Ratings Percentage Index for D1 College Hockey (2013-2014)

© 1999-2013, Joe Schlobotnik (archives)

URL for this frameset: http://www.elynah.com/tbrw/tbrw.cgi?2014/rpi.shtml

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

Today's RPI (including games of 2014 March 22)

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
Minnesota 1 .5932 2T 25-6-6 .7568 3 .7557 2 .5277 7 .5445 4 .5211 .0085 1 .6110
Boston Coll 2 .5881 2T 26-7-4 .7568 2 .7514 5 .5227 17 .5234 2 .5224 .0082 3 .5859
Union 3 .5873 1 28-6-4 .7895 1 .7790 14 .5169 18 .5220 16 .5149 .0049 2 .5860
Wisconsin 4 .5662 5 24-10-2 .6944 7 .6818 4 .5228 42 .4936 1 .5341 .0037 16 .5364
Ferris State 5 .5617 4 28-10-3 .7195 4 .7182 31 .5087 31 .5057 25 .5098 .0006 7 .5502
Mass-Lowell 6 .5614 6T 25-10-4 .6923 6 .6791 18 .5152 29 .5070 9 .5183 .0052 4 .5612
Quinnipiac 7 .5544 6T 24-9-6 .6923 5 .6852 39 .5043 37 .4987 30 .5065 .0048 6 .5543
Notre Dame 8 .5520 12 23-14-2 .6154 20 .5756 1 .5340 2 .5698 7 .5201 .0076 8 .5486
St Cloud 9 .5495 9 21-10-5 .6528 8 .6158 6 .5220 16 .5246 5 .5210 .0040 13 .5408
MSU-Mankato 10 .5478 8 26-13-1 .6625 12 .6380 22 .5139 10 .5395 36 .5039 .0028 10 .5422
Providence 11 .5470 10 21-10-6 .6486 9 .6264 21 .5144 27 .5084 12 .5167 .0046 11 .5414
Colgate 12 .5398 15 20-13-5 .5921 14 .5781 15 .5167 9 .5434 31 .5064 .0077 5 .5567
Vermont 13 .5396 18 20-14-3 .5811 15 .5806 8 .5210 13 .5355 14 .5153 .0037 9 .5476
North Dakota 14 .5384 11 23-13-3 .6282 10 .6126 27 .5114 44 .4856 3 .5215 .0016 19 .5197
Michigan 15 .5369 19 18-13-4 .5714 21 .5714 11 .5190 23 .5159 6 .5202 .0048 17 .5342
Northeastern 16 .5352 20T 19-14-4 .5676 18 .5780 23 .5125 38 .4983 10 .5180 .0063 22 .5128
Cornell 17 .5347 13 17-10-5 .6094 11 .6019 29 .5096 26 .5141 27 .5079 .0021 12 .5411
New Hampshire 18 .5280 25 22-18-1 .5488 26 .5320 7 .5220 14 .5342 11 .5172 .0035 14 .5396
Ohio State 19 .5268 24 18-14-5 .5541 27 .5345 12 .5179 11 .5358 20 .5110 .0047 15 .5388
Yale 20 .5263 16 17-11-5 .5909 16 .5886 41 .5031 45 .4843 24 .5105 .0018 21 .5134
Denver U 21 .5220 22 20-15-6 .5610 22 .5665 37 .5050 46 .4795 15 .5150 .0016 30 .5028
Minn-Duluth 22 .5187 33 16-16-4 .5000 32 .4947 10 .5208 8 .5444 18 .5116 .0044 18 .5308
Western Mich 23 .5184 29 19-16-5 .5375 24 .5394 34 .5080 41 .4937 17 .5135 .0026 33 .5025
Maine 24 .5180 32 16-15-4 .5143 33 .5162 26 .5118 34 .5017 13 .5157 .0051 31 .5027
Clarkson 25 .5138 26 21-17-4 .5476 25 .5468 44 .5003 49 .4742 23 .5105 .0019 34 .4979
Bowling Green 26 .5133 28 18-15-6 .5385 29 .5376 43 .5006 43 .4891 34 .5050 .0035 27 .5087
AK-Anchorage 27 .5121 30 18-16-4 .5263 31 .5367 45 .4991 36 .5002 46 .4987 .0036 23 .5105
AK-Fairbanks 28 .5063 27 18-15-4 .5405 28 .5220 47 .4979 40 .4945 44 .4992 .0024 24 .5103
NE-Omaha 29 .5048 34T 17-18-2 .4865 35 .4731 25 .5124 15 .5253 28 .5074 .0022 25 .5103
RPI 30 .5043 34T 15-16-6 .4865 34 .4835 35 .5071 22 .5159 38 .5037 .0030 26 .5088
Miami 31 .5021 41 15-20-3 .4342 39 .4392 20 .5147 4 .5509 43 .5006 .0063 20 .5183
Mercyhurst 32 .5008 14 21-13-7 .5976 13 .6059 48 .4657 50 .4590 50 .4683 .0000 32 .5026
St Lawrence 33 .4995 38 15-19-4 .4474 37 .4531 30 .5088 19 .5215 37 .5038 .0046 29 .5030
Lake Superior 34 .4988 36 16-19-1 .4583 36 .4696 40 .5034 21 .5172 47 .4980 .0039 28 .5044
Air Force 35 .4934 17 21-14-4 .5897 17 .5882 52 .4605 56 .4405 48 .4683 .0009 35 .4860
Michigan Tech 36 .4922 39T 14-19-7 .4375 41 .4500 38 .5045 33 .5033 35 .5049 .0013 37 .4831
Brown 37 .4873 43 11-17-3 .4032 44 .4150 33 .5082 35 .5014 21 .5109 .0024 39 .4810
Bentley 38 .4868 20T 19-14-4 .5676 19 .5856 57 .4539 59 .4234 52 .4657 .0000 49 .4666
Mich State 39 .4864 44 11-18-7 .4028 47 .3839 17 .5160 28 .5071 8 .5194 .0034 47 .4696
Northern Mich 40 .4834 42 15-21-2 .4211 42 .4341 46 .4984 39 .4966 45 .4991 .0011 40 .4805
Harvard 41 .4807 47 10-17-4 .3871 46 .3871 28 .5103 20 .5181 29 .5072 .0013 41 .4783
Connecticut 42 .4788 23 18-14-4 .5556 23 .5511 59 .4529 55 .4417 57 .4572 .0014 42 .4749
Dartmouth 43 .4781 49 10-20-4 .3529 48 .3684 24 .5125 24 .5155 19 .5113 .0016 50 .4663
Robert Morris 44 .4736 31 19-17-5 .5244 30 .5202 54 .4580 58 .4317 49 .4683 .0000 52 .4572
Boston Univ 45 .4719 50 10-21-4 .3429 51 .3210 16 .5160 12 .5356 26 .5084 .0046 38 .4820
Bemidji State 46 .4704 48 10-21-7 .3553 49 .3545 36 .5061 30 .5059 32 .5061 .0022 45 .4720
Mass-Amherst 47 .4697 52 8-22-4 .2941 53 .3018 9 .5208 6 .5473 22 .5105 .0036 44 .4721
Canisius 48 .4641 37 17-21-3 .4512 38 .4646 49 .4639 48 .4756 55 .4593 .0000 48 .4674
Merrimack 49 .4594 54 8-22-3 .2879 54 .2778 13 .5173 3 .5530 39 .5034 .0020 43 .4744
Niagara 50 .4591 39T 15-20-5 .4375 40 .4479 50 .4628 47 .4785 58 .4567 .0000 51 .4657
Penn State 51 .4535 56 8-26-2 .2500 56 .2346 3 .5247 1 .5858 42 .5009 .0013 36 .4849
CO College 52 .4533 55 7-24-6 .2703 55 .2614 19 .5152 5 .5492 41 .5019 .0016 46 .4713
Holy Cross 53 .4464 45 14-22-3 .3974 43 .4050 53 .4584 51 .4584 56 .4584 .0014 53 .4426
RIT 54 .4454 46 12-20-5 .3919 45 .3934 51 .4627 52 .4525 51 .4667 .0000 54 .4323
Princeton 55 .4316 57 6-26 .1875 58 .1962 32 .5083 25 .5153 33 .5056 .0013 55 .4191
Sacred Heart 56 .4291 51 12-24 .3333 50 .3429 55 .4562 54 .4452 54 .4604 .0013 56 .4163
American Intl 57 .4182 53 10-25-1 .2917 52 .3107 56 .4540 57 .4356 53 .4612 .0000 57 .3967
AL-Huntsville 58 .3956 59 2-35-1 .0658 59 .0745 42 .5026 32 .5043 40 .5020 .0000 58 .3828
Army 59 .3897 58 6-28 .1765 57 .1977 58 .4537 53 .4463 59 .4565 .0000 59 .3684

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

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