Ratings Percentage Index for D1 College Hockey (2006-2007)

© 1999-2007, Joe Schlobotnik (archives)

URL for this frameset: http://www.slack.net/~whelan/tbrw/tbrw.cgi?2007/rpi.shtml

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

Today's RPI (including games of 2007 March 17)

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
Minnesota 1 .5840 2 30-9-3 .7500 2 30-9-3 .7500 5 .5287 12 .5256 2 .5299 1 .5884
Notre Dame 2 .5782 1 31-6-3 .8125 1 27-6-3 .7917 26 .5070 20 .5149 31 .5040 2 .5781
Clarkson 3 .5645 3 25-8-5 .7237 3 25-8-5 .7237 18 .5114 15 .5210 20 .5076 3 .5778
St Cloud 4 .5621 7 22-10-7 .6538 7 22-10-7 .6538 4 .5315 6 .5400 4 .5282 4 .5719
New Hampshire 5 .5618 4 26-10-2 .7105 4 23-10-2 .6857 11 .5204 8 .5321 11 .5159 8 .5610
Boston Coll 6 .5603 5 26-11-1 .6974 5 23-11-1 .6714 9 .5232 4 .5435 12 .5154 6 .5648
North Dakota 7 .5542 14 22-13-5 .6125 14 22-13-5 .6125 2 .5348 3 .5489 3 .5293 5 .5667
Michigan 8 .5495 6 26-13-1 .6625 6 26-13-1 .6625 17 .5118 14 .5226 21 .5076 7 .5618
Boston Univ 9 .5447 9 20-9-9 .6447 9 20-9-9 .6447 19 .5113 24 .5108 13 .5115 10 .5483
Mich State 10 .5400 13 22-13-3 .6184 13 22-13-3 .6184 13 .5139 7 .5352 26 .5056 9 .5585
St Lawrence 11 .5384 11 23-13-2 .6316 11 23-13-2 .6316 24 .5074 19 .5153 30 .5043 11 .5479
Denver U 12 .5329 19 21-15-4 .5750 19 21-15-4 .5750 12 .5189 25 .5103 8 .5222 18 .5284
Mass-Amherst 13 .5328 15 20-12-5 .6081 15 20-12-5 .6081 23 .5077 17 .5188 33 .5034 13 .5438
Miami 14 .5320 12 23-13-4 .6250 12 23-13-4 .6250 39 .5010 39 .4908 29 .5049 19 .5284
Maine 15 .5306 16 21-14-2 .5946 16 21-14-2 .5946 21 .5093 26 .5100 16 .5090 16 .5337
Wisconsin 16 .5292 29 19-18-4 .5122 29 19-18-4 .5122 1 .5349 1 .5617 7 .5244 12 .5478
Dartmouth 17 .5280 17 18-12-3 .5909 17 18-12-3 .5909 25 .5071 13 .5234 38 .5007 14 .5423
Quinnipiac 18 .5238 18 21-14-5 .5875 18 21-14-5 .5875 34 .5025 23 .5109 41 .4993 17 .5323
CO College 19 .5232 27 18-17-4 .5128 27 18-17-4 .5128 6 .5266 5 .5419 10 .5206 15 .5338
Michigan Tech 20 .5223 28 18-17-5 .5125 28 18-17-5 .5125 7 .5256 11 .5261 6 .5254 20 .5223
Vermont 21 .5166 23 18-16-5 .5256 23 18-16-5 .5256 15 .5135 16 .5204 14 .5109 21 .5219
Lake Superior 22 .5096 25 21-19-3 .5233 25 21-19-3 .5233 29 .5051 28 .5094 32 .5034 24 .5133
Cornell 23 .5071 26 14-13-4 .5161 26 14-13-4 .5161 31 .5041 18 .5178 43 .4987 23 .5174
NE-Omaha 24 .5055 24 18-16-8 .5238 24 18-16-8 .5238 41 .4994 45 .4768 18 .5082 31 .4900
RIT 25 .5054 8 21-11-2 .6471 8 21-11-2 .6471 54 .4582 57 .4427 50 .4642 27 .4999
MSU-Mankato 26 .5041 41 13-19-6 .4211 41 13-19-6 .4211 3 .5318 2 .5584 9 .5214 22 .5199
Western Mich 27 .5036 30T 18-18-1 .5000 30T 18-18-1 .5000 30 .5047 35 .5015 25 .5060 26 .5011
Sacred Heart 28 .5033 10 21-11-4 .6389 10 21-11-4 .6389 55 .4581 56 .4451 53 .4631 28 .4994
Niagara 29 .5007 21 18-13-6 .5676 21 18-13-6 .5676 49 .4784 51 .4590 46 .4859 32 .4894
Harvard 30 .4989 35 14-17-2 .4545 35 14-17-2 .4545 14 .5137 9 .5311 24 .5070 25 .5097
Ohio State 31 .4975 33 15-17-5 .4730 33 15-17-5 .4730 28 .5057 31 .5075 27 .5050 29 .4978
Princeton 32 .4929 32 15-16-3 .4853 32 15-16-3 .4853 43 .4954 43 .4873 44 .4986 33 .4867
AK-Anchorage 33 .4913 46 13-21-3 .3919 46 13-21-3 .3919 8 .5245 27 .5097 1 .5302 39 .4767
Northeastern 34 .4907 37T 13-18-5 .4306 37T 13-18-5 .4306 20 .5108 21 .5149 15 .5091 30 .4913
Bemidji State 35 .4905 30T 14-14-5 .5000 30T 14-14-5 .5000 45 .4873 50 .4606 45 .4977 42 .4716
Minn-Duluth 36 .4902 44T 13-21-5 .3974 44T 13-21-5 .3974 10 .5211 29 .5092 5 .5257 37 .4779
Army 37 .4840 20 17-12-5 .5735 20 17-12-5 .5735 59 .4542 55 .4497 58 .4560 34 .4843
Union 38 .4833 37T 14-19-3 .4306 37T 14-19-3 .4306 40 .5009 37 .4999 37 .5013 36 .4805
Colgate 39 .4824 40 15-21-4 .4250 40 15-21-4 .4250 37 .5015 33 .5053 39 .5000 35 .4828
Air Force 40 .4807 22 19-15-5 .5513 22 19-15-5 .5513 58 .4571 59 .4391 51 .4641 43 .4705
Ferris State 41 .4790 44T 14-22-3 .3974 44T 14-22-3 .3974 27 .5061 30 .5091 28 .5050 38 .4778
Northern Mich 42 .4784 47 15-24-2 .3902 47 15-24-2 .3902 22 .5078 34 .5048 17 .5090 41 .4727
Yale 43 .4773 43 11-17-3 .4032 43 11-17-3 .4032 36 .5020 36 .5014 36 .5023 40 .4739
Brown 44 .4761 36 11-15-6 .4375 36 11-15-6 .4375 44 .4889 53 .4541 35 .5025 51 .4494
RPI 45 .4715 48 10-18-8 .3889 48 10-18-8 .3889 42 .4990 40 .4895 34 .5027 47 .4613
Robert Morris 46 .4662 39 14-19-2 .4286 39 14-19-2 .4286 48 .4787 44 .4808 49 .4779 45 .4662
AK-Fairbanks 47 .4655 50 11-22-6 .3590 50 11-22-6 .3590 38 .5011 32 .5058 42 .4992 46 .4647
Providence 48 .4648 54T 10-23-3 .3194 54T 10-23-3 .3194 16 .5133 10 .5264 19 .5082 44 .4685
AL-Huntsville 49 .4628 42 13-19-3 .4143 42 13-19-3 .4143 47 .4790 46 .4764 48 .4800 48 .4590
Connecticut 50 .4612 34 16-18-2 .4722 34 16-18-2 .4722 56 .4576 58 .4420 52 .4636 50 .4505
Mass-Lowell 51 .4579 54T 8-21-7 .3194 54T 8-21-7 .3194 32 .5040 38 .4950 22 .5076 52 .4458
Wayne State 52 .4551 49 12-21-2 .3714 49 12-21-2 .3714 46 .4830 42 .4892 47 .4805 49 .4562
Bentley 53 .4341 51T 12-22-1 .3571 51T 12-22-1 .3571 51 .4597 48 .4670 57 .4568 53 .4363
Holy Cross 54 .4323 51T 10-20-5 .3571 51T 10-20-5 .3571 57 .4574 54 .4498 54 .4603 56 .4239
Bowling Green 55 .4305 58 7-29-2 .2105 58 7-29-2 .2105 33 .5038 22 .5142 40 .4997 54 .4292
Mercyhurst 56 .4294 53 9-20-6 .3429 53 9-20-6 .3429 53 .4583 52 .4566 55 .4589 55 .4248
Canisius 57 .4201 56 9-23-3 .3000 56 9-23-3 .3000 50 .4601 47 .4678 56 .4571 57 .4208
Merrimack 58 .4134 59 3-27-4 .1471 59 3-27-4 .1471 35 .5022 41 .4894 23 .5072 59 .3936
American Intl 59 .4064 57 8-25-1 .2500 57 8-25-1 .2500 52 .4586 49 .4658 59 .4558 58 .4054

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.

Additionally, the NCAA rewards "quality wins" on the road in non-conference games. A quality win is one against a team in the top 15 of the RPI (before the quality wins bonus is added, of course). For some reason the NCAA refuses to disclose just what this bonus is

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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