Me:

>> On my ranking comparison page (see link above) I've also added a
>> "strength of schedule" table to compare the SOS measures used by KRACH
>> and RPI; note that Minnesota's schedule is 6th toughest in the country
>> and SCSU's 8th by KRACH's standards, but RPI's SOS measure has them at
>> 23rd and 42nd, respectively.

>> I think what this means is that Minnesota and St. Cloud have teams on
>> their schedules with losing records against tough opponents.  (E.g.,
>> Alaska-Anchorage, who play the toughest schedule in the country by
>> either standard.)

Craig Powers:

> Both Minnesota and St. Cloud have played games against Bemidji State,
> who I believe currently have the worst winning pct. in D1 (though by
> KRACH at least Bentley was the worst team last I looked).  It doesn't
> matter much to KRACH, because both teams won those games, but the SofS
> in RPI doesn't care what kind of result the teams had in those games.

> About the only way to get around those games is the way KRACH does -
> discount them heavily in their effect of SofS if they're won and only
> make them a factor if they're lost or tied (any sort of mean that's not
> weighted by results rather than games played will otherwise be
> affected).

Actually, KRACH does *not* directly take the outcomes of individual
games into account when reckoning strength of schedule.  For example,
Quinnipiac beat Union, Union beat Cornell, and Cornell tied
Quinnipiac.  If you change those three results so that Union tied both
Quinnipiac and Cornell, and Quinnipiac beat Cornell, you would get
*exactly* the same set of KRACH ratings.  The effect you're thinking
of is that if you play a much weaker team, your KRACH goes up a little
if you beat them and down a lot if you lose to them.  The contribution
to your strength of schedule is basically the same either way, but if
you win, the reduction in SOS is always offset by the improvement in
your record, while if you lose, your SOS and your record both go down.

The relevant property in this context is that winning a game should
never lower your KRACH rating, while it can lower your RPI.  When
Bemidji State had lost all of their games, and had a 0 KRACH rating,
wins against them had no effect on anyone's KRACH, since according to
the ratings a victory was a sure thing.  On the other hand, with a
.000 contribution to opponents' winning percentage, playing Bemidji
State was guaranteed to lower the RPI of any team with an RPI above
.500.  This effect was more pronounced with the old 25-50-25 weighting
in the definition of RPI and presumably led to the current 35-50-15
division.
                                          John Whelan, Cornell '91
                                                 [log in to unmask]
                                     http://www.amurgsval.org/joe/

Consider the alternative: http://slack.net/~whelan/cgi-bin/tbrw.cgi?kpairwise