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Rémi Coulom

Joined: 24 Apr 2006
Posts: 350

Post subject: Re: Advantage for White; Bayeselo (to Rémi Coulom)    Posted: Sun Mar 04, 2012 3:52 pm

hgm wrote:
 Rémi Coulom wrote: If the frequency does not match the model, then it is a sign that the model is bad. But if it does match the model, it does not mean that the model is good, because the ratings were computed with the model in the first place.

I am not sure I buy that. The number of games is so large, that splitting the data set in two and derive ratings from that would not give significantly different predictions for the ratings. And the other half of the data set would be good enough to define the empirical curve using those derived ratings.

If these empirical frequencies then match the model prediction, the model is by definition perfect. Because that was all the model was supposed to do: derive ratings that could be used to accurately predict frequencies.

It is not so obvious.

Imagine the extreme case where the model consists in saying that all the players have the same rating, and there is a given probability of winning and drawing. You can make this model fit the data perfectly. But its predictions are not good.

So your definition of "perfect" may make sense, but "perfect" in the sense of being unbiased is not "perfect" in the sense of making the best possible predictions.

For instance, we could imagine multi-dimensional models that make much better predictions than a "perfect" one-dimensional model.

Even for one-dimensional models, I can imagine distributions of player ratings that have no bias in predicting the winning frequency, but produce poor predictions.

Rémi
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Subject Author Date/Time
Edmund Moshammer Sat Mar 03, 2012 11:22 pm
H.G.Muller Sun Mar 04, 2012 6:56 am
Edmund Moshammer Sun Mar 04, 2012 8:49 am
H.G.Muller Sun Mar 04, 2012 10:44 am
Lucas Braesch Sun Mar 04, 2012 11:06 am
H.G.Muller Sun Mar 04, 2012 11:29 am
Edmund Moshammer Sun Mar 04, 2012 2:42 pm
Edmund Moshammer Sun Mar 04, 2012 2:52 pm
H.G.Muller Sun Mar 04, 2012 3:26 pm
Edmund Moshammer Sun Mar 04, 2012 4:13 pm
H.G.Muller Sun Mar 04, 2012 4:33 pm
Edmund Moshammer Sun Mar 04, 2012 5:18 pm
Adam Hair Sat Jun 30, 2012 11:00 pm
Adam Hair Mon Jul 02, 2012 1:25 pm
Adam Hair Sun Jul 01, 2012 3:48 am
Adam Hair Sun Jul 01, 2012 8:47 pm
Edmund Moshammer Sun Jul 01, 2012 9:55 pm
Adam Hair Mon Jul 02, 2012 12:37 am
Adam Hair Mon Jul 02, 2012 1:27 pm
Marco Costalba Sun Jul 01, 2012 7:17 am
Lucas Braesch Sun Mar 04, 2012 8:53 am
Daniel Shawul Sun Mar 04, 2012 12:01 pm
Rémi Coulom Sun Mar 04, 2012 1:29 pm
H.G.Muller Sun Mar 04, 2012 2:20 pm
Re: Advantage for White; Bayeselo (to Rémi Coulom) Rémi Coulom Sun Mar 04, 2012 3:52 pm
H.G.Muller Sun Mar 04, 2012 4:12 pm
Rémi Coulom Sun Mar 04, 2012 5:13 pm
H.G.Muller Sun Mar 04, 2012 5:27 pm
Rémi Coulom Sun Mar 04, 2012 5:32 pm
Daniel Shawul Wed Sep 12, 2012 12:18 am

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