Ratings Percentage Index for D1 College Hockey (2010-2011)

© 1999-2010, Joe Schlobotnik (archives)

URL for this frameset: http://slack.net/~whelan/tbrw/tbrw.cgi?2011/rpi.shtml

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

Today's RPI (including games of 2011 March 19)

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
North Dakota 1 .5873 3 30-8-3 .7683 3 26-8-3 .7432 1 .5354 1 .5681 1 .5226 1 .5966
Boston Coll 2 .5821 2 30-7-1 .8026 2 27-7-1 .7857 14 .5142 15 .5234 16 .5106 2 .5846
Yale 3 .5790 1 27-6-1 .8088 1 26-6-1 .8030 32 .5044 30 .4998 23 .5061 3 .5810
Miami 4 .5620 7 23-9-6 .6842 7 23-9-6 .6842 4 .5212 12 .5303 5 .5177 4 .5734
Michigan 5 .5565 6 26-10-4 .7000 5 26-10-4 .7000 20 .5086 23 .5099 20 .5081 7 .5632
Denver U 6 .5562 8 24-11-5 .6625 8 24-11-5 .6625 6 .5207 8 .5343 11 .5155 5 .5702
Union 7 .5526 4 26-9-4 .7179 4 25-9-4 .7105 37 .5000 39 .4870 25 .5051 10 .5476
Merrimack 8 .5520 5 25-9-4 .7105 6 23-9-4 .6944 31 .5045 25 .5078 34 .5032 8 .5516
Minn-Duluth 9 .5481 9 22-10-6 .6579 9 22-10-6 .6579 16 .5115 34 .4964 7 .5174 12 .5416
New Hampshire 10 .5433 10 21-10-6 .6486 10 21-10-6 .6486 21 .5082 24 .5085 21 .5081 9 .5477
Notre Dame 11 .5429 11 23-13-5 .6220 11 23-13-5 .6220 9 .5165 5 .5459 26 .5050 6 .5672
NE-Omaha 12 .5330 19 21-15-2 .5789 19 21-15-2 .5789 8 .5176 22 .5124 3 .5197 16 .5310
Western Mich 13 .5302 18 19-12-10 .5854 18 19-12-10 .5854 15 .5118 11 .5326 31 .5038 11 .5474
Dartmouth 14 .5285 15 19-12-3 .6029 15 19-12-3 .6029 34 .5036 28 .5010 28 .5046 17 .5296
Boston Univ 15 .5276 16 19-12-8 .5897 16 19-12-8 .5897 24 .5070 31 .4997 19 .5098 20 .5249
CO College 16 .5264 24 22-18-3 .5465 24 22-18-3 .5465 7 .5197 10 .5330 13 .5146 14 .5368
Maine 17 .5247 21 17-12-7 .5694 21 17-12-7 .5694 18 .5097 14 .5253 32 .5037 13 .5376
RPI 18 .5237 13 20-12-5 .6081 13 20-12-5 .6081 44 .4955 48 .4769 35 .5028 24 .5136
Wisconsin 19 .5205 23 21-16-4 .5610 23 21-16-4 .5610 23 .5070 41 .4833 9 .5162 28 .5050
Minnesota 20 .5178 25 16-14-6 .5278 25 16-14-6 .5278 13 .5145 26 .5064 6 .5176 26 .5124
AK-Anchorage 21 .5138 32 16-18-3 .4730 32 16-18-3 .4730 3 .5275 4 .5488 4 .5192 18 .5275
Air Force 22 .5120 12 20-11-6 .6216 12 20-11-6 .6216 48 .4755 45 .4798 49 .4738 21 .5195
St Cloud 23 .5113 33T 15-18-5 .4605 33T 15-18-5 .4605 2 .5282 2 .5596 10 .5160 15 .5319
Princeton 24 .5106 22 17-13-2 .5625 22 17-13-2 .5625 45 .4934 53 .4651 30 .5043 33 .4924
AK-Fairbanks 25 .5089 30 16-17-5 .4868 30 16-17-5 .4868 11 .5162 6 .5421 22 .5062 19 .5266
Ferris State 26 .5080 26 18-16-5 .5256 26 18-16-5 .5256 35 .5021 42 .4821 18 .5098 32 .4943
Cornell 27 .5078 27 16-15-3 .5147 27 16-15-3 .5147 27 .5055 21 .5156 36 .5016 23 .5154
RIT 28 .5061 14 19-11-8 .6053 14 19-11-8 .6053 50 .4731 46 .4775 52 .4713 25 .5133
Bemidji State 29 .5060 33T 15-18-5 .4605 33T 15-18-5 .4605 5 .5212 7 .5376 12 .5148 22 .5160
Quinnipiac 30 .5032 29 16-15-8 .5128 29 16-15-8 .5128 38 .5000 37 .4881 27 .5046 31 .4950
Robert Morris 31 .4992 17 18-12-5 .5857 17 18-12-5 .5857 52 .4703 55 .4541 47 .4766 34 .4910
MSU-Mankato 32 .4979 40T 14-18-6 .4474 40T 14-18-6 .4474 12 .5147 36 .4946 2 .5225 37 .4814
Niagara 33 .4972 20 18-13-4 .5714 20 18-13-4 .5714 51 .4725 50 .4662 48 .4750 30 .4957
Northeastern 34 .4970 31 14-16-8 .4737 31 14-16-8 .4737 30 .5048 17 .5186 40 .4994 27 .5060
Lake Superior 35 .4950 38T 13-17-9 .4487 38T 13-17-9 .4487 17 .5104 27 .5051 14 .5125 35 .4893
Mich State 36 .4916 40T 15-19-4 .4474 40T 15-19-4 .4474 25 .5063 32 .4969 17 .5100 36 .4830
Ohio State 37 .4890 35T 15-18-4 .4595 35T 15-18-4 .4595 41 .4988 38 .4877 33 .5032 39 .4798
Northern Mich 38 .4887 38T 15-19-5 .4487 38T 15-19-5 .4487 36 .5020 51 .4656 8 .5162 48 .4608
Clarkson 39 .4833 42 15-19-2 .4444 42 15-19-2 .4444 43 .4963 40 .4860 38 .5003 44 .4744
Brown 40 .4811 44 10-16-5 .4032 44 10-16-5 .4032 22 .5070 9 .5331 44 .4969 29 .4967
Holy Cross 41 .4784 28 17-16-5 .5132 28 17-16-5 .5132 54 .4668 54 .4551 51 .4713 45 .4714
St Lawrence 42 .4747 45 13-22-5 .3875 45 13-22-5 .3875 33 .5038 19 .5168 43 .4987 38 .4806
Harvard 43 .4707 48 12-21-1 .3676 48 12-21-1 .3676 28 .5050 16 .5210 41 .4988 41 .4780
Mercyhurst 44 .4704 35T 15-18-4 .4595 35T 15-18-4 .4595 49 .4740 43 .4813 53 .4711 42 .4752
Vermont 45 .4650 50 8-20-8 .3333 50 8-20-8 .3333 19 .5089 20 .5162 24 .5061 46 .4650
Connecticut 46 .4646 35T 15-18-4 .4595 35T 15-18-4 .4595 55 .4663 52 .4652 56 .4667 47 .4636
Canisius 47 .4631 43 13-19-6 .4211 43 13-19-6 .4211 47 .4771 35 .4953 54 .4700 43 .4745
Providence 48 .4614 49 8-18-8 .3529 49 8-18-8 .3529 42 .4975 44 .4799 29 .5044 49 .4443
Colgate 49 .4536 51 11-28-3 .2976 51 11-28-3 .2976 26 .5056 3 .5494 46 .4886 40 .4789
Bowling Green 50 .4475 52 10-27-4 .2927 52 10-27-4 .2927 39 .4991 33 .4965 39 .5002 51 .4394
Mass-Amherst 51 .4430 54 6-23-6 .2571 54 6-23-6 .2571 29 .5050 18 .5169 37 .5003 50 .4442
Bentley 52 .4389 46 10-18-6 .3824 46 10-18-6 .3824 58 .4578 58 .4289 55 .4690 54 .4159
Army 53 .4387 47 11-20-4 .3714 47 11-20-4 .3714 56 .4611 57 .4300 50 .4732 55 .4136
Michigan Tech 54 .4268 57 4-30-4 .1579 57 4-30-4 .1579 10 .5164 13 .5285 15 .5118 52 .4247
Mass-Lowell 55 .4258 56 5-25-4 .2059 56 5-25-4 .2059 40 .4991 29 .5001 42 .4987 53 .4177
Sacred Heart 56 .4113 55 6-25-6 .2432 55 6-25-6 .2432 53 .4673 49 .4694 57 .4665 56 .4061
American Intl 57 .4096 53 8-24-1 .2576 53 8-24-1 .2576 57 .4602 56 .4507 58 .4639 57 .3966
AL-Huntsville 58 .4056 58 4-26-2 .1562 58 4-26-2 .1562 46 .4887 47 .4773 45 .4931 58 .3874

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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