Ratings Percentage Index for D1 College Hockey (2016-2017)

© 1999-2016, Joe Schlobotnik (archives)

URL for this frameset: http://elynah.com/tbrw/tbrw.cgi?2017/rpi.shtml

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

Today's RPI (including games of 2017 March 18)

Team RPI Record RPIRecord Sched Strength Opp Pct Opp Opp Pct QWB RPIStr
Rk Rating Rk W-L-T Pct Rk Pct Rk SOS Rk OPct Rk OOPct Rk Rating
Denver U 1 .6041 2 29-7-4 .7750 2 .7704 6 .5369 22 .5161 1 .5450 .0088 3 .5903
Minn-Duluth 2 .6033 3 25-6-7 .7500 3 .7382 1 .5441 4 .5565 2 .5392 .0107 1 .6118
Harvard 3 .5968 1 26-5-2 .8182 1 .8088 15 .5194 10 .5444 21 .5096 .0051 2 .5941
Minnesota 4 .5637 9T 23-11-3 .6622 8T .6610 9 .5236 12 .5388 11 .5177 .0057 7 .5676
Mass-Lowell 5 .5636 6 26-10-3 .7051 4 .7041 20 .5112 37 .4906 9 .5191 .0042 10 .5559
Western Mich 6 .5629 15T 22-12-5 .6282 16 .6162 7 .5364 9 .5446 5 .5332 .0065 6 .5681
Boston Univ 7 .5614 9T 23-11-3 .6622 8T .6610 12 .5209 7 .5463 18 .5110 .0055 4 .5838
Union 8 .5570 4 25-9-3 .7162 6 .7041 29 .5050 23 .5110 31 .5027 .0022 12 .5504
Penn State 9 .5556 8 24-11-2 .6757 10 .6471 14 .5203 17 .5246 10 .5186 .0036 14 .5482
North Dakota 10 .5510 21 21-15-3 .5769 23 .5619 3 .5408 6 .5471 3 .5383 .0049 9 .5576
Cornell 11 .5504 7 21-8-5 .6912 7 .6802 31 .5038 34 .4975 26 .5062 .0025 13 .5495
Air Force 12 .5476 5 26-9-5 .7125 5 .7057 40 .4935 25 .5059 40 .4886 .0011 11 .5525
Providence 13 .5472 11 22-11-5 .6447 12 .6484 22 .5068 39 .4877 14 .5142 .0051 18 .5328
Notre Dame 14 .5464 12 21-11-5 .6351 15 .6124 16 .5161 8 .5456 29 .5046 .0063 5 .5707
Ohio State 15 .5430 13T 21-11-6 .6316 11 .6294 26 .5060 43 .4782 13 .5169 .0062 21 .5231
Boston Coll 16 .5395 22 21-15-4 .5750 21 .5732 10 .5222 5 .5536 19 .5101 .0045 8 .5609
Vermont 17 .5341 20 20-13-5 .5921 20 .5856 19 .5137 20 .5191 16 .5116 .0025 17 .5381
Wisconsin 18 .5337 24 20-15-1 .5694 22 .5538 13 .5208 16 .5298 12 .5173 .0047 15 .5394
NE-Omaha 19 .5308 30 17-17-5 .5000 30 .5050 8 .5334 13 .5356 6 .5326 .0045 19 .5274
St Cloud 20 .5281 35 16-19-1 .4583 35 .4659 5 .5384 11 .5395 4 .5379 .0078 27 .5149
Quinnipiac 21 .5270 19 23-15-2 .6000 19 .5995 35 .5000 41 .4847 27 .5060 .0021 26 .5151
Northeastern 22 .5267 27 18-15-5 .5395 29 .5447 17 .5157 19 .5210 15 .5137 .0037 20 .5260
St Lawrence 23 .5205 25T 17-13-7 .5541 25 .5537 27 .5055 14 .5306 39 .4958 .0029 16 .5384
Clarkson 24 .5178 29 18-16-5 .5256 28 .5281 21 .5076 18 .5220 32 .5020 .0051 24 .5176
Canisius 25 .5137 15T 21-11-7 .6282 14 .6349 52 .4717 56 .4520 45 .4793 .0012 32 .5027
Robert Morris 26 .5133 13T 22-12-4 .6316 13 .6203 46 .4760 46 .4736 50 .4769 .0012 23 .5184
Michigan Tech 27 .5131 18 23-14-7 .6023 18 .6103 44 .4800 49 .4696 41 .4841 .0005 28 .5120
MSU-Mankato 28 .5121 17 22-13-4 .6154 17 .6250 48 .4733 44 .4773 57 .4718 .0009 22 .5189
Bemidji State 29 .5044 23 22-16-3 .5732 24 .5616 42 .4844 35 .4970 44 .4795 .0007 25 .5173
Merrimack 30 .5029 31 15-16-6 .4865 31 .4725 24 .5066 31 .4979 20 .5100 .0048 33 .4964
Miami 31 .4971 49 9-20-7 .3472 49 .3468 4 .5396 1 .5784 8 .5245 .0057 29 .5113
Yale 32 .4963 34 13-15-5 .4697 34 .4656 30 .5047 21 .5189 35 .4992 .0014 31 .5052
Princeton 33 .4954 33 15-16-3 .4853 33 .4810 37 .4988 33 .4977 36 .4992 .0011 36 .4869
Connecticut 34 .4927 36 12-16-8 .4444 36 .4514 33 .5008 36 .4915 30 .5044 .0042 40 .4750
New Hampshire 35 .4920 37 15-20-5 .4375 37 .4425 28 .5054 32 .4977 23 .5084 .0024 38 .4818
Army 36 .4916 25T 18-14-5 .5541 26 .5517 53 .4708 53 .4622 54 .4741 .0006 34 .4893
Michigan 37 .4899 42 13-19-3 .4143 44 .3958 18 .5146 15 .5305 24 .5084 .0051 30 .5055
Bowling Green 38 .4891 28 21-18-2 .5366 27 .5392 51 .4719 54 .4593 51 .4768 .0004 39 .4814
CO College 39 .4834 55 8-24-4 .2778 54 .2903 2 .5417 2 .5690 7 .5311 .0046 35 .4872
Holy Cross 40 .4771 32 14-15-7 .4861 32 .4826 49 .4725 55 .4581 48 .4781 .0021 43 .4675
Bentley 41 .4742 39 13-19-7 .4231 40 .4337 41 .4867 27 .5034 43 .4801 .0008 37 .4843
Sacred Heart 42 .4733 40T 13-19-5 .4189 39 .4385 43 .4834 40 .4868 42 .4821 .0011 44 .4673
Dartmouth 43 .4705 47 10-18-3 .3710 47 .3691 34 .5007 26 .5040 34 .4993 .0027 42 .4684
Arizona State 44 .4669 52 8-19-3 .3167 51 .3401 23 .5066 24 .5087 28 .5058 .0019 45 .4635
Mercyhurst 45 .4656 38 15-20-4 .4359 38 .4450 50 .4724 48 .4699 55 .4734 .0000 46 .4576
Maine 46 .4635 48 11-21-4 .3611 50 .3455 32 .5011 45 .4745 17 .5115 .0013 52 .4369
Mich State 47 .4598 56 7-24-4 .2571 56 .2650 11 .5217 3 .5571 25 .5079 .0023 41 .4712
Northern Mich 48 .4583 46 13-22-4 .3846 45 .3929 45 .4795 42 .4820 47 .4786 .0005 47 .4533
Ferris State 49 .4574 40T 13-19-5 .4189 41 .4220 57 .4689 57 .4455 49 .4780 .0002 51 .4406
Colgate 50 .4561 51 9-22-6 .3243 53 .3239 36 .4992 29 .5017 37 .4983 .0008 50 .4458
RIT 51 .4529 44 14-22-1 .3919 43 .3874 47 .4748 47 .4703 52 .4765 .0000 48 .4531
AK-Fairbanks 52 .4518 45 12-20-4 .3889 42 .3989 55 .4694 50 .4668 59 .4704 .0000 49 .4469
Lake Superior 53 .4503 43 11-18-7 .4028 46 .4072 59 .4646 60 .4283 46 .4787 .0000 53 .4234
American Intl 54 .4356 50 8-20-8 .3333 48 .3444 58 .4655 58 .4420 53 .4746 .0004 55 .4139
RPI 55 .4302 57 8-28-1 .2297 57 .2260 39 .4969 38 .4889 33 .5001 .0010 56 .4130
AL-Huntsville 56 .4268 53 9-22-3 .3088 52 .3257 60 .4605 59 .4360 60 .4700 .0000 59 .4004
AK-Anchorage 57 .4256 54 7-21-6 .2941 55 .2917 54 .4703 52 .4641 56 .4727 .0000 54 .4196
Mass-Amherst 58 .4190 58T 5-29-2 .1667 60 .1554 25 .5063 30 .4998 22 .5089 .0004 57 .4090
Brown 59 .4150 60 4-25-2 .1613 59 .1656 38 .4982 28 .5029 38 .4963 .0000 58 .4030
Niagara 60 .3965 58T 5-31-3 .1667 58 .1789 56 .4691 51 .4645 58 .4709 .0000 60 .3860

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: 2020 February 1

Joe Schlobotnik / joe@amurgsval.org

HTML 4.0 compliant CSS2 compliant