How the Other Rating Systems Screw Up Strength of Schedule

Well, austigers on twoplustwo forums asked
why the strength of schedules I give differ
from sagarin and other methods when I use
sagarin heavily for inputs....

My response must've been good, because
NebraskaSucks from phog.net hunted it down
on a poker forum to post it to the phog.net.

Hence, I'll repost it here
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Sagarin and most other rating systems screw
up strentgh of schedule

they'll often just do an arithmetic or
geometric mean of the rankings of all
opponents played

that doesn't work when trying to evaluate
how tough it is to win a game

for instance, a home favortie of 21.5 has
won 94.7% of their games from 1993 to
2006 while a home favorite of 27.5 has
won 97.5%. That isn't much difference
for 6 points. However, a home favorite of
3 has won 54.5% of their games while a
home favorite of 9 has won 74.1% of the
time. That difference is huge. Here,
almost all rating systems just look at the
opponent being 6 points different. A
team that played the 21.5 and 9 point
favorite would be getting just as much
credit as the team playing as a 27.5 and 3
point favorite. However, it was much,
much, much more difficult for the latter
team to win both games.

In summary, all the strength of schedules
I've seen publicized fail because they do
not account for the non-linearity of win/
loss pcts in relation to the ranking of the
opponent.

I use the same inputs as sagarin, but feel
it's a much better methodology for getting
the output.

The other methods fail Kansas due to
Kansas playing some really bad squads...
so bad that I gave Kansas an outright 100%
chance to win some games instead of
capping at 99%. However, there shouldn't
be a huge difference due to Kansas playing
a 100% gimme like SE Louisiana and
Arizona St playing SDST at home (a game
they over 97% of the time). Yet, ASU is
getting credit for playing the #100 overall
(#73 predictor) team while Kansas gets
credit for #203 overall (#186 predictor).
When the schedules are weighted, that will
plummet Kansas even though the onfield
win/loss difference is minimal.

Kansas has had the toughest schedule of
the undefeated so far because they have
played @ K St, @ Colorado, and @ Texas
A&M...all of which are very losable games
even for a #5 team.


This idea had buzzed around my head for
a long time, but I finally broke through
conceptualizing it when I read the
coltonindex criticism of the rpi in college
basketball. The rpi is a sham that has teams
gaming the system to secure automatic
wins from teams rated 130 instead of 270.
The same phenomena is showing up in
college football only the football teams
haven't really thought of 'gaming' the
system yet.