Steve Christopher asks:
 
>> PERFORMANCE is based on won-lost record only; game sites and margin of victor
   y
>> are not considered, for example. Performance ranges from +100 (for an undefea
   t
>> and untied team) to -100 (for a winless and untied team), with a .500 winning
>> percentage getting a zero performance.
>>
>> SCHEDULE is the average rating of a team's opponents.
>>
>> RATING is the sum of performance and schedule and represents an evaluation
>> of how each team has done so far with respect to the rest of the league.
>>
>Which comes first, the weekly calculation of the ratings, or the
>schedules?  That is, when figuring out a team's schedule strength, are
>its opponents' PREVIOUS ratings averaged, and then that number added to
>the performance rating, or are the NEW ratings calculcated first and
>then added to the peformance score to get the new ratings.  (Actually, I
>suppose the answer is obvious--how could you have new ratings until
>you've done the calculation?  Hey!  This is confusing!)
>
 
I'll venture to answer some of these questions.  I'm sure Keith will
correct me where I've erred :-).
 
Everything is done simultaneously.  Each team's rating and its
opponents ratings are computed at the same time.
 
One should really think of TCHCR more as a "sorting" system than a
"rating" system like RPICH.  It assumes that a victory for team A
over team B means that team A is at least better than team B.  TCHCR
will take the results of each game and attempt to sort teams given
all these inequalities.  The trouble enters when team B beats team C
and team C turns around and beats team A.  TCHCR realizes that such
events take place and compensates by minimizing the number of
incorrect inequalities it is given by adjusting the teams' ratings.
In math-speak, this is "minimizing chi-squared".
 
In a hypothetical situation, assume that there are nine teams in a
league, they have played each other often, and everyone knows who is
in what place.  Suppose a tenth spontaneously enters that league,
beats the fourth place team and loses to the third place team.  Despite
the fact that the new team only has a .500 record, it will be the
new fourth place team in TCHCR, no matter what the records of the teams
it played are.
 
The algorithm for computing the ratings is nifty.  Since there are
currently 44 Div I teams (I think), 44 ratings must be figured out
simultaneously.  Again, in math-speak, we have 44 equations with
44 unknowns.  This implies an inversion of a 43x43 matrix (not worth
describing how one fell out), which can only be done comfortably on
a computer (thus the second "C" in TCHCR).
 
I believe that Keith gives us numbers for a team's PERFORMANCE and
SCHEDULE in order to help us understand why teams are rated as they
are.  TCHCR only computes these numbers as an afterthought.  I think
that TCHCR can produce more numbers as afterthoughts which would be
quite revealing, such as the importance of connections between teams
which are only distantly related.  If Northeastern can overtake Miami
in the standings by beating them in only one game, the connection
between the two teams is not that significant.  TCHCR contains
such information.
 
Hope this helps.
 
Stephen Leroy  (Cornell '88)                 | Disclaimer:  Caltech knows
Division of Geological and Planetary Science | better than to take
California Institute of Technology           | responsibility for what I
leroy@(cluster,satur1).gps.caltech.edu       | may claim.
 
P.S. Patiently awaiting the Freeze-out so that I can actually see
some hockey!