Andew Brecher says:
 
> Anything that just factors in "strength of schedule" (like RPI and
> associates) won't distinguish between winning or losing to good teams,
> winning or losing to bad teams.  My 'ideal' would factor that in.
 
Andrew's 'ideal' isn't any better than RPICH.
Suppose we win a game and lose a game.
 
Case 1: We lose to a great team and we beat a crummy team. Andrew would say
we don't get penalized very much for losing to a great team, but we also
don't get rewarded very much for beating the crummy team. Net result: It's a
wash and we wind up with a middle-of-the-road rating.
 
Case 2: We lose to the crummy team and beat the great team. Andrew would say
we get lots of points for beating the great team, but you lose lots of points
for losing to the crummy team.  Net result: It's a wash and we wind up with a
middle-of-the-road rating.
 
RPICH (or anything else) says you have a .500 record against (on average)
.500 opponents, so you're a mediocre, middle-of-the-road team.
 
In the end, Andrew's simply-expressed 'ideal' results in essentially the same
kind of rating we already have.
 
The problem is that first order statistics can't distinguish between the
above two
cases. The difference is really in the second order statistics, where a
variance would give a measure of how volatile the two teams are. (The team in
case 2 is much more volatile than the one in case 1.)
 
And then we could all argue about whether volatility is good or bad, instead
of just about whether Princeton cheats or RPI's band is too rude :-)
 
Bob Stagat
RPI '64 & '68