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
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