Ratings Percentage Index for D1 College Hockey (2004-2005)

© 1999-2004, Joe Schlobotnik (archives)

URL for this frameset: http://slack.net/~whelan/tbrw/tbrw.cgi?2005/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. USCHO also has a form that allows you to examine the effects of the NCAA's "quality wins" fudge factor. For Joe Schlobotnik's geeky analysis of the system, with ratings recalculated daily, read on.

Today's RPI (including games of 2005 March 19)

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
CO College 1 .5953 3 29-8-3 .7625 9 .5396 10 .5416 5 .5357 3 .6889
Denver U 2 .5890 5 28-9-2 .7436 10 .5374 14 .5340 1 .5443 5 .6737
Boston Coll 3 .5885 4 25-6-7 .7500 11 .5347 13 .5357 6 .5327 4 .6786
Cornell 4 .5880 1 26-4-3 .8333 29 .5062 27 .5085 33 .5016 1 .7250
Michigan 5 .5754 2 30-7-3 .7875 31 .5048 32 .4979 19 .5185 2 .6910
New Hampshire 6 .5708 8 25-10-5 .6875 13 .5319 16 .5323 8 .5311 6 .6358
Minnesota 7 .5680 11 26-14-1 .6463 7 .5419 9 .5417 2 .5421 10 .6115
Boston Univ 8 .5675 13T 23-13-4 .6250 5 .5483 4 .5591 12 .5267 11 .6030
Harvard 9 .5660 9 21-9-3 .6818 16 .5273 11 .5379 28 .5063 8 .6338
North Dakota 10 .5610 20 22-14-5 .5976 3 .5489 5 .5582 9 .5302 15 .5844
Maine 11 .5607 18 20-12-7 .6026 6 .5468 6 .5577 14 .5249 14 .5876
Wisconsin 12 .5527 13T 23-13-4 .6250 15 .5286 19 .5268 7 .5322 12 .5923
Ohio State 13 .5494 6 27-10-4 .7073 36 .4968 39 .4889 23 .5126 7 .6345
Colgate 14 .5468 7 25-10-3 .6974 37 .4966 37 .4944 34 .5010 9 .6297
Mass-Lowell 15 .5376 16 20-12-4 .6111 27 .5131 28 .5073 15 .5248 17 .5765
Vermont 16 .5362 21 21-14-4 .5897 21 .5184 21 .5251 31 .5049 19 .5682
Mich State 17 .5348 24 20-17-4 .5366 12 .5343 7 .5485 29 .5058 22 .5406
Northeastern 18 .5290 32T 15-18-5 .4605 2 .5519 2 .5661 16 .5233 28 .4957
Dartmouth 19 .5240 19 20-13-2 .6000 34 .4987 33 .4967 32 .5027 20 .5656
Northern Mich 20 .5239 12 22-11-7 .6375 42 .4861 43 .4685 17 .5212 16 .5812
Bemidji State 21 .5179 10 23-12-1 .6528 44 .4730 44 .4653 44 .4883 13 .5903
MSU-Mankato 22 .5169 37 13-19-6 .4211 4 .5488 3 .5600 13 .5265 34 .4674
Minn-Duluth 23 .5092 30T 15-17-6 .4737 18 .5211 25 .5136 4 .5360 31 .4870
AK-Fairbanks 24 .5080 28 17-16-4 .5135 30 .5061 29 .5064 30 .5056 25 .5111
AL-Huntsville 25 .5044 13T 18-10-4 .6250 47 .4642 48 .4549 45 .4828 18 .5683
St Lawrence 26 .5037 30T 17-19-2 .4737 26 .5137 24 .5162 25 .5086 30 .4879
St Cloud 27 .5028 41 14-23-3 .3875 8 .5413 8 .5473 10 .5292 39 .4408
Brown 28 .4993 25 16-14-3 .5303 40 .4890 40 .4860 41 .4950 24 .5155
NE-Omaha 29 .4992 23 19-16-4 .5385 41 .4862 42 .4743 24 .5098 23 .5171
Bowling Green 30 .4984 29 16-16-4 .5000 35 .4979 38 .4934 27 .5070 27 .4978
AK-Anchorage 31 .4964 38T 12-19-6 .4054 17 .5268 22 .5220 3 .5364 38 .4443
Miami 32 .4912 32T 15-18-5 .4605 33 .5015 36 .4945 22 .5155 33 .4718
Mass-Amherst 33 .4899 47 13-23-2 .3684 14 .5304 12 .5368 21 .5177 42 .4245
Michigan Tech 34 .4894 54 8-25-4 .2703 1 .5624 1 .5802 11 .5269 49 .3736
Western Mich 35 .4889 38T 14-21-2 .4054 23 .5168 20 .5267 38 .4969 37 .4458
Ferris State 36 .4846 43 13-22-4 .3846 22 .5180 17 .5288 39 .4963 41 .4327
Providence 37 .4805 44T 12-21-4 .3784 24 .5146 26 .5114 18 .5209 43 .4227
Niagara 38 .4787 35 15-19-2 .4444 39 .4901 34 .4962 46 .4778 35 .4617
Lake Superior 39 .4728 49 9-22-7 .3289 20 .5207 15 .5335 40 .4952 48 .3971
Clarkson 40 .4708 46 13-23-3 .3718 32 .5038 30 .5053 35 .5007 46 .4163
Quinnipiac 41 .4667 17 21-13-3 .6081 56 .4196 56 .4100 54 .4386 21 .5421
Union 42 .4653 44T 13-22-2 .3784 38 .4942 35 .4951 43 .4924 44 .4173
Mercyhurst 43 .4645 22 18-15-4 .5405 51 .4392 51 .4386 53 .4402 26 .5066
Wayne State 44 .4595 34 14-17-4 .4571 48 .4603 49 .4521 47 .4766 36 .4555
Holy Cross 45 .4538 26 16-14-6 .5278 52 .4292 52 .4247 55 .4381 29 .4934
Air Force 46 .4527 36 14-19-3 .4306 49 .4601 46 .4608 48 .4587 40 .4407
RPI 47 .4527 40 14-22-2 .3947 45 .4720 47 .4606 42 .4947 45 .4167
Canisius 48 .4472 27 16-15-4 .5143 54 .4249 55 .4150 51 .4447 32 .4812
Merrimack 49 .4436 55 8-26-2 .2500 28 .5082 31 .5031 20 .5183 54 .3344
Notre Dame 50 .4432 56 5-27-6 .2105 19 .5208 18 .5270 26 .5083 56 .3160
Princeton 51 .4332 51 8-20-3 .3065 43 .4755 45 .4633 36 .4999 51 .3587
Yale 52 .4324 58 5-25-2 .1875 25 .5140 23 .5215 37 .4991 57 .2988
Sacred Heart 53 .4308 42 13-21-1 .3857 50 .4458 50 .4472 52 .4430 47 .4062
Robert Morris 54 .4296 52 8-21-4 .3030 46 .4718 41 .4791 49 .4571 50 .3617
Bentley 55 .4003 50 8-20-6 .3235 53 .4259 53 .4237 56 .4303 53 .3569
Connecticut 56 .3971 48 11-23-3 .3378 57 .4168 58 .4000 50 .4505 52 .3586
Army 57 .3861 53 7-21-3 .2742 55 .4234 54 .4210 58 .4283 55 .3231
American Intl 58 .3563 57 4-23-4 .1935 58 .4105 57 .4012 57 .4291 58 .2628

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 2003-2004 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 26

Joe Schlobotnik / joe@amurgsval.org

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