Dear fellow hockey geeks (non-geeks will probably not be interested),

Those familiar with the Bradley-Terry or KRACH rating system (see
<http://slack.net/~whelan/tbrw/tbrw.cgi?krach> for details) may recall
that you can't define a standard set of ratings on the same scale
unless you connect any two teams with a chain of wins and/or ties.
But you can still assign a consistent set of ratings within groups
that are connected in that way.  Between such groups, if one team is
connected with another by only wins and ties, that team's KRACH is
measured on a different scale, and is effectively infinitely higher
than the second teams.  If two teams can't be connected by a chain of
wins and/or ties in either direction, their ratings can't be
meaningfully compared.

Below is a chart summarizing the ratings of the 52 teams which have
played official games already.  They are grouped into boxes in which
all the teams are "comparable" based on the current results.  Teams
are "infinitely better" than those in boxes directly above them and
"infinitely worse" than those in boxes directly below them.  Teams in
"sideways separated" boxes (not connected by arrows) can't be compared
on the basis of the results to date.  The teams are listed by their
two-letter abbreviations (which are listed in
<http://slack.net/~whelan/tbrw/tbrw.cgi?tourney.diy>); the first
number is the KRACH rating which can be compared to those of other
teams inside the box, and the second is the RRWP, the expected winning
percentage if the team played the other 57 Division I teams one time
each (the expected head-to-head winning percentages with teams in the
same group are calculated using the KRACH ratings; those with teams
from "better" groups are .000, those with teams from "worse" groups
are 1.000, and those with teams from "incomparable" groups (including
the six Ivies) are .500).

+---------------+        +---------------+        +---------------+
| DU 100.0 .930 |        | MA 100.0 .930 |        | Me 100.0 .930 |
+---------------+        +---------------+        +---------------+
        |                        |                        |
        V                        V                        V
+------------------------------------------------------------------+
| SC 14374 .880    Nt 420.7 .712    Mm 100.8 .588    HC 22.28 .458 |
| MT 2619. .828    AA 289.4 .682    Fi 99.88 .588    LS 12.97 .417 |
| Mi 2107. .818    SL 288.3 .681    AF 81.26 .569    MD 12.24 .413 |
| NM 1776. .809    BG 271.8 .676    ML 58.94 .540    Pv 9.579 .397 |
| Wi 1525. .800    WS 169.7 .635    Ni 43.80 .514    Vt 8.879 .392 |
| Mh 941.6 .771    Qn 161.7 .631    NH 38.99 .504    Ca 7.426 .381 |
| Un 937.7 .771    ND 135.9 .615    Ck 31.25 .485    Mr 5.593 .364 |
| CC 528.9 .730    Ak 127.5 .610    BU 27.68 .475    Mk 2.309 .324 |
| OS 420.8 .712    BC 115.1 .600    MS 25.84 .470    BS 1.846 .316 |
+------------------------------------------------------------------+
        |                        |                        |
        V                        V                        V
+---------------+        +---------------+        +---------------+
| Mn 100.0 .202 |        | AH 100.0 .184 |        | SH 100.0 .158 |
+---------------+        | Ct 100.0 .184 |        +---------------+
        |                | RP 100.0 .184 |
        V                +---------------+
+---------------+                |
| WM 123.3 .154 |                V
| FS 123.3 .154 |        +---------------+
| Cg 123.3 .154 |        | Ar 100.0 .149 |
| NE 123.3 .154 |        +---------------+
| NO 41.10 .132 |                |
+---------------+                V
                         +---------------+
                         | By 100.0 .132 |
                         +---------------+
                                 |
                                 V
                         +---------------+
                         | AI 100.0 .114 |
                         +---------------+

                                          John Whelan, Cornell '91
                                                 [log in to unmask]
                                     http://www.amurgsval.org/joe/

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