- Feb 25, 2004******************************************************************

DeanO wrote:

1. A Kalman Filter can be used to estimate an offensive ability, a

defensive ability, and an overall rank at the same time -- something

that Sagarin does, Massey does, etc. for the BCS. It basically

estimates how many points an offense should score against some

defense, then readjusts based on the actual results of the game. It

does the same for the defense, then defines power by offense minus

defense or divided by or whatever. (What defines the method as a

Kalman filter is a certain use of different stats. My guess is that

none of these guys use a Kalman filter exactly, but they do

continuously estimate and re-estimate -- they use "filters.")

I think something more like this was done because of some of the

things that were reported about WINVAL -- that they get offensive and

defensive rankings for all players, plus the overall number you have.

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DanR replies:

I have figured out how I can break out offensive and defensive

rating separately (and add in pace), so I don't think this is a

distinguishing feature between what I am doing and what

Sagarin/Massey is doing. I have hesitated in doing this, because it

is not completely straightforward how to come up with standard

errors for these separate offensive and defensive ratings -

something which I suspect Sagarin and Massery don't worry about

doing.

This method of estimating and then "readjusting" is exactly what I

think filters are most applicable for, i.e. cases where re-

estimating the model over in its entirety is too time consuming.

(Those are the examples always mentioned in the Kalman filter

literature that you pointed me to.)

However, in this case it only take six seconds to completely re-

estimate the model from scratch, so there doesn't appear to be a

need to use a filter whose main advantage relative to OLS is that it

can get estimates in a fraction of the time it takes OLS.

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DeanO wrote:

Whether it's most "efficient," (an economist's term) I dunno. I know

that there are references that describe the Kalman as "the optimal

linear filter." Basically, my sense is that both regression and

Kalman Filters use variances to optimize their estimates. The Kalman

does it assuming one model of interaction between the offense and the

defense, estimating both the offense and defense. Regression does it

without the interaction modeled, just viewing the point difference as

The Result and I don't think it can easily back out estimates of

offense and defense. There are advantages to both. I personally do

think that the model of interaction between offense and defense in

most filters is not right (doesn't adequately account for garbage

time), but estimating offensive and defensive ability is important.

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DanR replies:

"Efficiency" is commonly referred to in economics, but I was using

it in the statistical sense.

http://www.ruf.rice.edu/~lane/hyperstat/A12977.html

Yes, I have seen the Kalman filter referred to as an

optimal "filter," but OLS is not a filter per se, so that is not

comparing to OLS.

Now in doing a little more reading, there are times where the Kalman

Filter may be more efficient than OLS, but these are generally cases

where we assume that the beta estimates are time-varying or that

there is some form of serial correlation in the errors. These both

would be sensible (but hard to implement) assumptions in this case,

but as far as I can tell, you are not proposing implementing either

of these assumptions.

So other than lower computational costs, I cannot see the advantage

of the Kalman Filter in this application. But I have been wrong

before, and certainly could be wrong here.

The OLS model that I use fully accounts for the interaction between

offense and defense without really specifying a particular

functional form. And again, I can estimate separate offensive and

defensive ratings, but I am not sure I can get credible estimates of

the standard errors for these without resorting to something like

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