I would like to make one last comment on "Yet Another Method" before
I get off the subject. For those who have found this boring, I
apologize for taking up the bandwidth; but, there is a significant portion
of the population which finds this discussion very germane.
First, what are we trying to do with a ranking? Well, in B-ball,
from whence sprung the RPI, a significant trend had started to develop.
All the coaches had noticed that around 18 victories got you into the big
dance. For stronger conferences such as the ACC and Big East the number
could sometimes be less, but nonetheless pressure developed to schedule cream-
puff opponents to inflate the record to the magic mark.
In addition, B-ball has a problem somewhat unlike hockey. There
are a million conferences, some with absolutely no connectivity to others.
How are the evaluators to assess the differences between widely spaced
conferences? How also to put a stop to cream-puff scheduling?
By contrast, although everyone in hockey bemoans the fact that there
is not enough intersectional play, viewed globally hockey has much more
than b-ball. The conferences have much more connectivity than in b-ball
and everyone knows a fair amount about everyone else. In addition, the
conferences aren't much different in strength compared to the differences
found in b-ball. Sure, the ECAC, year in year out, is *slightly*
weaker than the others, but that difference is small potatoes compared
to differences in that other sport.
So, what should the objective in a ranking system for hockey be??
I would submit that there should be only one: to measure accomplishment
by each team to date. We don't need to perform social engineering by
artificially weighting schedule and by separating schedule from win %.
We don't need to tie together widely unconnected conferences. We need
only to measure accomplishment to date.
How to do that? As I've said before, I think it is obvious that
the relationship between win% and strength of schedule needs to be
multiplicative. The problem really is what metric to use for strength of
schedule? Toward that end, I proposed the YAM -- which I will now
call the YAM1. It featured the product of win%, opp%, and o-opp% in
normalized form for convenience. I think that without a doubt that it
does a better job than RPI, but as many have pointed out, there may
be other formulations which are simply better yet.
Leaving aside what we mean by "better" at the moment, let me make
a comment about YAM1. As Ralph B. has pointed out, the terms in YAM1
can take on added or less weight through the use of exponents. In fact,
YAM1 has already done that. Multiplying opp% and o-opp% essentially gives
strength of schedule a weight of order 2!! In addition, opp% and o-opp%
have equal weight in the formulation -- and that is intuitively wrong.
O-opp% should have less weight than opp%.
Sooo ... (please no groans) ... I would like to propose another
incarnation of the YAM which perhaps satifies us more. We seek a multi-
plicative relationship between strength of schedule and win%, we want
equal weight on sched. strength and win%, and we want declining influence as
we go from opp to o-opp to o-o-opp ....
This incarnation we will call YAM2. It's simple. Strength of
schedule is 2 parts opp% added to 1 part o-opp%. I like to normalize that to
the toughest schedule measured that way -- but you don't have to. Makes
no difference. Multiply schedule strength by win% to get the final rank.
The YAM2 has features that many of us find attractive, but I should warn
you that it has even less weight on strength of schedule than YAM1. But how
does it compare to RPI-like formulations with different weights?
Last year Erik compiled an end of year RPICH in which he also included
a 50/25/25 formulation. Mike M. has been kind enough to forward the particular
post from last summer. I include that in comparisons for 93/94 and for
the last 94/95 year-to-date. In addition, since 50/25/25 does not have
the "declining influence" feature, I include a 50/33/17 ranking for comparison.
The actual numerical values of the ranking parameters have not been included
but I will do so as soon as I figue out a way to go from Excel to ascii in
a way which doesn't mess things up.
1993/1994 Year End:
RPICH YAM1 YAM2 50/33/ 50/25/ SCHOOL
1 1 1 1 1 BU
2 2 2 2 2 MI
3 3 3 3 3 HU
4 6 7 8 8 NH
5 5 6 6 6 MN
6 4 5 5 5 MA-LOWELL
7 8 8 7 7 WI
8 7 4 4 4 LSU
9 9 14 14 14 NU
10 10 9 9 10 WMU
11 13 10 10 11 RPI
12 12 12 13 13 MSU
13 11 11 11 9 CC
14 14 14 15 15 SCU
15 15 13 12 12 CU
16 16 16 16 16 NMU
1994/1995 Year-To-Date:
RPICH YAM1 YAM2 50/33/ 50/25/ School
1 1 1 1 1 ME
2 2 2 2 2 CC
3 3 3 3 3 BU
4 4 6 7 8 DU
5 6 8 9 9 MN
6 5 4 4 3 Brown
7 7 5 5 5 MI
8 8 7 6 7 MSU
9 9 9 8 6 NH
10 14 14 14 14 HU
11 10 12 12 12 NU
12 11 11 11 11 CU
13 12 10 10 10 BGSU
14 13 13 13 13 RPI
15 18 20 20 21 NDK
16 15 17 17 17 WI
I aplologize for any non-standard abreviations. What I will do is
now get off this topic for awhile, and at a couple of times during the
rest of the season present a more complete comparison. Then we can have
a good discusion on how to accurately measure accomplishment and what the
figure of merit should be. Thanks.
-- Dick Tuthill
Btw, I'm happy nobody caught me on the statement about multiplication
being associative and commutative. Meant to say associative and reflexive:-)
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