Ratings Percentage Index for D1 College Hockey (2019-2020)

© 1999-2017, Joe Schlobotnik (archives)

URL for this frameset: http://elynah.com/tbrw/tbrw.cgi?2020/rpi.shtml

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

Today's RPI (including games of 2020 March 8)

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
North Dakota 1 .6121 3 26-5-4 .8000 3 .7945 1 .5389 2 .5661 3 .5283 .0093 1 .6069
MSU-Mankato 2 .5997 2 31-5-2 .8421 2 .7727 5 .5322 1 .6204 33 .4979 .0074 2 .5950
Cornell 3 .5930 1 23-2-4 .8621 1 .8287 23 .5098 6 .5507 36 .4939 .0035 3 .5892
Minn-Duluth 4 .5776 6 22-10-2 .6765 6 .6786 3 .5347 5 .5523 4 .5279 .0068 5 .5831
Boston Coll 5 .5761 4 24-8-2 .7353 4 .7343 16 .5191 18 .5258 16 .5165 .0032 6 .5815
Denver U 6 .5688 7 21-9-6 .6667 8 .6724 10 .5271 8 .5465 12 .5196 .0053 4 .5834
Penn State 7 .5554 11T 20-10-4 .6471 11 .6369 12 .5235 20 .5190 8 .5252 .0035 8 .5555
Mass-Amherst 8 .5527 11T 21-11-2 .6471 10 .6524 19 .5145 19 .5229 21 .5112 .0037 7 .5583
Clarkson 9 .5496 5 23-8-3 .7206 5 .7193 42 .4902 40 .4818 37 .4935 .0021 10 .5428
Ohio State 10 .5482 15 20-11-5 .6250 19 .5906 7 .5300 15 .5299 2 .5301 .0031 11 .5408
Mass-Lowell 11 .5413 17 18-10-6 .6176 15 .6105 22 .5115 26 .5095 18 .5122 .0051 14 .5398
Maine 12 .5400 16 18-10-5 .6212 17 .6309 28 .5036 39 .4831 20 .5116 .0046 26 .5216
Bemidji State 13 .5397 8 22-10-5 .6622 9 .6629 34 .4949 37 .4842 31 .4991 .0028 16 .5362
Arizona State 14 .5394 10 22-11-3 .6528 12 .6577 32 .4959 36 .4886 32 .4987 .0031 17 .5330
Michigan 15 .5370 25 18-14-4 .5556 26 .5475 9 .5280 12 .5317 5 .5265 .0042 15 .5365
Western Mich 16 .5361 23 18-13-5 .5694 24 .5669 14 .5209 16 .5297 15 .5174 .0037 12 .5406
Quinnipiac 17 .5357 11T 21-11-2 .6471 13 .6562 39 .4918 24 .5111 47 .4842 .0028 9 .5509
Minnesota 18 .5323 28 16-14-7 .5270 29 .5081 2 .5358 7 .5466 1 .5316 .0035 13 .5400
Northeastern 19 .5299 22 18-13-3 .5735 22 .5833 25 .5082 31 .5041 22 .5098 .0029 22 .5253
Notre Dame 20 .5281 32T 15-15-7 .5000 31 .4973 6 .5304 9 .5414 6 .5261 .0060 20 .5284
Bowling Green 21 .5246 18 21-13-4 .6053 16 .6071 35 .4944 50 .4717 27 .5033 .0020 31 .5070
Providence 22 .5212 26 15-12-6 .5455 25 .5476 27 .5064 22 .5145 26 .5033 .0045 24 .5227
Sacred Heart 23 .5198 9 21-10-3 .6618 7 .6556 53 .4740 51 .4713 53 .4750 .0004 19 .5298
St Cloud 24 .5183 38 13-15-6 .4706 38 .4724 11 .5239 10 .5403 14 .5176 .0072 18 .5318
Michigan Tech 25 .5179 21 21-15-3 .5769 18 .5845 37 .4934 29 .5047 41 .4891 .0017 23 .5230
American Intl 26 .5171 14 21-12-1 .6324 14 .6424 50 .4753 44 .4799 54 .4734 .0000 28 .5198
Harvard 27 .5152 20 15-10-6 .5806 20 .5737 40 .4911 28 .5074 46 .4847 .0035 29 .5181
Mich State 28 .5128 40T 15-19-2 .4444 40 .4469 8 .5300 4 .5540 11 .5206 .0036 27 .5199
NE-Omaha 29 .5111 39 14-17-5 .4583 39 .4581 15 .5208 25 .5107 9 .5248 .0059 36 .4947
Boston Univ 30 .5110 32T 13-13-8 .5000 34 .4910 20 .5132 14 .5306 23 .5065 .0033 21 .5254
New Hampshire 31 .5105 32T 15-15-4 .5000 36 .4938 24 .5097 30 .5045 19 .5117 .0048 33 .5026
Wisconsin 32 .5100 43T 14-20-2 .4167 44 .4118 4 .5334 3 .5578 10 .5240 .0070 25 .5220
Connecticut 33 .5078 32T 15-15-4 .5000 33 .4970 26 .5075 23 .5127 24 .5055 .0029 30 .5091
Northern Mich 34 .5072 29 18-16-4 .5263 28 .5206 29 .5003 34 .4948 28 .5024 .0018 34 .5001
RIT 35 .5020 19 19-13-4 .5833 21 .5862 55 .4732 54 .4682 52 .4752 .0005 35 .4986
RPI 36 .5012 27 17-15-2 .5294 27 .5382 43 .4869 46 .4758 39 .4913 .0014 38 .4894
AK-Fairbanks 37 .5008 30T 16-15-5 .5139 30 .5027 31 .4962 33 .4987 34 .4952 .0030 32 .5036
Army 38 .4918 24 17-13-3 .5606 23 .5569 58 .4701 57 .4644 56 .4723 .0000 37 .4931
Yale 39 .4876 32T 15-15-2 .5000 35 .5000 46 .4829 49 .4749 45 .4860 .0005 39 .4809
CO College 40 .4798 47 11-20-3 .3676 47 .3663 18 .5167 35 .4943 7 .5254 .0007 43 .4645
Colgate 41 .4770 40T 12-16-8 .4444 41 .4438 44 .4858 48 .4749 40 .4900 .0017 40 .4673
Dartmouth 42 .4765 37 13-14-4 .4839 37 .4730 52 .4747 59 .4450 44 .4863 .0022 44 .4644
Lake Superior 43 .4716 46 14-23-4 .3902 46 .3949 33 .4956 41 .4813 29 .5012 .0012 47 .4537
Bentley 44 .4707 30T 17-16-3 .5139 32 .5029 60 .4600 60 .4276 55 .4725 .0000 46 .4548
Miami 45 .4696 50T 8-21-5 .3088 51 .3077 13 .5213 17 .5274 13 .5189 .0017 41 .4665
Merrimack 46 .4664 50T 9-22-3 .3088 50 .3099 17 .5177 13 .5308 17 .5126 .0006 42 .4657
Niagara 47 .4642 45 12-18-4 .4118 45 .4231 49 .4779 42 .4806 50 .4769 .0000 45 .4639
Air Force 48 .4569 43T 12-18-6 .4167 43 .4070 54 .4736 55 .4677 51 .4759 .0000 51 .4447
Robert Morris 49 .4557 42 13-19-5 .4189 42 .4098 57 .4710 52 .4696 58 .4716 .0000 48 .4531
Holy Cross 50 .4483 48 11-21-5 .3649 48 .3676 51 .4751 38 .4833 57 .4719 .0001 52 .4428
Canisius 51 .4449 49 10-20-6 .3611 49 .3636 56 .4720 43 .4806 60 .4687 .0000 49 .4497
Vermont 52 .4433 55 5-23-6 .2353 56 .2317 21 .5125 11 .5335 25 .5043 .0010 50 .4485
Brown 53 .4406 52 8-21-2 .2903 53 .2905 41 .4903 27 .5084 48 .4833 .0002 53 .4427
Union 54 .4342 54 8-25-4 .2703 54 .2802 45 .4849 47 .4756 42 .4886 .0005 55 .4200
Princeton 55 .4322 53 6-20-5 .2742 52 .2830 47 .4819 53 .4696 43 .4868 .0000 56 .4188
Ferris State 56 .4289 56 7-26-2 .2286 55 .2330 38 .4934 45 .4763 30 .5001 .0006 58 .4053
AK-Anchorage 57 .4216 57 4-25-7 .2083 57 .2012 36 .4939 32 .4992 38 .4918 .0009 54 .4242
AL-Huntsville 58 .4123 60 2-26-6 .1471 60 .1481 30 .5003 21 .5163 35 .4941 .0000 57 .4129
St Lawrence 59 .4068 58 4-27-5 .1806 58 .1917 48 .4783 56 .4673 49 .4826 .0002 59 .3920
Mercyhurst 60 .3929 59 5-29-2 .1667 59 .1667 59 .4673 58 .4586 59 .4707 .0008 60 .3741

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 March 9

Joe Schlobotnik / joe@amurgsval.org

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