Ratings Percentage Index for D1 College Hockey (2014-2015)

© 1999-2014, Joe Schlobotnik (archives)

URL for this frameset: http://elynah.com/tbrw/tbrw.cgi?2015/rpi.shtml

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

Today's RPI (including games of 2015 March 21)

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
MSU-Mankato 1 .5917 1 29-7-3 .7821 1 .7633 9 .5232 4 .5540 15 .5112 .0085 1 .5889
North Dakota 2 .5797 4 27-9-3 .7308 4 .7072 8 .5265 35 .4929 1 .5396 .0080 12 .5508
Boston Univ 3 .5720 3 25-7-5 .7432 3 .7302 15 .5146 23 .5110 11 .5159 .0035 3 .5769
Miami 4 .5690 7T 25-13-1 .6538 8 .6474 4 .5316 13 .5320 4 .5314 .0085 5 .5679
Denver U 5 .5678 11T 23-13-2 .6316 13 .6257 3 .5348 11 .5359 3 .5343 .0103 7 .5613
Minn-Duluth 6 .5656 24T 20-15-3 .5658 23 .5737 1 .5453 1 .5953 6 .5259 .0132 2 .5834
Michigan Tech 7 .5647 2 29-9-2 .7500 2 .7400 31 .5032 39 .4904 19 .5082 .0023 6 .5644
NE-Omaha 8 .5501 20 18-12-6 .5833 21 .5730 5 .5312 22 .5115 2 .5389 .0084 20 .5323
Harvard 9 .5499 13 21-12-3 .6250 10 .6319 16 .5140 7 .5427 34 .5028 .0065 8 .5586
Minnesota 10 .5499 9 23-12-3 .6447 12 .6441 13 .5154 29 .5001 9 .5214 .0023 15 .5429
Boston Coll 11 .5461 16 21-13-3 .6081 15 .6044 10 .5210 9 .5393 13 .5139 .0042 10 .5529
St Cloud 12 .5460 30 19-18-1 .5132 30 .5189 2 .5413 2 .5809 5 .5260 .0103 4 .5686
Quinnipiac 13 .5439 6 23-11-4 .6579 7 .6471 26 .5058 36 .4929 16 .5109 .0028 16 .5416
Yale 14 .5415 10 18-9-5 .6406 9 .6304 30 .5047 26 .5063 32 .5040 .0054 17 .5415
Providence 15 .5411 14 22-13-2 .6216 14 .6201 20 .5094 32 .4947 12 .5151 .0041 21 .5265
Bowling Green 16 .5409 7T 23-11-5 .6538 6 .6572 43 .4979 25 .5073 47 .4942 .0032 13 .5492
Colgate 17 .5392 11T 22-12-4 .6316 11 .6330 23 .5073 19 .5194 37 .5025 .0005 11 .5519
Mass-Lowell 18 .5374 15 21-12-6 .6154 16 .6011 17 .5133 12 .5339 27 .5053 .0022 9 .5544
Vermont 19 .5361 19 22-15-4 .5854 17 .5882 14 .5147 14 .5317 20 .5081 .0030 14 .5432
Michigan 20 .5288 17 22-15 .5946 19 .6023 36 .5003 33 .4943 36 .5026 .0030 22 .5237
St Lawrence 21 .5270 21T 20-14-3 .5811 20 .5889 35 .5014 40 .4903 25 .5058 .0037 24 .5147
Dartmouth 22 .5205 23 17-12-4 .5758 24 .5617 34 .5021 37 .4927 26 .5057 .0035 26 .5119
Northeastern 23 .5202 32T 16-16-4 .5000 32 .5000 11 .5210 5 .5461 14 .5112 .0045 19 .5349
AK-Fairbanks 24 .5202 18 19-13-2 .5882 18 .5915 48 .4911 52 .4568 31 .5044 .0040 31 .4989
Robert Morris 25 .5197 5 24-8-5 .7162 5 .7083 56 .4566 58 .4315 51 .4663 .0002 28 .5073
Western Mich 26 .5188 40T 14-18-5 .4459 38 .4570 6 .5306 6 .5433 7 .5256 .0066 25 .5127
Bemidji State 27 .5143 35 16-17-5 .4868 36 .4807 12 .5177 3 .5585 38 .5018 .0058 18 .5356
New Hampshire 28 .5123 32T 19-19-2 .5000 33 .5026 18 .5108 16 .5235 24 .5059 .0035 23 .5154
Union 29 .5100 31 19-18-2 .5128 28 .5276 40 .5000 43 .4823 23 .5069 .0031 33 .4911
Merrimack 30 .5073 37 16-18-4 .4737 37 .4860 19 .5099 17 .5217 28 .5053 .0035 27 .5098
Mich State 31 .5046 29 17-16-2 .5143 31 .5148 41 .4989 47 .4778 22 .5072 .0017 36 .4856
Penn State 32 .5037 26 18-15-4 .5405 29 .5296 47 .4933 48 .4774 39 .4995 .0014 32 .4975
Notre Dame 33 .5032 34 18-19-5 .4881 35 .4714 21 .5083 45 .4815 10 .5188 .0041 38 .4827
Ferris State 34 .4987 36 18-20-2 .4750 34 .4925 37 .5002 41 .4882 30 .5049 .0004 37 .4851
Northern Mich 35 .4951 39 14-18-6 .4474 39 .4574 33 .5028 44 .4822 17 .5108 .0036 42 .4678
Cornell 36 .4914 38 11-14-6 .4516 41 .4309 25 .5061 21 .5119 33 .5038 .0041 34 .4908
Ohio State 37 .4890 43 14-19-3 .4306 42 .4333 28 .5053 15 .5308 46 .4954 .0017 29 .5039
RIT 38 .4871 24T 19-14-5 .5658 25 .5591 51 .4630 50 .4731 57 .4591 .0000 30 .5020
Mercyhurst 39 .4844 27 19-16-4 .5385 26 .5417 49 .4645 51 .4706 53 .4621 .0006 35 .4894
Canisius 40 .4836 21T 18-12-7 .5811 22 .5714 57 .4544 59 .4214 50 .4672 .0000 41 .4688
Bentley 41 .4789 28 17-15-5 .5270 27 .5355 52 .4601 53 .4552 54 .4620 .0000 39 .4785
Maine 42 .4772 45 14-22-3 .3974 46 .3895 27 .5055 30 .5000 21 .5076 .0007 40 .4717
Connecticut 43 .4765 47 10-19-7 .3750 47 .3808 29 .5049 31 .4950 18 .5087 .0027 43 .4640
Clarkson 44 .4722 46 12-20-5 .3919 45 .3892 44 .4979 42 .4851 35 .5028 .0015 47 .4549
Mass-Amherst 45 .4636 48 11-23-2 .3333 49 .3295 24 .5065 24 .5097 29 .5052 .0014 46 .4588
RPI 46 .4630 49 12-26-3 .3293 48 .3417 32 .5029 20 .5123 40 .4992 .0004 44 .4625
Brown 47 .4560 50 8-20-3 .3065 50 .3161 38 .5002 28 .5034 41 .4989 .0018 48 .4495
Holy Cross 48 .4541 40T 14-18-5 .4459 40 .4372 53 .4598 57 .4344 49 .4697 .0000 52 .4354
Air Force 49 .4524 42 16-21-4 .4390 43 .4368 55 .4575 55 .4434 52 .4630 .0000 51 .4377
Sacred Heart 50 .4519 44 13-19-6 .4211 44 .4153 50 .4642 49 .4744 55 .4602 .0000 45 .4599
CO College 51 .4487 56 6-26-3 .2143 57 .2086 7 .5273 8 .5420 8 .5215 .0011 49 .4482
AK-Anchorage 52 .4434 51T 8-22-4 .2941 52 .2853 45 .4956 34 .4930 43 .4966 .0004 54 .4324
AL-Huntsville 53 .4412 53 8-26-4 .2632 53 .2778 46 .4951 38 .4924 45 .4962 .0004 55 .4293
Lake Superior 54 .4375 54 8-28-2 .2368 54 .2527 42 .4983 18 .5197 48 .4900 .0006 50 .4455
Wisconsin 55 .4252 58 4-26-5 .1857 58 .1676 22 .5079 10 .5378 44 .4962 .0024 53 .4346
Princeton 56 .4166 59 4-23-3 .1833 59 .1655 39 .5000 27 .5041 42 .4984 .0002 56 .4145
Army 57 .4136 51T 8-22-4 .2941 51 .2927 58 .4539 56 .4380 56 .4601 .0000 58 .3943
Niagara 58 .4028 55 7-28-4 .2308 55 .2366 54 .4582 46 .4789 59 .4502 .0000 57 .4145
American Intl 59 .3948 57 4-25-7 .2083 56 .2229 59 .4521 54 .4513 58 .4525 .0000 59 .3850

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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