Quote:
Originally Posted by wgardner
Here's a generalized perspective.
Let's say you pick r1, r2, r3, b1, b2, b3 to minimize the following error
E(w)= w*[ (R-B) - ( (r1+r2+r3)-(b1+b2+b3) ) ]^2 + (1-w) * [ (R-(r1+r2+r3))^2 + (B- (b1+b2+b3))^2]
if w=1, you're computing the WMPR solution (or any of the set of WMPR solutions with unspecified mean).
if w=0, you're computing the OPR solution.
if w=1-small epsilon, you're computing the nWMPR solution (as the relative values will be the WMPR but the mean will be selected to minimize the second part of the error, which will be the mean score in the tournament).
if w=0.5, you're computing the EPR solution.
I wonder how the various predictions of winning margin, score, and match outcomes are as w goes from 0 to 1?
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This is a very cool way of looking at it. By putting it this way, EPR seems to be half way between OPR and WMPR.
Again, I like it because it is one number instead of two numbers. I like it because it has a better chance to predict outcome regardless of the game, rather than OPR being good for some games and WMPR being good for some other games.