Author: Dieter Buerssner

Date: 09:23:00 01/07/04

Go up one level in this thread

On January 06, 2004 at 19:03:58, Peter Fendrich wrote: >On January 06, 2004 at 14:03:05, Dieter Buerssner wrote: > >>On January 05, 2004 at 18:11:25, Peter Fendrich wrote: >> >>>The rest is basic formulas for >>>the standard deviation. >> >>Actually, I am puzzled about these basic formulas for the standard deviation. >>Somehow I don't get it (in German, ich vermute, ich sitze auf der Leitung). In between, I got it. But still not yet for the case below. >>However, the function m vs. p(m) looks different, when I assume different w/d/l >>probabilities for white and black. So, we not only have W, D, L, but wW, wD, wL, >>bW, bD, bL and say nb, nw, mb, mw (typically nb=nw). Can you also give a formula >>for this scenario for s? >I'm sorry I've been quite busy today and will be for a while. There is no need to hurry. Also, it is not that important. I am just curios. >I must confess that I didn't study your examples carefully enough. >Anyway I'm not sure what you're after with the variables above. The variance in >the sample is what it is and is computed as I told before. In order to estimate >the standard deviation of the population and to use preknown distribution of >W/D/L you are into the Bayesian thing. Is this what you want? Perhaps I can myself clearer by another example. Assume again the 1000 games, W=510, D=0, L=490. Player a wins as white 255 games and as black 255 games. With your forumula we get for the result 0.51 +/- 0.01586 (67% margin). If I simualtate this match (1 million such matches), and plot p(m) vs. m, and I fit a curve 1/(sqrt(2*pi)*sigma*n)*exp(-0.5*(x-x0)^2/sigma^2) (I kept n constant at 1000, because the integral must be 1/1000), I get sigma=0.01581. As we can expect, practically the same number as calculated by your formula. But now assume Player A won all his games with white, and additionally 20 games with black. No draws. Again m=0.51. W/D/L the same as above. But we can already assume now (we know more about the match than just W/D/L), that here player a is most probably better (very similar to the W/D/L 20/980/0 case). The game might be a game, where typically white wins, and only when he does a sublte fault will lose. Player A showed, that he was clearly better, because he allowed B not a single win with black. The distribution of m will be much narrower. Actually, the fit yields sigma=3.1e-3 (although now - again not too surprisingly - the distribution is slightly tilted from the normal distribution; I did not try to do the mathematics, but I guess, it is a binominal distribution). This also shows, that player A ist stronger with big confidence. Your formula would not give an adequate error margin in this case, because it ignores the more detailled knowledge about performance as white and black. >Maybe we can continue by email - I will send you one when things are calmed down >here... No problem with me, to disuss it in email. I just thought, I post an followup here, and try to explain it a bit clearer. Perhaps, we are not the only 2 persons interested. >I did put your examples into my formulas and got slightly different Rating-Dif's >than you have. Maybe it's just decimal errors. Indeed, I had a few rounding error. I wrote down some intermediate results, rounded them (including one error I made in the last digit). And even more embarrassing, I did some circular calculation (from m to Elo and back, and did not recognize, that what came back was not exactly the same to what was put in) >I also used another formula than >you did. I guess, you are referring to the Elo calculations. I think, the Elo just complicates things, without giving more insight. I only used it, to be able to compare the numbers with elostat. Otherwise, your A (or without the factor 1.96 for the 95%, as in the examples above) should be enough. Regards, Dieter

- Re: A question about statistics...
**Peter Fendrich***05:53:58 01/09/04*- Re: A question about statistics...
**Dieter Buerssner***10:26:17 01/09/04*- Re: A question about statistics...
**Peter Fendrich***05:05:34 01/12/04*

- Re: A question about statistics...

- Re: A question about statistics...

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