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Unread 17-05-2015, 11:12
Oblarg Oblarg is offline
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Re: "standard error" of OPR values

Quote:
Originally Posted by wgardner View Post
That would be different, I think. N is match noise and an m x 1 vector. If I understand your equation correctly, O would be the OPR random variable with mean of the "actual" OPR and some variance, but O is t x 1 and not m x 1, so I don't think they're the same. And the noise that the regression is computing is truly the noise to be expected in each match outcome, not the noise in the OPR estimates themselves. Or am I misunderstanding what you're saying?
We need to distinguish, in our notation, between our model our measurements.

What I'm saying is that our model is that M = AO, where M and O are both vectors whose elements are random variables. Writing O as a vector of flat means and adding a noise vector N doesn't really gain you anything - in our underlying model, the *teams* have fundamental variances, not the matches. The match variances can be computed from the variances of each team's O variable.

Now, we have the problem that we cannot directly measure the variance of each element of O, because the only residuals we can measure are total for each match (the elements of the "noise vector" N). However, we can do another linear least-squares fit to assign estimated variance values for each team, which I believe is precisely what your solution ends up doing.
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Last edited by Oblarg : 17-05-2015 at 11:17.
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