Ratings Percentage Index for D1 College Hockey (2007-2008)

© 1999-2007, Joe Schlobotnik (archives)

URL for this frameset: http://slack.net/~whelan/tbrw/tbrw.cgi?2008/rpi.shtml

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

Today's RPI (including games of 2008 March 22)

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
Michigan 1 .5967 1 31-5-4 .8250 1 26-5-4 .8000 10 .5290 1 .5587 14 .5174 1 .6110
North Dakota 2 .5822 5 26-10-4 .7000 5 26-10-4 .7000 1 .5429 2 .5575 1 .5372 2 .5974
Miami 3 .5809 2 32-7-1 .8125 2 27-7-1 .7857 22 .5127 22 .5170 22 .5110 5 .5810
CO College 4 .5808 4 28-11-1 .7125 4 28-11-1 .7125 4 .5369 7 .5446 3 .5339 3 .5916
New Hampshire 5 .5715 3 25-9-3 .7162 3 25-9-3 .7162 12 .5232 13 .5286 11 .5211 4 .5811
Denver U 6 .5670 7T 26-13-1 .6625 7T 26-13-1 .6625 5 .5352 4 .5487 9 .5299 6 .5806
Mich State 7 .5516 7T 24-11-5 .6625 7T 24-11-5 .6625 20 .5146 19 .5216 21 .5119 8 .5611
Boston Coll 8 .5481 10 21-11-8 .6250 10 21-11-8 .6250 13 .5224 10 .5374 16 .5166 7 .5619
St Cloud 9 .5391 19 19-15-5 .5513 19 19-15-5 .5513 6 .5351 8 .5433 6 .5319 10 .5455
Clarkson 10 .5354 11 21-12-4 .6216 11 21-12-4 .6216 27 .5067 34 .5006 25 .5091 12 .5345
Minnesota 11 .5324 21 19-16-9 .5341 21 19-16-9 .5341 8 .5318 9 .5413 10 .5282 11 .5393
Princeton 12 .5310 12 21-13 .6176 12 21-13 .6176 31 .5021 20 .5205 41 .4949 9 .5477
Notre Dame 13 .5298 13 24-15-4 .6047 13 24-15-4 .6047 29 .5048 29 .5064 29 .5042 13 .5339
MSU-Mankato 14 .5272 20 19-16-4 .5385 20 19-16-4 .5385 11 .5235 35 .5006 5 .5324 23 .5112
Wisconsin 15 .5228 31 15-16-7 .4868 31 15-16-7 .4868 7 .5348 6 .5472 8 .5300 14 .5303
Harvard 16 .5209 18 17-13-4 .5588 18 17-13-4 .5588 25 .5082 21 .5172 28 .5047 16 .5289
Boston Univ 17 .5208 25 19-17-4 .5250 25 19-17-4 .5250 14 .5194 11 .5316 18 .5146 15 .5298
Vermont 18 .5193 23T 17-15-7 .5256 23T 17-15-7 .5256 18 .5172 15 .5273 20 .5133 18 .5269
Cornell 19 .5177 15 19-14-3 .5694 15 19-14-3 .5694 36 .5005 26 .5122 39 .4959 17 .5283
Minn-Duluth 20 .5139 40 13-17-6 .4444 40 13-17-6 .4444 3 .5370 5 .5478 4 .5328 19 .5189
Niagara 21 .5107 6 22-10-4 .6667 6 22-10-4 .6667 53 .4587 56 .4413 50 .4655 27 .5044
Michigan Tech 22 .5100 43 14-20-5 .4231 43 14-20-5 .4231 2 .5389 3 .5495 2 .5348 21 .5141
Northern Mich 23 .5097 28T 20-20-4 .5000 28T 20-20-4 .5000 21 .5129 17 .5232 26 .5090 20 .5167
Quinnipiac 24 .5091 17 20-15-4 .5641 17 20-15-4 .5641 44 .4907 40 .4872 43 .4921 25 .5088
Mass-Amherst 25 .5068 35 14-16-6 .4722 35 14-16-6 .4722 15 .5184 12 .5289 19 .5143 22 .5130
Air Force 26 .5067 9 21-11-6 .6316 9 21-11-6 .6316 49 .4651 48 .4633 49 .4658 24 .5104
Northeastern 27 .5063 34 16-18-3 .4730 34 16-18-3 .4730 17 .5174 27 .5105 12 .5201 30 .5000
Mass-Lowell 28 .5041 32 16-17-4 .4865 32 16-17-4 .4865 24 .5100 39 .4873 13 .5188 37 .4871
Providence 29 .5032 38 14-17-5 .4583 38 14-17-5 .4583 16 .5182 16 .5250 17 .5155 26 .5063
Yale 30 .5015 22 16-14-4 .5294 22 16-14-4 .5294 43 .4922 46 .4700 32 .5009 38 .4866
Ferris State 31 .5010 23T 18-16-5 .5256 23T 18-16-5 .5256 41 .4928 45 .4746 33 .4999 35 .4889
Union 32 .5000 26 15-14-6 .5143 26 15-14-6 .5143 39 .4952 38 .4877 37 .4982 31 .4951
Colgate 33 .4975 28T 18-18-6 .5000 28T 18-18-6 .5000 38 .4967 32 .5040 42 .4939 29 .5029
NE-Omaha 34 .4965 33 17-19-4 .4750 33 17-19-4 .4750 30 .5037 25 .5145 35 .4994 28 .5035
RIT 35 .4948 14 19-12-6 .5946 14 19-12-6 .5946 51 .4616 50 .4561 52 .4638 32 .4948
Maine 36 .4940 42 13-18-3 .4265 42 13-18-3 .4265 19 .5166 24 .5159 15 .5168 34 .4908
Bowling Green 37 .4910 36 18-21 .4615 36 18-21 .4615 35 .5008 30 .5055 36 .4990 33 .4932
Dartmouth 38 .4856 41 12-16-4 .4375 41 12-16-4 .4375 32 .5017 36 .4973 30 .5034 39 .4805
Bemidji State 39 .4842 27 17-16-3 .5139 27 17-16-3 .5139 45 .4743 43 .4787 46 .4726 36 .4886
Merrimack 40 .4835 44 12-18-4 .4118 44 12-18-4 .4118 26 .5074 33 .5017 24 .5096 41 .4765
Army 41 .4775 16 19-14-4 .5676 16 19-14-4 .5676 59 .4474 59 .4153 54 .4599 49 .4579
Lake Superior 42 .4743 49 10-20-7 .3649 49 10-20-7 .3649 23 .5107 18 .5222 27 .5063 40 .4781
AK-Anchorage 43 .4735 55 7-21-8 .3056 55 7-21-8 .3056 9 .5295 14 .5274 7 .5303 43 .4653
Robert Morris 44 .4727 28T 15-15-4 .5000 28T 15-15-4 .5000 50 .4636 55 .4484 47 .4696 45 .4629
St Lawrence 45 .4727 45 13-20-4 .4054 45 13-20-4 .4054 40 .4951 41 .4832 34 .4997 47 .4614
Ohio State 46 .4641 51 12-25-4 .3415 51 12-25-4 .3415 28 .5049 28 .5098 31 .5031 46 .4627
Mercyhurst 47 .4640 39 15-19-7 .4512 39 15-19-7 .4512 46 .4682 47 .4678 48 .4684 44 .4631
RPI 48 .4613 50 11-23-4 .3421 50 11-23-4 .3421 34 .5011 23 .5165 40 .4950 42 .4677
AK-Fairbanks 49 .4582 53 9-21-5 .3286 53 9-21-5 .3286 33 .5014 44 .4780 23 .5105 51 .4362
Sacred Heart 50 .4575 37 16-19-3 .4605 37 16-19-3 .4605 55 .4564 49 .4582 58 .4558 48 .4588
Canisius 51 .4445 47 11-20-6 .3784 47 11-20-6 .3784 47 .4665 42 .4800 53 .4613 50 .4515
Brown 52 .4387 57T 6-21-4 .2581 57T 6-21-4 .2581 37 .4989 31 .5051 38 .4965 52 .4359
Holy Cross 53 .4361 48 10-19-7 .3750 48 10-19-7 .3750 54 .4564 54 .4501 56 .4589 53 .4290
Connecticut 54 .4352 46 13-21-3 .3919 46 13-21-3 .3919 58 .4497 58 .4256 55 .4590 56 .4162
Western Mich 55 .4318 59 8-27-3 .2500 59 8-27-3 .2500 42 .4924 37 .4949 44 .4914 54 .4264
Wayne State 56 .4287 54 11-25-2 .3158 54 11-25-2 .3158 48 .4663 57 .4390 45 .4769 58 .4045
Bentley 57 .4252 52 9-21-6 .3333 52 9-21-6 .3333 56 .4559 52 .4524 57 .4572 55 .4191
American Intl 58 .4112 56 8-23-5 .2917 56 8-23-5 .2917 57 .4510 53 .4504 59 .4512 57 .4059
AL-Huntsville 59 .4103 57T 6-21-4 .2581 57T 6-21-4 .2581 52 .4610 51 .4527 51 .4642 59 .3982

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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