Ratings Percentage Index for D1 College Hockey (2008-2009)

© 1999-2008, Joe Schlobotnik (archives)

URL for this frameset: http://slack.net/~whelan/tbrw/tbrw.cgi?2009/rpi.shtml

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

Today's RPI (including games of 2009 March 21)

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
Boston Univ 1 .5963 2 31-6-4 .8049 2 24-6-4 .7647 1 .5401 1 .5566 1 .5337 1 .6004
Notre Dame 2 .5908 1 31-5-3 .8333 1 29-5-3 .8243 24 .5130 25 .5139 24 .5126 2 .5977
Michigan 3 .5698 4 29-11 .7250 4 29-11 .7250 20 .5181 11 .5314 23 .5129 3 .5856
Northeastern 4 .5621 7 25-11-4 .6750 7 25-11-4 .6750 8 .5245 15 .5262 6 .5238 5 .5679
Denver U 5 .5594 9 23-11-5 .6538 9 23-11-5 .6538 3 .5279 4 .5464 12 .5207 4 .5765
Yale 6 .5554 3 24-7-2 .7576 3 23-7-2 .7500 43 .4906 47 .4727 36 .4975 10 .5472
Vermont 7 .5499 11 20-11-5 .6250 11 20-11-5 .6250 7 .5249 16 .5251 4 .5249 7 .5531
Minn-Duluth 8 .5443 14T 21-12-8 .6098 14T 21-12-8 .6098 14 .5225 14 .5263 10 .5210 8 .5497
North Dakota 9 .5439 12 24-14-4 .6190 12 24-14-4 .6190 18 .5189 26 .5128 8 .5213 17 .5425
New Hampshire 10 .5423 17 19-12-5 .5972 17 19-12-5 .5972 11 .5240 17 .5217 5 .5249 16 .5429
Cornell 11 .5405 6 21-9-4 .6765 6 21-9-4 .6765 34 .4951 39 .4935 37 .4958 12 .5447
Miami 12 .5369 16 20-12-5 .6081 16 20-12-5 .6081 23 .5131 27 .5105 20 .5141 18 .5379
Princeton 13 .5367 8 22-11-1 .6618 8 22-11-1 .6618 36 .4950 31 .5030 41 .4919 9 .5474
Air Force 14 .5339 5 27-10-2 .7179 5 25-10-2 .7027 45 .4776 37 .4940 47 .4712 11 .5452
Ohio State 15 .5338 14T 23-14-4 .6098 14T 23-14-4 .6098 28 .5085 29 .5063 26 .5094 19 .5353
Wisconsin 16 .5336 23 20-16-4 .5500 23 20-16-4 .5500 2 .5281 8 .5405 7 .5233 15 .5432
Boston Coll 17 .5333 19T 18-14-5 .5541 19T 18-14-5 .5541 5 .5264 7 .5405 11 .5209 13 .5443
Mass-Lowell 18 .5331 21T 20-16-2 .5526 21T 20-16-2 .5526 4 .5267 6 .5409 9 .5211 14 .5442
St Lawrence 19 .5330 13 21-12-5 .6184 13 21-12-5 .6184 30 .5045 10 .5330 39 .4935 6 .5569
Minnesota 20 .5328 19T 17-13-7 .5541 19T 17-13-7 .5541 6 .5258 20 .5197 2 .5281 20 .5293
CO College 21 .5241 21T 16-12-10 .5526 21T 16-12-10 .5526 21 .5145 33 .4992 13 .5205 23 .5142
St Cloud 22 .5169 29 18-17-3 .5132 29 18-17-3 .5132 19 .5181 9 .5345 25 .5118 21 .5285
Northern Mich 23 .5164 28 19-17-5 .5244 28 19-17-5 .5244 22 .5137 28 .5068 18 .5164 25 .5117
AK-Fairbanks 24 .5105 30 17-16-6 .5128 30 17-16-6 .5128 26 .5098 24 .5140 27 .5081 24 .5137
MSU-Mankato 25 .5092 35 15-17-6 .4737 35 15-17-6 .4737 15 .5210 13 .5310 16 .5171 22 .5149
RIT 26 .5076 10 23-13-2 .6316 10 23-13-2 .6316 50 .4663 52 .4534 46 .4713 27 .5033
AK-Anchorage 27 .5071 36 14-17-5 .4583 36 14-17-5 .4583 13 .5233 22 .5165 3 .5260 29 .5002
Mass-Amherst 28 .5020 37 16-20-3 .4487 37 16-20-3 .4487 16 .5197 19 .5202 14 .5195 30 .5002
Union 29 .5013 27 19-17-3 .5256 27 19-17-3 .5256 41 .4932 45 .4761 33 .4998 32 .4899
NE-Omaha 30 .4974 34 15-17-8 .4750 34 15-17-8 .4750 29 .5048 21 .5167 32 .5002 26 .5050
Mercyhurst 31 .4959 18 22-15-3 .5875 18 22-15-3 .5875 51 .4653 54 .4462 45 .4728 34 .4858
Dartmouth 32 .4941 31T 14-14-3 .5000 31T 14-14-3 .5000 42 .4922 46 .4754 35 .4987 35 .4823
Maine 33 .4888 44T 13-22-4 .3846 44T 13-22-4 .3846 12 .5236 3 .5476 19 .5143 28 .5020
Quinnipiac 34 .4885 31T 18-18-3 .5000 31T 18-18-3 .5000 44 .4846 48 .4720 44 .4895 36 .4799
Bentley 35 .4848 26 19-17-2 .5263 26 19-17-2 .5263 47 .4709 41 .4869 53 .4647 31 .4980
Western Mich 36 .4840 38 14-20-7 .4268 38 14-20-7 .4268 31 .5030 34 .4988 30 .5046 37 .4786
Bemidji State 37 .4824 24 18-15-1 .5441 24 18-15-1 .5441 53 .4618 53 .4473 50 .4674 39 .4744
Colgate 38 .4761 39 12-18-7 .4189 39 12-18-7 .4189 35 .4951 35 .4972 38 .4943 38 .4753
Mich State 39 .4753 49T 10-23-5 .3289 49T 10-23-5 .3289 10 .5241 2 .5525 22 .5130 33 .4899
Lake Superior 40 .4734 44T 11-20-8 .3846 44T 11-20-8 .3846 32 .5029 38 .4937 29 .5065 42 .4632
Ferris State 41 .4726 40T 12-19-7 .4079 40T 12-19-7 .4079 39 .4942 44 .4782 31 .5004 45 .4585
Niagara 42 .4716 25 16-14-6 .5278 25 16-14-6 .5278 56 .4529 57 .4187 52 .4662 49 .4492
Harvard 43 .4679 43 9-16-6 .3871 43 9-16-6 .3871 37 .4949 42 .4839 34 .4991 46 .4568
Clarkson 44 .4644 46T 10-19-7 .3750 46T 10-19-7 .3750 38 .4942 30 .5060 43 .4896 40 .4694
Bowling Green 45 .4644 49T 11-24-3 .3289 49T 11-24-3 .3289 27 .5095 23 .5161 28 .5069 41 .4637
Merrimack 46 .4636 51 9-21-4 .3235 51 9-21-4 .3235 25 .5102 32 .5017 21 .5136 48 .4518
Canisius 47 .4624 33 15-16-6 .4865 33 15-16-6 .4865 54 .4543 58 .4164 49 .4691 53 .4360
Providence 48 .4594 53 7-22-5 .2794 53 7-22-5 .2794 17 .5194 18 .5209 15 .5188 47 .4533
Michigan Tech 49 .4556 55T 6-25-7 .2500 55T 6-25-7 .2500 9 .5241 5 .5422 17 .5171 44 .4604
Holy Cross 50 .4530 40T 13-20-5 .4079 40T 13-20-5 .4079 49 .4681 50 .4617 48 .4706 51 .4467
RPI 51 .4474 52 10-27-2 .2821 52 10-27-2 .2821 33 .5025 12 .5311 42 .4913 43 .4614
Army 52 .4441 42 11-19-6 .3889 42 11-19-6 .3889 52 .4625 49 .4625 57 .4625 52 .4419
Sacred Heart 53 .4382 48 11-23-4 .3421 48 11-23-4 .3421 48 .4703 40 .4900 56 .4626 50 .4486
Robert Morris 54 .4318 46T 10-19-7 .3750 46T 10-19-7 .3750 58 .4507 56 .4189 54 .4631 56 .4066
Brown 55 .4274 57 5-23-5 .2273 57 5-23-5 .2273 40 .4941 36 .4971 40 .4929 55 .4216
Connecticut 56 .4211 54 9-26-2 .2703 54 9-26-2 .2703 46 .4714 43 .4835 51 .4667 54 .4238
AL-Huntsville 57 .4013 55T 5-20-5 .2500 55T 5-20-5 .2500 57 .4517 51 .4576 58 .4494 57 .3995
American Intl 58 .3832 58 5-28-2 .1714 58 5-28-2 .1714 55 .4538 55 .4308 55 .4627 58 .3582

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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