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Re: RE: Réf. : [Bug-gnubg] Understanding the stats

From: Massimiliano . Maini
Subject: Re: RE: Réf. : [Bug-gnubg] Understanding the stats
Date: Fri, 22 Sep 2006 17:27:22 +0200

>The way I read the results below, Opponent won 3 points, but if
>he hadn't been so lucky he'd "only" have won 1.958 points. However,
>he is still coming out ahead, which means that he must have more
>net skill. However, the error analysis says Opponent was a worse player.

I think that the reason is simply that the luck adjusted results do not
take into account the error rate: it adjusts the actual result
according *only* to luck.

Only combining luck and error rate adjustment one could define an
advantage that *always* behave as expected (I've been luckier playing
then my edge is negative).

I don't know how Snowie computes a player's advantage, but I suppose that
depends only on the error rate (and not on the luck). And at the moment
there's no such a thing in gnubg (the closest thing is the FIBS rating
difference, depending only on the error rates and for match only).

BTW, notice that the stats said :

>Advantage (actual) in ppg          +0.4286        - 0.4286
>95% confidence interval (ppg)       3.1388          3.1388
>Advantage (luck adjusted) in ppg   +0.2797        - 0.2797
>95% confidence interval (ppg)       0.9709          0.9709

The 95% confidence intervals are wider that the ansolute values of the
advantages (actual and luck adjusted) ... the session was not long
enough to correctly estimate the advantage purely on luck.

If you play a looooong session, luck will cancel out and the luck
adjusted advantage will be equal to the actual advantage (itself
supposed to be a good estimation of your real advantage, since the
session was loooooong).

The only thing that luck adjustement does is the following : in a
"short" session, the luck adjusted advantage is closer to the real
advantage compared to the actual advantage.
Notice that that's true in Albert's case: assuming he his a better
player than his opponent, the luck adjusted advantage (+0.2797) is
closer to a negative number than the actual advantage (+0.4286) is.

Now you shoud adjust the luck adjusted advantage according to the
error rates ... could it be as easy as subtracting the error rate
(per game) from that ?

At least, that's my understanding of the thing.


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