Author: Andrew Dados
Date: 06:42:06 02/05/01
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On February 04, 2001 at 13:58:11, Andrew Dados wrote: > >I decided to find out 'true chance' of draw outcome from real games. >The below is summarized output from my twic game files. >Rdiff means difference of players ratings in the (range, range+25). >Integrestingly around range of 0 draws approaches 50% and better won about 25%. > >Now if you take 2 tosses of coin you'll get total score of 2 heads in 25%, 1 >head in 50% and 0 heads in 25%... > > > files: 176 games: 170464 decisive (counted) : 128803 > >Rdiff+ games %draws %better won >======================================= >0 14480 48.82 25.67 >25 15365 46.57 31.45 >50 15784 44.60 35.52 >75 15429 41.80 39.62 >100 14092 38.68 44.26 >125 12121 35.08 49.18 >150 9926 31.92 54.47 >175 8129 28.34 58.89 >200 6478 25.39 63.71 >225 4707 22.82 67.94 >250 3443 20.65 69.82 >275 2575 18.45 73.67 >300 1879 15.59 77.38 >325 1370 15.62 78.83 >350 970 10.52 85.46 >375 687 9.32 86.90 >400 453 7.06 89.18 > >Is one chess game statistically equivalent of 2 coin tosses? :) > >-Andrew- Since Vincent and Hermano raised valid point about expected different draw distribution among different strength of players, I post a re-run... While I wanted to provide tables down to 400 elo difference I decided to simply divide my small pgn sample in 2 with regard to 'average game rating'. Hi_won and Lo_won are respectively wins for higher and lower rated. Expected %score is practical achieved score (which according to rating system should not depend upon players ratings). Rdiff is difference of opponents ratings. 1) Data for games where average combined (R_white+R_black)/2 rating is 2400+ : ========================================================== files: 176 games: 170464 counted: 59172 Avg rating: 2500.76 Total draws %: 44.64 Rdiff games %draws Hi_won Lo_won | Expected %score ======================================= 0 8329 55.31 23.26 21.43 | 50.91 25 8745 53.06 28.03 18.91 | 54.56 50 8699 50.34 32.64 17.02 | 57.81 75 7989 47.90 36.48 15.62 | 60.43 100 6712 44.80 41.15 14.05 | 63.55 125 5282 40.57 47.03 12.40 | 67.31 150 3863 35.78 52.58 11.65 | 70.46 175 2976 31.42 57.73 10.85 | 73.44 200 2262 28.47 62.78 8.75 | 77.01 225 1427 24.60 67.90 7.50 | 80.20 250 951 20.08 72.13 7.78 | 82.18 275 665 18.35 76.69 4.96 | 85.86 300 427 16.63 76.58 6.79 | 84.89 325 302 14.57 79.47 5.96 | 86.75 350 203 12.32 85.71 1.97 | 91.87 375 112 13.39 83.04 3.57 | 89.73 400 61 9.84 85.25 4.92 | 90.16 2) Data for games where average combined rating is below 2400 : ========================================================== files: 176 games: 170464 counted: 69227 Avg player: 2278.28 Total draws %: 30.36 Rdiff games %draws Hi_won Lo_won | Expected %score ======================================= 0 6105 39.89 31.47 28.65 | 51.41 25 6594 37.99 35.99 26.02 | 54.98 50 7032 37.47 39.12 23.41 | 57.86 75 7393 35.20 42.99 21.82 | 60.58 100 7336 33.04 47.18 19.78 | 63.70 125 6817 30.81 50.86 18.34 | 66.26 150 6017 29.47 55.66 14.87 | 70.39 175 5139 26.52 59.60 13.87 | 72.86 200 4169 23.72 64.21 12.07 | 76.07 225 3269 22.09 67.94 9.97 | 78.98 250 2471 20.84 68.88 10.28 | 79.30 275 1904 18.49 72.58 8.93 | 81.83 300 1445 15.36 77.58 7.06 | 85.26 325 1062 15.91 78.63 5.46 | 86.58 350 763 10.09 85.45 4.46 | 90.50 375 575 8.52 87.65 3.83 | 91.91 400 390 6.67 89.74 3.59 | 93.08 Indeed there is huge difference in draw distributions... and very little in expected score. Note that around difference of 250 elo draw % converges. More games needed... -Andrew-
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