About a week ago, as John, Ken and I were discussing the purposes and goals of ranking systems, John wrote, in part.. > Incidentally I'll repeat a suggest I made last year on how HEAL could > be Quinnipiac-proofed: Instead of saying that a team's Tournament > Index is (up to an overall factor) the weighted (by number of games > against that opponent) sum of the Preliminary Indices of the teams > it's beaten [counting each tie as half a win] divided by the number of > games, why not recursively define the TI as the weighted sum of the > TIs of the teams you've beaten, divided by your number of games? ... Such a challenge! :-) The ratings that follow implement John's suggestion of a "Recursive HEAL", that I'll call RHEAL. I post it here on Hockey-L, since it is part of Hockey-L's discussion, and because it is so radically different from HEAL ratings, that I don't quite know what we're measuring! But it certainly is "Quinnipiac-proofed", for better or worse. By the way, ECAC RHEAL converges to a steady state in about 10 iterations, making only slight adjustments to HEAL. Since John has published a Bradley-Terry ECAC ranking, I've discontinued ECAC HEAL. The Men's D-I ranking requires many iterations (> 10 and < 100) to settle into a steady state. No matter what (PI) seeding I used, it converged to the same steady state. So here we go ... "Weak schedules" need not apply ... RHEAL for Men's Division I College Hockey, through 2000-02-20 Compiled by Wayne T. Smith This report includes results from 748 Division I games. Last Rank Week School Played Record HEAL RHEAL 1 Wisconsin 32 25- 6- 1 100.00( 1) 100.00 2 New Hampshire 32 20- 7- 5 96.38( 2) 96.59 3 Michigan 32 22- 7- 3 88.06( 8) 89.80 4 North Dakota 32 22- 7- 3 88.62( 7) 87.56 5 Boston University 33 20- 7- 6 89.97( 4) 86.97 6 Boston College 30 20- 9- 1 84.32(10) 85.17 7 Michigan State 32 21- 9- 2 78.62(11) 79.33 8 Maine 30 19- 7- 4 88.91( 6) 78.29 9 St Lawrence 26 17- 7- 2 85.97( 9) 77.46 10 Colgate 26 18- 7- 1 89.28( 5) 77.14 11 Ferris State 32 17-13- 2 72.98(14) 73.77 12 St Cloud 28 16-10- 2 71.94(15) 71.43 13 Providence 32 16-15- 1 68.53(17) 68.84 14 Minnesota 32 17-13- 2 68.74(16) 68.69 15 Northern Michigan 32 19- 9- 4 64.52(20) 68.02 16 Lake Superior 30 15-13- 2 64.84(19) 67.76 17 Northeastern 30 12-13- 5 66.97(18) 67.09 18 MSU-Mankato 28 16-11- 1 63.87(21) 62.65 19 Miami 30 13-14- 3 59.20(25) 61.60 20 Rensselaer 29 17-10- 2 74.35(12) 59.46 21 Colorado College 33 16-15- 2 60.06(23) 55.77 22 Nebraska-Omaha 32 12-15- 5 53.10(30) 54.77 23 Princeton 22 9-10- 3 60.30(22) 53.89 24 Cornell 24 11-11- 2 55.89(28) 53.51 25 Merrimack 31 11-15- 5 52.26(32) 51.01 26 Notre Dame 36 14-15- 7 49.63(34) 50.91 27 Niagara 23 16- 6- 1 90.46( 3) 50.14 28 Clarkson 27 11-13- 3 59.64(24) 48.28 29 Bowling Green 28 11-16- 1 46.44(38) 47.93 30 Western Michigan 30 10-17- 3 49.72(33) 47.92 31 Yale 24 9-11- 4 55.61(29) 46.79 32 Minnesota-Duluth 28 10-18- 0 45.28(39) 46.07 33 Alaska-Anchorage 30 12-15- 3 47.05(36) 44.37 34 Vermont 17 5- 9- 3 49.61(35) 43.71 35 Ohio State 30 8-18- 4 41.72(43) 42.28 36 Harvard 24 8-14- 2 42.63(42) 42.09 37 Dartmouth 24 8-12- 4 44.83(40) 41.82 38 Mass Amherst 30 10-16- 4 47.03(37) 41.00 39 Denver 34 11-21- 2 40.11(44) 40.06 40 Brown 24 6-16- 2 37.49(48) 34.56 41 Union 27 7-19- 1 38.63(46) 29.71 42 Mass Lowell 31 8-20- 3 34.62(49) 28.44 43 Alaska-Fairbanks 28 4-23- 1 20.31(52) 20.31 44 Michigan Tech 34 4-30- 0 13.89(53) 15.24 45 Air Force 16 7- 8- 1 43.01(41) 7.94 46 Army 19 7-10- 2 39.29(45) 5.55 47 Iona 22 11- 8- 3 56.69(27) 3.11 48 Quinnipiac 25 18- 4- 3 73.34(13) 2.51 49 Sacred Heart 24 12- 9- 3 57.57(26) 2.40 50 Canisius 21 11- 9- 1 52.43(31) 1.75 51 American Int'l 18 5-10- 3 23.61(51) 1.30 52 Connecticut 23 8-14- 1 38.37(47) 1.28 53 Holy Cross 25 6-17- 2 25.19(50) 0.88 54 Fairfield 24 1-21- 2 8.53(54) 0.46 Average ranking of each league(#teams): This week WCHA(10): 21.80 HEA(09): 17.33 CCHA(12): 21.33 ECAC(12): 27.75 MAAC(08): 50.50 CHA(03): 39.33 Average rating of each league(#teams): This week WCHA(10): 59.18 HEA(09): 67.04 CCHA(12): 58.70 ECAC(12): 50.70 MAAC(08): 1.71 CHA(03): 21.21 cheers, wayne Wayne T. Smith mailto:[log in to unmask] Systems Group - UNET University of Maine System Co-owner of the College Hockey mailing lists HOCKEY-L is for discussion of college ice hockey; send information to [log in to unmask], The College Hockey Information List.