Ratings Percentage Index for D1 College Hockey (2002-2003)

© 1999-2003, Joe Schlobotnik (archives)

URL for this frameset: http://slack.net/~whelan/tbrw/tbrw.cgi?2003/rpi.shtml

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

Up-to-the-minute RPI On USCHO.com NEW!

If you're looking for the current RPI, calculated from the latest scores, you should go to US College Hockey Online. For Joe Schlobotnik's geeky analysis of the system, with ratings recalculated daily, read on.

Today's RPI (including games of 2003 March 23)

Team RPI Record Sched Strength Opp Pct Opp Opp Pct RPIStr
Rk Rating Rk W-L-T Pct Rk SOS Rk OPct Rk OOPct Rk Rating
Cornell 1 .5958 1 28-4-1 .8636 30 .5065 28 .5078 31 .5039 1 .7450
CO College 2 .5913 2 29-6-5 .7875 20 .5259 23 .5224 8 .5329 2 .6991
Minnesota 3 .5910 8 24-8-9 .6951 3 .5563 3 .5693 12 .5302 6 .6532
New Hampshire 4 .5894 5 25-7-6 .7368 9 .5403 12 .5408 3 .5393 4 .6715
Boston Univ 5 .5854 13 24-13-3 .6375 1 .5681 1 .5849 5 .5344 11 .6200
Maine 6 .5807 6 24-9-5 .6974 7 .5418 9 .5464 9 .5327 7 .6470
Boston Coll 7 .5792 10 23-10-4 .6757 6 .5471 7 .5476 1 .5461 9 .6330
Michigan 8 .5689 4 28-9-3 .7375 27 .5127 29 .5065 17 .5252 5 .6605
Ferris State 9 .5660 3 30-9-1 .7625 31 .5005 37 .4919 23 .5178 3 .6723
Harvard 10 .5583 7 22-9-2 .6970 28 .5121 24 .5173 33 .5018 8 .6371
North Dakota 11 .5574 9 26-11-5 .6786 25 .5170 27 .5143 20 .5223 10 .6238
MSU-Mankato 12 .5528 14T 20-10-10 .6250 17 .5287 21 .5280 13 .5301 13 .5927
St Cloud 13 .5507 27T 17-15-5 .5270 2 .5586 2 .5757 18 .5245 22 .5432
Ohio State 14 .5497 11 25-12-5 .6548 26 .5147 26 .5154 27 .5133 12 .6083
Denver U 15 .5490 18 21-14-6 .5854 12 .5369 11 .5427 15 .5254 16 .5711
Providence 16 .5444 20 19-14-3 .5694 13 .5361 15 .5343 2 .5398 19 .5577
Mich State 17 .5423 16 23-14-2 .6154 24 .5180 25 .5172 22 .5195 14 .5827
Northern Mich 18 .5326 23 22-17-2 .5610 23 .5232 22 .5243 21 .5208 21 .5488
Mass-Amherst 19 .5306 27T 19-17-1 .5270 15 .5318 19 .5297 4 .5360 24 .5279
Minn-Duluth 20 .5275 19 22-15-5 .5833 29 .5089 34 .4968 7 .5331 20 .5545
Dartmouth 21 .5252 17 20-13-1 .6029 32 .4993 31 .5002 39 .4976 17 .5687
Notre Dame 22 .5185 30T 17-17-6 .5000 21 .5247 17 .5316 29 .5110 29 .5105
Merrimack 23 .5151 40 12-18-6 .4167 4 .5479 4 .5563 11 .5310 37 .4632
Yale 24 .5114 22 18-14 .5625 37 .4944 36 .4926 37 .4979 23 .5392
Western Mich 25 .5106 39 15-21-2 .4211 8 .5405 6 .5534 26 .5148 36 .4652
Miami 26 .5058 25 21-17-3 .5488 39 .4915 40 .4829 30 .5088 26 .5268
Mass-Lowell 27 .5046 45T 11-20-5 .3750 5 .5479 5 .5558 10 .5320 41 .4353
Brown 28 .4988 26 16-14-5 .5286 40 .4889 38 .4858 40 .4953 28 .5143
AK-Fairbanks 29 .4984 29 15-14-7 .5139 38 .4932 41 .4822 24 .5153 30 .5033
Mercyhurst 30 .4960 12 22-12-2 .6389 52 .4483 50 .4461 50 .4528 15 .5746
Wisconsin 31 .4931 45T 13-23-4 .3750 14 .5325 14 .5352 14 .5270 44 .4284
NE-Omaha 32 .4926 42 13-22-5 .3875 18 .5277 16 .5341 25 .5148 40 .4364
AL-Huntsville 33 .4926 24 18-14-3 .5571 45 .4710 43 .4687 45 .4757 25 .5277
Northeastern 34 .4875 51 10-21-3 .3382 11 .5373 13 .5394 6 .5331 46 .4053
Michigan Tech 35 .4835 53 10-24-4 .3158 10 .5394 8 .5464 16 .5252 49 .3927
Quinnipiac 36 .4806 14T 22-13-1 .6250 56 .4325 56 .4258 54 .4459 18 .5586
Wayne State 37 .4788 21 21-16-2 .5641 48 .4503 55 .4354 44 .4802 27 .5212
Colgate 38 .4786 35 17-19-4 .4750 42 .4798 42 .4754 43 .4886 33 .4751
Niagara 39 .4786 36 15-17-5 .4730 41 .4804 39 .4847 46 .4720 32 .4769
Bemidji State 40 .4769 30T 14-14-8 .5000 46 .4692 44 .4682 47 .4712 31 .4894
Vermont 41 .4725 41 13-20-3 .4028 36 .4958 35 .4946 36 .4981 42 .4334
Clarkson 42 .4704 43 12-20-3 .3857 34 .4986 32 .4990 38 .4977 45 .4235
Union 43 .4646 37 14-18-4 .4444 44 .4713 47 .4599 42 .4940 39 .4496
Bowling Green 44 .4592 57 8-25-3 .2639 22 .5243 18 .5307 28 .5117 54 .3528
RPI 45 .4581 52 12-25-3 .3375 35 .4983 33 .4970 34 .5007 50 .3907
Sacred Heart 46 .4527 33 14-15-6 .4857 55 .4417 52 .4420 56 .4411 34 .4711
Lake Superior 47 .4508 58 6-28-4 .2105 16 .5309 10 .5451 32 .5025 57 .3221
St Lawrence 48 .4487 47 11-21-5 .3649 43 .4767 45 .4653 35 .4994 48 .3983
Holy Cross 49 .4439 32 17-18-1 .4861 57 .4298 57 .4237 55 .4419 35 .4653
Army 50 .4377 34 15-16 .4839 59 .4223 59 .4136 58 .4398 38 .4604
Canisius 51 .4268 44 12-21-4 .3784 54 .4429 54 .4390 52 .4506 47 .3986
AK-Anchorage 52 .4267 60 1-28-7 .1250 19 .5272 20 .5289 19 .5240 59 .2596
Bentley 53 .4257 38 15-19 .4412 60 .4206 60 .4126 60 .4364 43 .4317
Findlay 54 .4232 49T 10-21-4 .3429 49 .4500 51 .4426 48 .4647 52 .3761
American Intl 55 .4228 48 10-20-2 .3438 51 .4491 48 .4551 59 .4371 51 .3809
Iona 56 .4194 49T 11-22-2 .3429 53 .4449 53 .4415 51 .4516 53 .3757
Air Force 57 .4134 56 8-24-3 .2714 47 .4607 46 .4646 49 .4530 56 .3358
Connecticut 58 .4072 54 8-23-3 .2794 50 .4498 49 .4508 53 .4477 55 .3365
Princeton 59 .4064 59 3-26-2 .1290 33 .4989 30 .5012 41 .4941 60 .2531
Fairfield 60 .3875 55 8-23-2 .2727 58 .4258 58 .4184 57 .4405 58 .3213

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, .50 times their opponents' winning percentage (q.v.) and .25 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.
Sched Strength
The Strength Of Schedule (SOS) as measured by RPI is given by 2/3 times a team's opponents' winning percentage (q.v.) plus 1/3 times their opponents' opponents' winning percentage (q.v.).
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 2/3 times their winning percentage plus 1/3 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 RPIStr is much more heavily weighted towards winning percentage than RPI itself.

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 + 0.50 * ∑j(Nij/Ni)*(Vj-Vji)/(Nj-Nji) + 0.25 * ∑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 has been changed back to the original 25/50/25, effective with the start of the 2002-2003 season.

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 has 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, remain.

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 25

Joe Schlobotnik / joe@amurgsval.org

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