On Tue, 22 Feb 2000, Wayne T. Smith wrote:
>
> 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.
 
No question about that!
 
>     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.
 
This last is encouraging.
 
The slow convergence is probably connected with the radical difference
between HEAL and RHEAL: it takes time (and iterations) for the effect of a
rapidly-moving team to filter through its opposition (and then their
opposition, and so on). This is undoubtedly not helped by the MAAC's
schedule being so nearly self-contained.
 
<snip actual ranking>
 
I found that the RHEAL ranking is most similar to those of KRACH and
Massey -- and most different to RPI and HEAL! (This surprises me a bit:
some time ago, I tried to work out a recursive RPI along the same lines as
recursive HEAL, and it differed little from ordinary RPI.)
 
For those that are interested, here's how seven of the rating systems
agree (or disagree) with each other. The figures in the table are Spearman
rank correlations: 1.00 means that the rankings are identical, 0 would
mean no relationship between the rankings, and -1 would mean complete
disagreement (the top team on one is the bottom on the other). "Med" is a
consensus ranking using all seven rating systems.
 
Spearman rank correlations:
 
        cchp chodr  heal krachmassey rheal   rpi   med
  cchp  1.00  0.99  0.78  0.96  0.96  0.92  0.82  0.97
 chodr  0.99  1.00  0.78  0.94  0.95  0.91  0.81  0.96
  heal  0.78  0.78  1.00  0.84  0.85  0.84  0.97  0.87
 krach  0.96  0.94  0.84  1.00  0.99  0.96  0.86  0.99
massey  0.96  0.95  0.85  0.99  1.00  0.96  0.86  0.99
 rheal  0.92  0.91  0.84  0.96  0.96  1.00  0.82  0.97
   rpi  0.82  0.81  0.97  0.86  0.86  0.82  1.00  0.87
   med  0.97  0.96  0.87  0.99  0.99  0.97  0.87  1.00
 
Executive summary:
 
- CCHP and CHODR agree very strongly with each other at one extreme
- HEAL and RPI agree strongly with each other at the other extreme
- KRACH and Massey agree strongly with each other in the middle
- RHEAL agrees most strongly with KRACH and Massey (and the consensus
ranking "med").
 
Most of the difference between rankings comes, I would guess, in the
treatment of the MAAC and CHA teams. RPI and HEAL like them (at least, the
ones with good win %), while CCHP and CHODR hate them.
 
The first three of the observations in the summary have been consistently
true this season (and last, as far as I remember).
 
--
Ken Butler, Dept. of Mathematics & Statistics, Dalhousie University
      [log in to unmask]  /  http://www.mscs.dal.ca/~butler
                 Tants caps, tants barrets.
 
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