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Color statistics finally in
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NoTruces wrote
at 4:45 PM, Monday August 31, 2009 EDT
I have finally finished off the long anticipated color win percentage tabulation. Calculated from the last 100 games I was in, tracking where each players color finished, and awarding placement weightings accordingly (7 points for 1st... 1 point for 7th), here are the results:
Purple: 547 points Red: 411 points Teal (or whatever): 406 points Green: 397 points Brown: 389 points Blue: 353 point Yellow: 297 points So from the sample set, purple clearly wins more often and yellow loses more often. 100 samples is lots enough to say we have an issue in the dice distribution algorithm. |
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IIlIIIlIII wrote
at 5:24 PM, Monday August 31, 2009 EDT Purple is the royal colour.
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kam|k2 wrote
at 5:31 PM, Monday August 31, 2009 EDT well, lets ask skrum about that ;D
but seriously, serg is right? oh come on... |
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skrumgaer wrote
at 6:31 PM, Monday August 31, 2009 EDT If there is no color bias, the scores would follow a normal distribution. The standard deviation (I think) goes as the inverse of the square root of the sample size. The median scorer (green) is a tad below the mean (which would be 400); whether this is significant is hard to say. When I have time, I will try running this through an online software program available at wessa.net. With the raw percentages I could run a TAPL (Pearson's chi-square test) which would be accurate in this case because all colors have the same sample size.
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kam|k2 wrote
at 6:32 PM, Monday August 31, 2009 EDT thanks in advance skrum. (:
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skrumgaer wrote
at 7:40 PM, Monday August 31, 2009 EDT Here is the wessa.net analysis. I replicated the data 100 times. I don't know much about how to use these results since I don't use the normal distribution much. But someone else might be able to pull out the relevant test of significance.
Variability - Ungrouped Data Absolute range 250 Relative range (unbiased) 3.54753155353031 Relative range (biased) 3.55006822282372 Variance (unbiased) 4966.23748211731 Variance (biased) 4959.14285714286 Standard Deviation (unbiased) 70.4715366805444 Standard Deviation (biased) 70.4211818783444 Coefficient of Variation (unbiased) 0.176178841701361 Coefficient of Variation (biased) 0.176052954695861 Mean Squared Error (MSE versus 0) 164959.142857143 Mean Squared Error (MSE versus Mean) 4959.14285714286 Mean Absolute Deviation from Mean (MAD Mean) 46.8571428571429 Mean Absolute Deviation from Median (MAD Median) 46.4285714285714 Median Absolute Deviation from Mean 11 Median Absolute Deviation from Median 14 Mean Squared Deviation from Mean 4959.14285714286 Mean Squared Deviation from Median 4968.14285714286 Interquartile Difference (Weighted Average at Xnp) 58 Interquartile Difference (Weighted Average at X(n+1)p) 58 Interquartile Difference (Empirical Distribution Function) 58 Interquartile Difference (Empirical Distribution Function - Averaging) 58 Interquartile Difference (Empirical Distribution Function - Interpolation) 58 Interquartile Difference (Closest Observation) 58 Interquartile Difference (True Basic - Statistics Graphics Toolkit) 58 Interquartile Difference (MS Excel (old versions)) 58 Semi Interquartile Difference (Weighted Average at Xnp) 29 Semi Interquartile Difference (Weighted Average at X(n+1)p) 29 Semi Interquartile Difference (Empirical Distribution Function) 29 Semi Interquartile Difference (Empirical Distribution Function - Averaging) 29 Semi Interquartile Difference (Empirical Distribution Function - Interpolation) 29 Semi Interquartile Difference (Closest Observation) 29 Semi Interquartile Difference (True Basic - Statistics Graphics Toolkit) 29 Semi Interquartile Difference (MS Excel (old versions)) 29 Coefficient of Quartile Variation (Weighted Average at Xnp) 0.0759162303664921 Coefficient of Quartile Variation (Weighted Average at X(n+1)p) 0.0759162303664921 Coefficient of Quartile Variation (Empirical Distribution Function) 0.0759162303664921 Coefficient of Quartile Variation (Empirical Distribution Function - Averaging) 0.0759162303664921 Coefficient of Quartile Variation (Empirical Distribution Function - Interpolation) 0.0759162303664921 Coefficient of Quartile Variation (Closest Observation) 0.0759162303664921 Coefficient of Quartile Variation (True Basic - Statistics Graphics Toolkit) 0.0759162303664921 Coefficient of Quartile Variation (MS Excel (old versions)) 0.0759162303664921 Number of all Pairs of Observations 244650 Squared Differences between all Pairs of Observations 9932.47496423462 Mean Absolute Differences between all Pairs of Observations 72.1847537298181 Gini Mean Difference 72.1847537298181 Leik Measure of Dispersion 0.499461782137748 Index of Diversity 0.998527150510204 Index of Qualitative Variation 0.99995565859391 Coefficient of Dispersion 0.118028067650234 Observations 700 |
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NoTruces wrote
at 11:38 AM, Tuesday September 1, 2009 EDT skrumgaer, I understand that analysis completely. It means purple wins more often, and yellow loses more often.
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gereffi wrote
at 12:04 PM, Tuesday September 1, 2009 EDT Do it 100 more times. You'll get completely different results.
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gereffi wrote
at 12:04 PM, Tuesday September 1, 2009 EDT Do it 100 more times. You'll get completely different results.
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skrumgaer wrote
at 12:14 PM, Tuesday September 1, 2009 EDT The coefficient of dispersion (the next to the last number in the wessa.net output) is very small. This suggests under-dispersion. Which means that the results are probably not statistically significant.
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NoTruces wrote
at 12:36 PM, Tuesday September 1, 2009 EDT lol. No, it means the exact opposite and simply reflects your 100 times duplication of the data. A perfect 1/7 distribution for each color would have no dispersion.
So in summary, purple clearly wins more often and yellow loses more often, as the statistics clearly announce. |
