One way to correct for the unbalanced schedule would be to make games between teams who only play twice worth 4 points, like the CHA is doing this year, and I believe the WCHA did some time in the past. However, that still benefits weak teams who only play strong teams twice, since they could get lucky and pull off a win or tie, which they would get double-credit for, when they would have been very unlikely to repeat the feat. Another correction would be to project how each team would have fared if they'd played a full balanced schedule. One way to do this is to calculate a Bradley-Terry, or KRACH, rating based only on games within the conference. The result of this is a KRACH for each team which is proportional to its "odds" of winning any game; if you add up the resulting probabilities of winning each of the games on a team's schedule, you'll get the number they actually won. Ranking teams by KRACH is equivalent to ranking them by Round-Robin Winning Percentage, which is the average of their probabilities of winning a game with each other team in the league, or by RRP, the number of points KRACH says they would get if they played each other team a specified number of times. If a league plays a balanced schedule, ranking by KRACH/RRWP/RRP is guaranteed to be the same as ranking by winning percentage. For example, here are the results of last season's Hockey East race; each team played each other team three times, and the actual number of points they received in those games are listed below: Tm PF/GP Pct RRWP NH Me BC Pv BU MA ML Mr NE NH 39/24 .812 .812 --- 4/3 3/3 4/3 4/3 6/3 6/3 6/3 6/3 Me 36/24 .750 .750 2/3 --- 4/3 6/3 4/3 3/3 6/3 6/3 5/3 BC 32/24 .667 .667 3/3 2/3 --- 3/3 4/3 6/3 6/3 4/3 4/3 Pv 25/24 .521 .521 2/3 0/3 3/3 --- 6/3 4/3 4/3 4/3 2/3 BU 19/24 .396 .396 2/3 2/3 2/3 0/3 --- 4/3 4/3 3/3 2/3 MA 18/24 .375 .375 0/3 3/3 0/3 2/3 2/3 --- 2/3 6/3 3/3 ML 18/24 .375 .375 0/3 0/3 0/3 2/3 2/3 4/3 --- 4/3 6/3 Mr 15/24 .312 .312 0/3 0/3 2/3 2/3 3/3 0/3 2/3 --- 6/3 NE 14/24 .292 .292 0/3 1/3 2/3 4/3 4/3 3/3 0/3 0/3 --- Notice that the RRWP is exactly equal to the actual winning percentage for each team. That's because the teams really did play a round-robin schedule. Here are the actual KRACH ratings and the probabilities they predict of winning against each opponent: Tm KRACH RRP/TGP NH Me BC Pv BU MA ML Mr NE NH 428.5 39.0/24 .--- .584 .677 .797 .868 .878 .878 .904 .912 Me 304.7 36.0/24 .416 .--- .599 .737 .824 .837 .837 .871 .881 BC 204.1 32.0/24 .323 .401 .--- .652 .759 .774 .774 .818 .832 Pv 109.0 25.0/24 .203 .263 .348 .--- .627 .647 .647 .706 .725 BU 64.95 19.0/24 .132 .176 .241 .373 .--- .522 .522 .589 .612 MA 59.48 18.0/24 .122 .163 .226 .353 .478 .--- .500 .568 .591 ML 59.48 18.0/24 .122 .163 .226 .353 .478 .500 .--- .568 .591 Mr 45.32 15.0/24 .096 .129 .182 .294 .411 .432 .432 .--- .524 NE 41.24 14.0/24 .088 .119 .168 .275 .388 .409 .409 .476 .--- For example, UNH's conference KRACH is 428.5, about four times Providence's rating of 109.0, so the predicted odds that they'll win each game against PC are around four-to-one; more precisely, the probability is .797=428.5/(428.5+109.0). Their RRP are found by multiplying their head-to-head probability against each team by 3 (since the round-robin in question is three games between each pair of teams), so .584 times 3 plus .677 times 3, etc. That adds up to 39, which is exactly the number of points they actually got. Now, apply this to a schedule that wasn't balanced, like last year's WCHA: Tm PF/GP Pct RRWP ND CC DU Wi Mn AA SC MT MD ND 50/28 .893 .898 --- 6/4 8/4 6/4 7/4 4/2 8/4 4/2 7/4 CC 40/28 .714 .728 2/4 --- 4/4 2/2 8/4 8/4 4/4 8/4 4/2 DU 32/28 .571 .593 0/4 4/4 --- 5/4 3/2 4/4 6/4 8/4 2/2 Wi 29/28 .518 .511 2/4 2/2 3/4 --- 3/4 3/4 4/2 4/4 8/4 Mn 26/28 .464 .472 1/4 0/4 1/2 5/4 --- 4/4 4/4 4/2 7/4 AA 25/28 .446 .432 0/2 0/4 4/4 5/4 4/4 --- 2/2 4/4 6/4 SC 20/28 .357 .360 0/4 4/4 2/4 0/2 4/4 2/2 --- 0/4 8/4 MT 18/28 .321 .304 0/2 0/4 0/4 4/4 0/2 4/4 8/4 --- 2/4 MD 12/28 .214 .202 1/4 0/2 2/2 0/4 1/4 2/4 0/4 6/4 --- Tm KRACH RRP/TGP ND CC DU Wi Mn AA SC MT MD ND 863.1 57.5/32 .--- .751 .852 .892 .907 .920 .940 .953 .972 CC 286.8 46.6/32 .249 .--- .657 .732 .764 .793 .840 .871 .919 DU 149.8 37.9/32 .148 .343 .--- .588 .628 .667 .732 .779 .856 Wi 104.8 32.7/32 .108 .268 .412 .--- .542 .584 .657 .712 .806 Mn 88.61 30.2/32 .093 .236 .372 .458 .--- .543 .618 .676 .778 AA 74.65 27.6/32 .080 .207 .333 .416 .457 .--- .577 .637 .747 SC 54.76 23.1/32 .060 .160 .268 .343 .382 .423 .--- .563 .684 MT 42.47 19.5/32 .047 .129 .221 .288 .324 .363 .437 .--- .627 MD 25.29 12.9/32 .028 .081 .144 .194 .222 .253 .316 .373 .--- Everyone played 4 games against seven opponents and 2 against the other two. The KRACH ratings are as always defined so that they predict the correct number of points against whatever schedule was actually played. For instance, UMD played 2 games each against Colorado College and Denver, so if you add 4 (number of games against North Dakota) times .028 (predicted probability of beating UND), 2 times .081 (for CC), 2 times .144 (for DU), 4 times .194 (for Wisconsin), etc, you get 12, the number of points UMD actually got against that schedule. However, to obtain the round-robin points or winning percentage, we need to include an equal number of games against each team, for instance by adding two hypothetical games each against CC and DU. That would give UMD an additional 2 times .081 plus 2 times .144, or 0.9 points for a total of 12.9 against a 32-game balanced schedule. Since the four "unplayed games" for UMD were against two of the strongest teams in the league, their RRWP of .202 is lower than their winning percentage of .214. As it turns out, correcting for the unbalanced schedule wouldn't have changed the ranking of the teams last season, partly because it was only slightly unbalanced. Here is the same analysis for the WCHA so far this season: Tm PF/GP Pct RRWP Wi ND SC Mn CC Mk AA MD DU MT Wi 36/22 .818 .811 --- 4/2 6/4 4/2 4/2 2/2 2/2 2/2 4/2 8/4 ND 33/24 .688 .700 0/2 --- 5/4 5/4 3/2 2/2 8/4 4/2 2/2 4/2 SC 26/22 .591 .622 2/4 3/4 --- 3/2 0/0 4/2 4/2 4/4 2/2 4/2 Mn 24/22 .545 .587 0/2 3/4 1/2 --- 4/4 2/2 2/2 8/4 4/2 0/0 CC 26/22 .591 .555 0/2 1/2 0/0 4/4 --- 2/2 3/2 4/4 8/4 4/2 Mk 25/22 .568 .525 2/2 2/2 0/2 2/2 2/2 --- 3/4 0/0 6/4 8/4 AA 23/24 .479 .459 2/2 0/4 0/2 2/2 1/2 5/4 --- 0/0 5/4 8/4 MD 16/22 .364 .341 2/2 0/2 4/4 0/4 4/4 0/0 0/0 --- 2/2 4/4 DU 15/24 .312 .319 0/2 2/2 2/2 0/2 0/4 2/4 3/4 2/2 --- 4/2 MT 4/24 .083 .080 0/4 0/2 0/2 0/0 0/2 0/4 0/4 4/4 0/2 --- Tm KRACH RRP/TGP Wi ND SC Mn CC Mk AA MD DU MT Wi 433.4 58.4/36 .--- .642 .718 .748 .774 .795 .838 .898 .908 .980 ND 242.0 50.4/36 .358 .--- .587 .624 .656 .684 .743 .832 .847 .965 SC 170.1 44.8/36 .282 .413 .--- .539 .573 .604 .670 .776 .795 .951 Mn 145.7 42.3/36 .252 .376 .461 .--- .534 .566 .635 .748 .769 .943 CC 126.9 40.0/36 .226 .344 .427 .466 .--- .532 .602 .721 .743 .935 Mk 111.6 37.8/36 .205 .316 .396 .434 .468 .--- .571 .695 .718 .927 AA 83.81 33.1/36 .162 .257 .330 .365 .398 .429 .--- .631 .657 .905 MD 48.99 24.6/36 .102 .168 .224 .252 .279 .305 .369 .--- .528 .847 DU 43.82 22.9/36 .092 .153 .205 .231 .257 .282 .343 .472 .--- .832 MT 8.830 5.7/36 .020 .035 .049 .057 .065 .073 .095 .153 .168 .--- Micheal Neal is right that Minnesota is punished by their stronger schedule; they are the 6th place team according to winning percentage (or total points) and 4th place according to conference KRACH/RRWP/RRP. Of course, that's working with a partially-completed schedule, so it's even more unbalanced (Minnesota hasn't played Michigan Tech at all, for instance). I tried inventing hypothetical results for the last few weeks of the season which looked more or less reasonable, and got the following as one possibility: Tm PF/GP Pct RRWP Wi ND SC Mn CC Mk AA DU MD MT Wi 46/28 .821 .821 --- 4/2 6/4 8/4 7/4 2/2 5/4 4/2 2/2 8/4 ND 40/28 .714 .715 0/2 --- 5/4 5/4 3/2 5/4 8/4 2/2 8/4 4/2 SC 34/28 .607 .627 2/4 3/4 --- 5/4 2/2 4/2 4/2 6/4 4/4 4/2 Mn 30/28 .536 .575 0/4 3/4 3/4 --- 4/4 2/2 2/2 4/2 8/4 4/2 CC 31/28 .554 .558 1/4 1/2 2/2 4/4 --- 4/4 3/2 8/4 4/4 4/2 Mk 32/28 .571 .547 2/2 3/4 0/2 2/2 4/4 --- 3/4 6/4 4/2 8/4 AA 27/28 .482 .478 3/4 0/4 0/2 2/2 1/2 5/4 --- 5/4 3/2 8/4 DU 19/28 .339 .319 0/2 2/2 2/4 0/2 0/4 2/4 3/4 --- 2/2 8/4 MD 17/28 .304 .296 2/2 0/4 4/4 0/4 4/4 0/2 1/2 2/2 --- 4/4 MT 4/28 .071 .064 0/4 0/2 0/2 0/2 0/2 0/4 0/4 0/4 4/4 --- Tm KRACH RRP/TGP Wi ND SC Mn CC Mk AA DU MD MT Wi 473.1 59.1/36 .--- .640 .729 .772 .786 .793 .839 .917 .926 .986 ND 266.5 51.5/36 .360 .--- .602 .656 .674 .684 .746 .862 .876 .975 SC 176.1 45.2/36 .271 .398 .--- .558 .577 .588 .660 .805 .823 .963 Mn 139.7 41.4/36 .228 .344 .442 .--- .520 .531 .607 .766 .787 .954 CC 129.1 40.1/36 .214 .326 .423 .480 .--- .511 .588 .752 .774 .951 Mk 123.3 39.4/36 .207 .316 .412 .469 .489 .--- .577 .743 .766 .948 AA 90.61 34.4/36 .161 .254 .340 .393 .412 .423 .--- .680 .706 .931 DU 42.58 22.9/36 .083 .138 .195 .234 .248 .257 .320 .--- .530 .864 MD 37.76 21.3/36 .074 .124 .177 .213 .226 .234 .294 .470 .--- .849 MT 6.713 4.6/36 .014 .025 .037 .046 .049 .052 .069 .136 .151 .--- Note that because of their varying strengths of schedule, Minnesota, Colorado College, and Mankato State are ranked in opposite order according to RRWP and (unbalanced) winning percentage. John Whelan, Cornell '91 [log in to unmask] http://www.amurgsval.org/joe/ HOCKEY-L is for discussion of college ice hockey; send information to [log in to unmask], The College Hockey Information List.