H4 or S5 !?

[Ajedrecista]

Hello Jesus,

I added games to the matches, so now we have:

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S1                            : 3000 (+1225,=631,-1144), 51.4 %
S2                            : 3000 (+513,=602,-1885), 27.1 %
S3                            : 3000 (+191,=405,-2404), 13.1 %
S4                            : 3000 (+ 61,=227,-2712),  5.8 %
S5                            : 3000 (+  8,=118,-2874),  2.2 %
S12                           : 3000 (+1845,=578,-577), 71.1 %
S13                           : 3000 (+2398,=353,-249), 85.8 %
S14                           : 3000 (+2608,=262,-130), 91.3 %
S15                           : 3000 (+2659,=233,-108), 92.5 %

Fitted function is:

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d^a = C*w*(1-d-w)

I get a contour plot for least squares:

And values for minimum:
a = 1.83
c = 0.40
With this many games one can safely assume:
1 win + 1 loss = 1.85 +/- 0.2 draws (this time error is 2 Standard Deviations).
BayesElo model (Rao-Kupper) is pretty much ruled out.

Can you confirm my results?
Thanks!

Thanks for adding more games. My first run produced a minimum near a = 1.828 and C ~ 0.401027888282, so I was doing things properly. Then I focused in a more limited area with more precision. I finally got more less:

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a ~ 1.8281154999999999        C ~ 0.40091678288809675      sum(errors) ~ 1.92351811018034291E-03

The minimum is close to a = 1.82812 and C ~ 0.40092. Your result is confirmed and your graph is enough telltale. Just by curiosity: with what software did you plot the contour of least squares?

Regards from Spain.

Ajedrecista.

[Laskos]

The minimum is close to a = 1.82812 and C ~ 0.40092. Your result is confirmed and your graph is enough telltale. Just by curiosity: with what software did you plot the contour of least squares?

Regards from Spain.

Ajedrecista.

Thanks Jesus. In all these computations, I used Mathematica 8.

[Ajedrecista]

Hello Kai:

Andreas' lists are superb: http://www.fastgm.de/

Fitted function for all the following cases: D^a = C*W*(1 - W - D); D = (C*W*L)^(1/a). First I run a try in a wide area of a and C, then I refine the mesh in a smaller area where the minimum error is supposed to be. My results can be wrong, of course.

http://www.fastgm.de/3.75+0.0375.html

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 1 Houdini 3         : 3215  27000 (+18341,=6310,-2349), 79.6 %
 2 Critter 1.6a      : 3125  27000 (+14174,=8799,-4027), 68.8 %
 3 Komodo CCT        : 3099  27000 (+13656,=7832,-5512), 65.1 %
 4 Bouquet 1.6       : 3074  27000 (+12068,=9007,-5925), 61.4 %
 5 Rybka 4.1         : 3056  27000 (+11625,=8388,-6987), 58.6 %
 6 Gull R375         : 2980  27000 (+8139,=8909,-9952),  46.6 %
 7 Stockfish 3       : 2970  27000 (+8019,=8221,-10760), 44.9 %
 8 Hannibal 1.3      : 2878  27000 (+4895,=7037,-15068), 31.2 %
 9 Naum 4.2          : 2823  27000 (+3646,=5798,-17556), 24.2 %
10 Protector 1.5.0   : 2781  27000 (+2689,=5195,-19116), 19.6 %

---------------------------------------------------------------

Games        : 135000 (finished)

White Wins   :  51198 (37.9 %)
Black Wins   :  46054 (34.1 %)
Draws        :  37748 (28.0 %)

White Perf.  : 51.9 %
Black Perf.  : 48.1 %

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a ~ 1.90840000000        C ~ 0.944899600000        sum(quadratic errors) ~ 1.462926347880E-02

The minimum is near a = 1.90840 and C = 0.94490.

========================

http://www.fastgm.de/15+0.15.html

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 1 Houdini 3       : 3180  27000 (+16433,=8056,-2511),  75.8 %
 2 Komodo CCT      : 3088  27000 (+12445,=9392,-5163),  63.5 %
 3 Critter 1.6a    : 3086  27000 (+11631,=10856,-4513), 63.2 %
 4 Bouquet 1.6     : 3049  27000 (+10149,=10791,-6060), 57.6 %
 5 Rybka 4.1       : 3033  27000 (+9778,=10167,-7055),  55.0 %
 6 Stockfish 3     : 3012  27000 (+8969,=9992,-8039),   51.7 %
 7 Gull R375       : 3000  27000 (+7922,=11039,-8039),  49.8 %
 8 Hannibal 1.3    : 2877  27000 (+4186,=8440,-14374),  31.1 %
 9 Naum 4.2        : 2869  27000 (+4164,=7885,-14951),  30.0 %
10 Protector 1.5.0 : 2806  27000 (+2606,=6816,-17578),  22.3 %

--------------------------------------------------------------

Games        : 135000 (finished)

White Wins   :  47628 (35.3 %)
Black Wins   :  40655 (30.1 %)
Draws        :  46717 (34.6 %)

White Perf.  : 52.6 %
Black Perf.  : 47.4 %

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a ~ 2.06098000000        C ~ 1.39071260000        sum(quadratic errors) ~ 1.885447435377E-02

The minimum is near a = 2.06098 and C = 1.39071.

========================

http://www.fastgm.de/60+0.60.html

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 1 Houdini 3         : 3159  27000 (+15165,=9303,-2532),  73.4 %
 2 Komodo CCT        : 3087  27000 (+11691,=10893,-4416), 63.5 %
 3 Critter 1.6a      : 3070  27000 (+10285,=12299,-4416), 60.9 %
 4 Bouquet 1.6       : 3031  27000 (+8586,=12453,-5961),  54.9 %
 5 Rybka 4.1         : 3022  27000 (+8686,=11516,-6798),  53.5 %
 6 Stockfish 3       : 3018  27000 (+8475,=11541,-6984),  52.8 %
 7 Gull R375         : 3001  27000 (+7336,=12370,-7294),  50.1 %
 8 Naum 4.2          : 2877  27000 (+3775,=9310,-13915),  31.2 %
 9 Hannibal 1.3      : 2876  27000 (+3592,=9573,-13835),  31.0 %
10 Protector 1.5.0   : 2859  27000 (+3262,=9036,-14702),  28.8 %

----------------------------------------------------------------

Games        : 135000 (finished)

White Wins   :  45106 (33.4 %)
Black Wins   :  35747 (26.5 %)
Draws        :  54147 (40.1 %)

White Perf.  : 53.5 %
Black Perf.  : 46.5 %

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a ~ 2.37562000000        C ~ 1.64279360000        sum(quadratic errors) ~ 2.014647717299E-02

The minimum is near a = 2.37562 and C = 1.64279.

========================

http://www.fastgm.de/240+2.40.html

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 1 Houdini 3                 : 3145  27000 (+14116,=10462,-2422), 71.7 %
 2 Komodo CCT                : 3089  27000 (+11259,=11961,-3780), 63.9 %
 3 Critter 1.6a              : 3059  27000 (+9157,=13693,-4150),  59.3 %
 4 Stockfish 3               : 3029  27000 (+8315,=12846,-5839),  54.6 %
 5 Bouquet 1.6               : 3021  27000 (+7467,=13824,-5709),  53.3 %
 6 Rybka 4.1                 : 3015  27000 (+7650,=12948,-6402),  52.3 %
 7 Gull R375                 : 2996  27000 (+6387,=13833,-6780),  49.3 %
 8 Naum 4.2                  : 2891  27000 (+3495,=10914,-12591), 33.2 %
 9 Hannibal 1.3              : 2882  27000 (+3288,=10643,-13069), 31.9 %
10 Protector 1.5.0           : 2873  27000 (+3149,=10310,-13541), 30.8 %

------------------------------------------------------------------------

Games        : 135000 (finished)

White Wins   :  42061 (31.2 %)
Black Wins   :  32222 (23.9 %)
Draws        :  60717 (45.0 %)

White Perf.  : 53.6 %
Black Perf.  : 46.4 %

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a ~ 3.23664000000        C ~ 1.28742040000        sum(quadratic errors) ~ 2.445504168462E-02

The minimum is near a = 3.23664 and C = 1.28742.

This result surprises me because I think I copied the correct numbers. The minimum quadratic error has grown with increasing time controls (with higher draw ratios), the same as the value of a.

========================

This list has 51 points with 11500 games each point, but I will not fit it.

I do not want to hijack Ingo's thread (thanks for your patience), so I think it is better to stop posting these things here.

Regards from Spain.

Ajedrecista.

[Laskos]

Thanks, Jesus. The only snag with these matches is that the Elo span is not that large, the points on the far tails are important too.

[Laskos]

Thanks, Jesus. The only snag with these matches is that the Elo span is not that large, the points on the far tails are important too.

I performed a test on 1500 Elo span, instead of 300-500 Elo span in your samples from Fastgm. I think that is more reliable. Now the engines are:
Anchor, SF depth = 6
Komodo, from depth=1 to depth=10.

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K1                            : 1000 (+986,= 12,-  2), 99.2 %
K2                            : 1000 (+930,= 60,- 10), 96.0 %
K3                            : 1000 (+837,= 95,- 68), 88.4 %
K4                            : 1000 (+663,=215,-122), 77.0 %
K5                            : 1000 (+488,=207,-305), 59.2 %
K6                            : 1000 (+192,=248,-560), 31.6 %
K7                            : 1000 (+ 84,=168,-748), 16.8 %
K8                            : 1000 (+ 18,=108,-874),  7.2 %
K9                            : 1000 (+ 14,= 46,-940),  3.7 %
K10                           : 1000 (+  2,= 26,-972),  1.5 %

Fitted function is:

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d^a = C*w*(1-d-w)

I get a contour plot for least squares:

And values for minimum:
a = 1.955
C = 0.426
This is again compatible with:
1 win + 1 loss = 2 draws
BayesElo model (Rao-Kupper) is pretty much ruled out. So, Use Ordo.