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Advantage for White; Bayeselo (to Rémi Coulom)
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Rémi Coulom



Joined: 24 Apr 2006
Posts: 350
PostPost subject: Re: Advantage for White; Bayeselo (to Rémi Coulom)    Posted: Sun Mar 04, 2012 3:52 pm Reply to topic Reply with quote
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
Advantage for White; Bayeselo (to Rémi Coulom) Edmund Moshammer Sat Mar 03, 2012 11:22 pm
      Re: Advantage for White; Bayeselo (to Rémi Coulom) H.G.Muller Sun Mar 04, 2012 6:56 am
            Re: Advantage for White; Bayeselo (to Rémi Coulom) Edmund Moshammer Sun Mar 04, 2012 8:49 am
                  Re: Advantage for White; Bayeselo (to Rémi Coulom) H.G.Muller Sun Mar 04, 2012 10:44 am
                        Re: Advantage for White; Bayeselo (to Rémi Coulom) Lucas Braesch Sun Mar 04, 2012 11:06 am
                              Re: Advantage for White; Bayeselo (to Rémi Coulom) H.G.Muller Sun Mar 04, 2012 11:29 am
                        Re: Advantage for White; Bayeselo (to Rémi Coulom) Edmund Moshammer Sun Mar 04, 2012 2:42 pm
                              Re: Advantage for White; Bayeselo (to Rémi Coulom) Edmund Moshammer Sun Mar 04, 2012 2:52 pm
                              Re: Advantage for White; Bayeselo (to Rémi Coulom) H.G.Muller Sun Mar 04, 2012 3:26 pm
                                    Re: Advantage for White; Bayeselo (to Rémi Coulom) Edmund Moshammer Sun Mar 04, 2012 4:13 pm
                                          Re: Advantage for White; Bayeselo (to Rémi Coulom) H.G.Muller Sun Mar 04, 2012 4:33 pm
                                                Re: Advantage for White; Bayeselo (to Rémi Coulom) Edmund Moshammer Sun Mar 04, 2012 5:18 pm
                                    Re: Advantage for White; Bayeselo (to Rémi Coulom) Adam Hair Sat Jun 30, 2012 11:00 pm
                                          Re: Advantage for White; Bayeselo (to Rémi Coulom) Adam Hair Mon Jul 02, 2012 1:25 pm
                              Re: Advantage for White; Bayeselo (to Rémi Coulom) Adam Hair Sun Jul 01, 2012 3:48 am
                                    Re: Advantage for White; Bayeselo (to Rémi Coulom) Adam Hair Sun Jul 01, 2012 8:47 pm
                                          Re: Advantage for White; Bayeselo (to Rémi Coulom) Edmund Moshammer Sun Jul 01, 2012 9:55 pm
                                                Re: Advantage for White; Bayeselo (to Rémi Coulom) Adam Hair Mon Jul 02, 2012 12:37 am
                                                      Re: Advantage for White; Bayeselo (to Rémi Coulom) Adam Hair Mon Jul 02, 2012 1:27 pm
                        Re: Advantage for White; Bayeselo (to Rémi Coulom) Marco Costalba Sun Jul 01, 2012 7:17 am
      Re: Advantage for White; Bayeselo (to Rémi Coulom) Lucas Braesch Sun Mar 04, 2012 8:53 am
      Re: Advantage for White; Bayeselo (to Rémi Coulom) Daniel Shawul Sun Mar 04, 2012 12:01 pm
      Re: Advantage for White; Bayeselo (to Rémi Coulom) Rémi Coulom Sun Mar 04, 2012 1:29 pm
            Re: Advantage for White; Bayeselo (to Rémi Coulom) 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
                        Re: Advantage for White; Bayeselo (to Rémi Coulom) H.G.Muller Sun Mar 04, 2012 4:12 pm
                              Re: Advantage for White; Bayeselo (to Rémi Coulom) Rémi Coulom Sun Mar 04, 2012 5:13 pm
                                    Re: Advantage for White; Bayeselo (to Rémi Coulom) H.G.Muller Sun Mar 04, 2012 5:27 pm
                                          Re: Advantage for White; Bayeselo (to Rémi Coulom) Rémi Coulom Sun Mar 04, 2012 5:32 pm
      Re: Advantage for White; Bayeselo (to Rémi Coulom) Daniel Shawul Wed Sep 12, 2012 12:18 am
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