288 5 .5462 8 .5221 1 .5906
Denver U 2 .5766 2 27-9-4 .7250 2 26-9-4 .7179 4 .5294 18 .5155 1 .5348 2 .5729
Wisconsin 3 .5685 7 25-10-4 .6923 7 25-10-4 .6923 6 .5272 19 .5154 2 .5318 5 .5649
Boston Coll 4 .5625 3T 25-10-3 .6974 3T 25-10-3 .6974 17 .5175 21 .5141 12 .5188 4 .5654
North Dakota 5 .5623 9 25-12-5 .6548 9 25-12-5 .6548 2 .5315 6 .5389 3 .5286 3 .5713
St Cloud 6 .5504 10 23-13-5 .6220 10 23-13-5 .6220 8 .5265 12 .5269 5 .5264 6 .5535
Cornell 7 .5462 5 21-8-4 .6970 5 21-8-4 .6970 34 .4960 38 .4902 34 .4982 8 .5481
Bemidji State 8 .5429 6 23-9-4 .6944 6 23-9-4 .6944 35 .4924 49 .4674 33 .5022 19 .5310
Yale 9 .5367 8 20-9-3 .6719 8 20-9-3 .6719 37 .4916 37 .4917 41 .4916 9 .5421
Northern Mich 10 .5348 13T 20-12-8 .6000 13T 20-12-8 .6000 21 .5131 24 .5095 20 .5144 12 .5348
Ferris State 11 .5334 13T 21-13-6 .6000 13T 21-13-6 .6000 23 .5112 23 .5101 26 .5117 11 .5352
Minn-Duluth 12 .5331 18 22-17-1 .5625 18 22-17-1 .5625 12 .5233 22 .5123 4 .5275 20 .5263
New Hampshire 13 .5330 19 17-13-7 .5541 19 17-13-7 .5541 9 .5260 4 .5509 17 .5164 7 .5518
Michigan 14 .5316 15 25-17-1 .5930 15 25-17-1 .5930 24 .5111 26 .5085 25 .5121 18 .5322
AK-Fairbanks 15 .5299 16 18-11-9 .5921 16 18-11-9 .5921 27 .5091 33 .4985 22 .5133 22 .5247
Vermont 16 .5261 21 17-14-7 .5395 21 17-14-7 .5395 14 .5216 9 .5363 18 .5159 10 .5372
Mich State 17 .5254 17 19-13-6 .5789 17 19-13-6 .5789 31 .5076 39 .4882 19 .5151 26 .5136
CO College 18 .5244 25T 19-17-3 .5256 25T 19-17-3 .5256 11 .5240 10 .5352 11 .5196 15 .5325
Union 19 .5231 11 21-12-6 .6154 11 21-12-6 .6154 36 .4924 32 .5000 44 .4895 17 .5323
Maine 20 .5212 25T 19-17-3 .5256 25T 19-17-3 .5256 15 .5198 8 .5364 21 .5133 13 .5334
NE-Omaha 21 .5192 20 20-16-6 .5476 20 20-16-6 .5476 26 .5098 17 .5176 30 .5067 21 .5260
Minnesota 22 .5192 34 18-19-2 .4872 34 18-19-2 .4872 3 .5299 3 .5510 9 .5216 14 .5332
Mass-Lowell 23 .5173 22 19-16-4 .5385 22 19-16-4 .5385 25 .5103 28 .5050 23 .5124 25 .5144
RIT 24 .5173 3T 26-11-1 .6974 3T 26-11-1 .6974 53 .4573 55 .4418 49 .4633 27 .5134
Boston Univ 25 .5172 29 18-17-3 .5132 29 18-17-3 .5132 16 .5186 14 .5241 15 .5165 23 .5210
Mass-Amherst 26 .5112 31T 18-18 .5000 31T 18-18 .5000 19 .5150 15 .5235 27 .5116 24 .5169
Northeastern 27 .5106 31T 16-16-2 .5000 31T 16-16-2 .5000 20 .5141 29 .5048 13 .5177 30 .5035
Ohio State 28 .5088 35 15-18-6 .4615 35 15-18-6 .4615 10 .5246 2 .5598 28 .5109 16 .5323
MSU-Mankato 29 .5036 38 16-20-3 .4487 38 16-20-3 .4487 13 .5219 13 .5256 10 .5204 29 .5041
Merrimack 30 .5027 37 16-19-2 .4595 37 16-19-2 .4595 18 .5172 16 .5190 16 .5164 31 .5023
St Lawrence 31 .5013 23 19-16-7 .5357 23 19-16-7 .5357 40 .4898 42 .4820 39 .4929 33 .4971
Lake Superior 32 .4967 36 15-18-5 .4605 36 15-18-5 .4605 28 .5087 20 .5149 31 .5063 32 .4996
Quinnipiac 33 .4966 27 20-18-2 .5250 27 20-18-2 .5250 46 .4871 50 .4669 36 .4949 38 .4832
Sacred Heart 34 .4955 12 21-13-4 .6053 12 21-13-4 .6053 50 .4589 51 .4658 54 .4562 28 .5048
RPI 35 .4949 30 18-17-4 .5128 30 18-17-4 .5128 43 .4889 45 .4796 40 .4926 34 .4889
Notre Dame 36 .4918 39 13-17-8 .4474 39 13-17-8 .4474 32 .5066 34 .4985 29 .5098 37 .4842
Colgate 37 .4907 31T 15-15-6 .5000 31T 15-15-6 .5000 45 .4876 43 .4818 42 .4898 35 .4869
AK-Anchorage 38 .4785 51T 11-23-2 .3333 51T 11-23-2 .3333 7 .5269 7 .5383 7 .5225 39 .4809
Princeton 39 .4762 40 12-16-3 .4355 40 12-16-3 .4355 41 .4897 44 .4805 38 .4933 44 .4679
Air Force 40 .4731 28 16-15-6 .5135 28 16-15-6 .5135 49 .4597 46 .4735 56 .4543 36 .4847
Providence 41 .4693 50 10-20-4 .3529 50 10-20-4 .3529 30 .5081 41 .4860 14 .5168 49 .4487
Brown 42 .4686 43T 13-20-4 .4054 43T 13-20-4 .4054 42 .4896 36 .4984 46 .4862 41 .4724
Canisius 43 .4680 24 17-15-5 .5270 24 17-15-5 .5270 58 .4484 56 .4258 52 .4571 46 .4541
Western Mich 44 .4674 51T 8-20-8 .3333 51T 8-20-8 .3333 22 .5121 11 .5333 32 .5039 40 .4773
AL-Huntsville 45 .4667 42 12-17-3 .4219 42 12-17-3 .4219 48 .4816 54 .4462 35 .4954 52 .4394
Niagara 46 .4616 47 12-20-4 .3889 47 12-20-4 .3889 47 .4858 31 .5005 48 .4800 43 .4692
Robert Morris 47 .4611 48 10-19-6 .3714 48 10-19-6 .3714 39 .4909 25 .5088 47 .4840 42 .4703
Dartmouth 48 .4564 49 10-19-3 .3594 49 10-19-3 .3594 44 .4887 40 .4866 43 .4896 47 .4510
Harvard 49 .4532 53 9-21-3 .3182 53 9-21-3 .3182 33 .4982 27 .5083 37 .4942 45 .4551
Mercyhurst 50 .4468 41 15-20-3 .4342 41 15-20-3 .4342 55 .4509 58 .4218 50 .4623 54 .4253
Army 51 .4446 45 11-18-7 .4028 45 11-18-7 .4028 51 .4585 48 .4683 55 .4547 48 .4499
Clarkson 52 .4429 54 9-24-4 .2973 54 9-24-4 .2973 38 .4915 30 .5030 45 .4870 51 .4454
Holy Cross 53 .4424 43T 12-19-6 .4054 43T 12-19-6 .4054 54 .4547 52 .4486 53 .4571 53 .4365
Michigan Tech 54 .4382 58 5-30-1 .1528 58 5-30-1 .1528 1 .5333 1 .5604 6 .5228 50 .4463
Bowling Green 55 .4369 56 5-25-6 .2222 56 5-25-6 .2222 29 .5084 35 .4984 24 .5123 55 .4211
Bentley 56 .4368 46 12-19-4 .4000 46 12-19-4 .4000 57 .4490 57 .4225 51 .4593 56 .4162
Connecticut 57 .4008 55 7-27-3 .2297 55 7-27-3 .2297 52 .4579 47 .4730 58 .4520 57 .4049
American Intl 58 .3912 57 5-24-4 .2121 57 5-24-4 .2121 56 .4509 53 .4465 57 .4526 58 .3809

Explanation of the Table

RPI
The Ratings Percentage Index is one of the NCAA's selection criteria for college hockey. It is a sum of .25 times a team's winning percentage, .21 times their opponents' winning percentage (q.v.) and .54 times their opponents' opponents' winning percentage (q.v.). Equivalently, it can be calculated as .25 times their winning percentage plus .75 times their Strength Of Schedule (SOS; q.v.).
Record
Winning percentage (Pct) is calculated as described on the rating system comparison page; in particular, it is calculated with a tie counting as half a win and half a loss.
RPI Record
This is the record in games that contribute towards a team's RPI, not including "bad" wins which were dropped because they would have lowered the rating.
Sched Strength
The Strength Of Schedule (SOS) as measured by RPI is given by 0.28 times a team's opponents' winning percentage (q.v.) plus 0.72 times their opponents' opponents' winning percentage (q.v.). This number, along with the OPct and OOPct, is calculated only from the games that are left after omitting "bad wins".
Opp Pct
The Opponents' Winning Percentage (OPct) for a team is calculated by averaging the winning percentages of all their opponents in games not involving that team. The weighting factor is the number of games a team played against a particular opponent. Because games against the team in question are left out, it is not simply a weighted average of the winning percentages.
Opp Opp Pct
The Opponents' Opponents' Winning Percentage (OOPct) for a team is a weighted average of the Opponents' Winning Percentages (OPct; q.v.) of each of their opponents. Once again, the weighting factor is the number of games played against each opponent, but this time no extra games are left out, so each opponent's contribution can be read from the OPct column for that opponent.
RPIStr
The "strength" of a team (as a prospective opponent) for RPI purposes is given by 0.28 times their winning percentage plus 0.72 times their Opponents' Winning Percentage (OPct; q.v.). Since head-to-head games have to be left out of the RPI calculation, a team's strength of schedule is not exactly the weighted average of the RPIStr numbers for all its opponents, but RPIStr gives a sense of how RPI will evaluate the strength of each opponent. (Each team's name in the table above is a link to a rundown of selection criteria which includes a list of their opponents with their actual contribution to that team's strength of schedule.) Note that with the original formula (see below) RPIStr was much more heavily weighted towards winning percentage than RPI itself, but with the 25/21/54 weightings, it's much less so.

RPI Fudges

Because of various shortcomings of the RPI (see below), the NCAA has over the years added assorted tweaks and hacks.

To deal with the fact that their rating system allows teams to hurt their ratings by beating a sufficiently weak opponent, the NCAA simply omits from a team's RPI any wins which would lower their overall RPI. This is implemented in the table above, and the difference between "Record" and "RPI Record" shows how many wins have been dropped.

The Nitty-Gritty

The definitions above provide all the information needed to calculate the RPI, but to spell out the formula explicitly, if Vij is the number of times team i has beaten team j (with ties as always counting as half a win and half a loss), Nij=Vij+Vji is the number of times they've played, Vi=∑jVij is the total number of wins for team i and Ni=∑jNij is the total number of games they've played, then team i's RPI is given by

0.25*Vi/Ni + 0.21 * ∑j(Nij/Ni)*(Vj-Vji)/(Nj-Nji) + 0.54 * ∑j(Nij/Ni)*[∑k(Njk/Nj)*(Vk-Vkj)/(Nk-Nkj)]

Some Background

The RPI was developed for general-purpose use within the NCAA over the course of the past couple of decades. The original definition weighted the terms at 25, 50, and 25 percent for Winning Percentage, Opponents' Winning Percentage, and Opponents' Opponents' Winning Percentage, respectively. However, the impact of strength of schedule on the ratings meant it was possible for a team to hurt its RPI by playing a weak opponent, even if they won the game. (Specific examples of this from the 1994-1995 season were Colorado College vs Air Force and Bowling Green vs Ohio State. In the latter case BGSU split two non-conference games with OSU and fell just short of making the NCAAs; if they had won both games, they still would have missed the tournament, but not playing them at all would have improved their RPI enough to get an at-large bid.)

Presumably in response to this, the weighting of the terms in college hockey's RPI was changed to the 35/50/15. However, that was found to give too little weight to strength of schedule (see "Shortcomings of RPI" below), so the weighting was changed back to the original 25/50/25, effective with the start of the 2003-2004 season.

In an attempt to try to avoid both problems, the NCAA has changed the weightings once again, to 25/21/54.

Shortcomings of RPI

A more extreme problem with the RPI was brought to light in the 1998-1999 season, when the Metro-Atlantic Athletic Conference (MAAC) began play and six more Division I teams were suddenly eligible for the NCAAs. Because they played most of their games against each other, the winning percentages which contributed to their strength of schedule were on average not much worse that those of the rest of the NCAA, even though those out of conference games that were played indicated that, top-to-bottom, the MAAC was nowhere near as strong as the other conferences. (The revised weighting, with increased improtance given to a team's own winning percentage, only exacerbated the situation.) This led to the fact that in the first two years of competition, MAAC regular season champion Quinnipiac ended up in the top 12 in the nation according to the RPI by compiling a high winning percentage against a mostly MAAC schedule. The NCAA selection committee anticipated this at the beginning of the MAAC's first season, and reserved the right to overrule RPI and the other selection criteria if it judged based on "overall conference strength" that there was a lack of "competitive equity" between conferences.

In response to this, the NCAA returned to the original weighting of 25/50/25. However, the previous shortcomings of possibly hurting one's RPI by beating a weak team, which prompted the change away from that weighting in the first place, remained.

Now they've changed once more, to the bizarre-looking 25/21/54. You can use our do-it-yourself ratings calculator to try any combination you want.

Alternatives to RPI

It was observed at the time that while Quinnipiac, for reasons described above, was rated significantly higher than they should have been by the RPI, several other rating systems ranked them much lower down, where it was felt they deserved to be. Many of the other ranking systems, like CHODR, CCHP, and Massey, take into consideration factors, like margin of victory and/or home ice, which are deliberately ignored by the RPI. The HEAL and RHEAL rating systems, while only considering won-lost-tied outcomes of each game, make distinctions based on which of a team's games it won or lost (so that beating a good team and losing to a bad team will get you more highly ranked than losing to a good team and beating a bad team).

One ranking system which, like the RPI, considers only a team's overall winning percentage and the strengths of the teams they played, is the Bradley-Terry ranking system, which goes under the name of KRACH when applied to college hockey. KRACH has been described as a system which does correctly what RPI is intended to do: provide a rating which evaluates a team's won-lost-tied performance over the entire season, taking into account the strength of their schedule. Much more on this system can be found at our KRACH page.

See also


Last Modified: 2012 March 26

Joe Schlobotnik / joe@amurgsval.org

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