PATRICK BLAKE wrote:
 
> With all of this talk lately about RPICH and others & and how they *all* seem
> to be so "unfair" in various respects, how difficult would it be for an
> informed math/stats guru to develop a new method which takes all of the
> meaningful criteria into account?
 
All of this talk of the inequitues involved in any ratings system
that could be used to select the NCAA tournament teams made me think of
a more basic inequity in the hockey team evaluation system: goals are not
a good criteria to judge the relative performance of two teams in a
particular game.  Surely, every hockey fan can think of many games when
Team A scored a goal or two more than Team B but Team B had more shots on goal,
more good scoring opportunities and the "territorial" advantage.  Is it fair
that Team A gets the win and 2 pts in the standings while Team B gets nothing?
 
In consideration of this fact, does it not make sense to consider a system in
which the winner of each game is determined by a committee of hockey experts
and not just by the number of goals scored.  In order to avoid a purely
arbitrary decision the panel should be guided by an index that would provide
a somewhat objective measure of the relative performance of the two teams,  The
index should include factors such as (along with many other possibilities):
 
1. Number of shots on goal
 
2. Number of quality scoring opportunities
 
3. Number of difficult saves made
 
4. Territorial edge (e.g. # of minutes in each attacking zone)
 
Of course, goals should also be considered as a significant factor.
However, it doesn't make sense to value all goals equally.  Should a
"garbage goal" scored off a scramble in front of the net count the same as
one that results from an exquisite display of passing and teamwork?
Of course not.  Furthermore, what can be the rationale in assigning
the same value to a goal scored by the team's leading scorer against
the opposing team's 2nd or 3rd set of defensemen as a goal scored
by an average goal scorer against the 1st-string defensemen?  Certainly,
a goal that results from a play that beats a top-notch defensemen
or defensive-minded center or winger should be worth more.
 
Many years ago the use of a complex formula that would consider all
these factors would have been impractical.  However, now that low cost
computer technology is ubiquitous, it wouldn't be much of a task
to update a game performance index (GPI) as the game progresses and
and display it on the scoreboard. Of course, the GPI would only be
a guide for the committee.  Committee members would be free to vote
for either team so that intangible factors that cannot be easily
quantified could be factored into the final outcome.  This certainly
could lead to some dramatic endings when one team is ahead on the
scoreboard (GPI) but the other wins the vote of the committee.
 
Another advantage of this system is that it would generate many
more statistical categories to compile and discuss.  Since each
of these would actually play a part in the determination of the outcome
of a game it would certainly be appropriate to analyze each at great length.
 
If we want to have the ultimately fair system, it seems only appropriate
that we achieve fairness at the game level before we tune our system
for fairness in Conference tournament seedings and NC$$ tournament
selections.
 
 
John Zack
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Cornell '77 '81