Ratings Percentage Index for D1 College Hockey (2012-2013)

© 1999-2012, Joe Schlobotnik (archives)

URL for this frameset: http://slack.net/~whelan/tbrw/tbrw.cgi?2013/rpi.shtml

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

Today's RPI (including games of 2013 January 12)

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
New Hampshire 1 .5935 3T 14-4-2 .7500 3 13-4-2 .7368 2 .5458 3 .5756 2 .5342 2 .6183
Boston Coll 2 .5899 5 13-4-2 .7368 6 11-4-2 .7059 1 .5513 1 .6150 7 .5265 1 .6201
Quinnipiac 3 .5881 1 17-3-3 .8043 1 17-3-3 .8043 19 .5160 23 .5175 19 .5155 3 .5978
Minnesota 4 .5827 2 16-3-3 .7955 2 16-3-3 .7955 24 .5117 47 .4697 6 .5281 9 .5609
Notre Dame 5 .5700 6 15-6 .7143 5 15-6 .7143 11 .5220 22 .5236 11 .5213 7 .5770
Boston Univ 6 .5672 12T 12-7 .6316 12T 12-7 .6316 3 .5457 2 .5800 4 .5324 4 .5945
North Dakota 7 .5599 8T 13-6-3 .6591 8T 13-6-3 .6591 4 .5268 25 .5109 3 .5330 10 .5524
Denver U 8 .5565 11 13-6-4 .6522 11 13-6-4 .6522 9 .5247 11 .5514 20 .5143 5 .5796
Yale 9 .5519 10 9-4-3 .6562 10 9-4-3 .6562 16 .5172 31 .5014 8 .5233 12 .5448
Miami 10 .5512 8T 12-5-5 .6591 8T 12-5-5 .6591 20 .5152 27 .5062 12 .5187 11 .5490
Dartmouth 11 .5505 14T 9-5-2 .6250 14 9-5-2 .6250 7 .5256 8 .5594 23 .5125 6 .5778
Western Mich 12 .5440 7 13-5-4 .6818 7 13-5-4 .6818 40 .4980 39 .4856 32 .5029 13 .5405
Mass-Lowell 13 .5435 16 11-7-1 .6053 16 11-7-1 .6053 10 .5229 37 .4901 1 .5357 18 .5224
Niagara 14 .5350 3T 13-3-4 .7500 4 11-3-4 .7222 48 .4726 54 .4343 44 .4876 32 .4952
NE-Omaha 15 .5311 19 13-9-2 .5833 21T 11-9-2 .5455 6 .5263 7 .5609 21 .5128 15 .5391
MSU-Mankato 16 .5302 14T 14-8-2 .6250 15 13-8-2 .6087 34 .5041 29 .5029 30 .5045 17 .5239
St Cloud 17 .5262 22 12-10 .5455 21T 12-10 .5455 14 .5198 34 .4914 5 .5309 27 .5065
Colgate 18 .5237 17T 11-7-2 .6000 19 9-7-2 .5556 22 .5131 19 .5309 28 .5062 21 .5158
Cornell 19 .5224 23 7-6-2 .5333 23 7-6-2 .5333 15 .5187 26 .5093 9 .5224 20 .5161
Robert Morris 20 .5220 12T 11-6-2 .6316 12T 11-6-2 .6316 45 .4855 15 .5385 55 .4649 8 .5646
Union 21 .5167 20 10-7-4 .5714 18 10-7-4 .5714 39 .4984 36 .4909 35 .5014 22 .5134
Wisconsin 22 .5114 24T 8-7-5 .5250 24 8-7-5 .5250 28 .5068 41 .4796 14 .5174 33 .4923
Northern Mich 23 .5102 29 9-10-4 .4783 29 9-10-4 .4783 12 .5209 6 .5643 31 .5040 14 .5402
Ohio State 24 .5095 30T 8-9-5 .4773 30T 8-9-5 .4773 13 .5202 18 .5324 18 .5155 19 .5169
Lake Superior 25 .5093 27 12-11-1 .5208 26 12-11-1 .5208 33 .5054 44 .4768 16 .5166 35 .4891
Providence 26 .5087 24T 9-8-3 .5250 27T 8-8-3 .5000 25 .5116 32 .4983 15 .5167 34 .4896
Ferris State 27 .5070 26 10-9-3 .5227 25 10-9-3 .5227 38 .5017 33 .4933 29 .5050 29 .5016
AK-Fairbanks 28 .5045 28 8-8-4 .5000 27T 8-8-4 .5000 30 .5060 24 .5140 33 .5028 24 .5101
Minn-Duluth 29 .4999 30T 9-10-3 .4773 30T 9-10-3 .4773 27 .5074 40 .4799 13 .5181 40 .4792
Holy Cross 30 .4998 17T 11-7-2 .6000 17 11-7-2 .6000 52 .4663 48 .4668 53 .4662 28 .5041
CO College 31 .4989 41 9-13-2 .4167 41 9-13-2 .4167 5 .5264 5 .5714 25 .5088 16 .5281
Mass-Amherst 32 .4940 44T 7-11-2 .4000 44T 7-11-2 .4000 8 .5253 12 .5504 17 .5156 26 .5083
Merrimack 33 .4925 33T 8-9-4 .4762 33T 8-9-4 .4762 41 .4979 46 .4712 26 .5083 42 .4726
Princeton 34 .4902 38 6-8-4 .4444 38 6-8-4 .4444 32 .5055 28 .5030 27 .5065 36 .4866
RPI 35 .4854 42T 6-10-5 .4048 42T 6-10-5 .4048 23 .5123 10 .5535 40 .4963 23 .5119
Harvard 36 .4831 46 5-8-1 .3929 46 5-8-1 .3929 21 .5132 13 .5416 34 .5022 30 .5000
St Lawrence 37 .4815 33T 9-10-2 .4762 33T 9-10-2 .4762 46 .4832 52 .4480 39 .4970 48 .4559
Brown 38 .4787 39 5-7-4 .4375 39 5-7-4 .4375 43 .4924 45 .4742 36 .4995 46 .4639
Bowling Green 39 .4782 42T 6-10-5 .4048 42T 6-10-5 .4048 36 .5026 17 .5329 43 .4909 31 .4970
Mercyhurst 40 .4772 21 10-8-1 .5526 20 10-8-1 .5526 56 .4521 59 .3926 49 .4752 52 .4374
Bemidji State 41 .4750 52 5-11-4 .3500 52 5-11-4 .3500 18 .5166 30 .5023 10 .5221 47 .4597
Vermont 42 .4746 48 6-11-4 .3810 48 6-11-4 .3810 31 .5059 21 .5241 38 .4988 38 .4840
Mich State 43 .4728 53 6-13-3 .3409 53 6-13-3 .3409 17 .5168 4 .5753 41 .4940 25 .5097
Michigan Tech 44 .4711 51 6-12-3 .3571 51 6-12-3 .3571 26 .5090 16 .5340 37 .4993 37 .4845
Michigan 45 .4709 50 7-13-2 .3636 50 7-13-2 .3636 29 .5067 35 .4910 22 .5127 49 .4554
Connecticut 46 .4708 35 8-9-2 .4737 35 8-9-2 .4737 50 .4698 38 .4879 56 .4627 39 .4839
Northeastern 47 .4705 47 6-10-2 .3889 47 6-10-2 .3889 42 .4977 49 .4639 24 .5108 51 .4429
Canisius 48 .4680 30T 8-9-5 .4773 30T 8-9-5 .4773 53 .4649 56 .4305 48 .4783 50 .4436
Air Force 49 .4662 36 7-9-5 .4524 36 7-9-5 .4524 49 .4708 42 .4789 52 .4676 43 .4715
Bentley 50 .4576 37 8-10-1 .4474 37 8-10-1 .4474 54 .4610 55 .4328 51 .4720 53 .4369
Maine 51 .4542 54T 5-13-3 .3095 54T 5-13-3 .3095 37 .5025 20 .5302 42 .4917 45 .4684
Army 52 .4473 40 7-10-3 .4250 40 7-10-3 .4250 55 .4547 57 .4260 54 .4659 54 .4257
Clarkson 53 .4457 54T 4-12-5 .3095 54T 4-12-5 .3095 44 .4911 14 .5399 50 .4721 41 .4754
Penn State 54 .4444 49 6-10 .3750 49 6-10 .3750 51 .4675 53 .4379 47 .4790 55 .4203
AK-Anchorage 55 .4405 57 3-13-4 .2500 57 3-13-4 .2500 35 .5040 9 .5572 45 .4834 44 .4712
RIT 56 .4360 44T 6-10-4 .4000 44T 6-10-4 .4000 57 .4480 58 .4191 57 .4593 56 .4137
American Intl 57 .4059 56 4-12-3 .2895 56 4-12-3 .2895 59 .4447 50 .4546 59 .4409 57 .4084
AL-Huntsville 58 .3812 58 1-16-1 .0833 58 1-16-1 .0833 47 .4805 43 .4772 46 .4819 58 .3669
Sacred Heart 59 .3466 59 0-19-2 .0476 59 0-19-2 .0476 58 .4462 51 .4509 58 .4444 59 .3380

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: 2013 January 13

Joe Schlobotnik / joe@amurgsval.org

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