Author: Bruce Moreland
Date: 10:39:30 12/25/00
Go up one level in this thread
On December 25, 2000 at 10:08:44, Amir Ban wrote: >Chess games are not random events. > >You failed to do the math: 3.5-0.5 *is* significant, with about 95% confidence. Interesting issue. The odds of getting 3.5-0.5 between two equal players changes depending upon the draw percentage, and this change is more than you might think. I wrote a program that figures out the percentage chance of outcomes of short matches. If you have two equal players A and B, the odds that B will avoid this outcome by scoring at least one point vary depending upon draw percentage: Draw% %chance to avoid 100% 100.00% 98% 100.00% 96% 100.00% 94% 99.99% 92% 99.98% 90% 99.95% 88% 99.92% 86% 99.88% 84% 99.82% 82% 99.75% 80% 99.67% 78% 99.57% 76% 99.45% 74% 99.32% 72% 99.17% 70% 99.00% 68% 98.82% 66% 98.62% 64% 98.40% 62% 98.17% 60% 97.92% 58% 97.66% 56% 97.38% 54% 97.09% 52% 96.79% 50% 96.48% 48% 96.17% 46% 99.47% 44% 95.52% 42% 95.20% 40% 94.87% 38% 94.55% 36% 94.23% 34% 93.93% 32% 93.63% 30% 93.35% 28% 93.09% 26% 92.86% 24% 92.65% 22% 92.47% 20% 92.32% 18% 92.21% 16% 92.15% 14% 92.13% 12% 92.16% 10% 92.25% 8% 92.41% 6% 92.63% 4% 92.92% 2% 93.29% 0% 93.75% If draw percentage is about 14%, there seems to be the highest chance that this outcome will be avoided, whereas if draw percentage is 90%, it's almost certain that this outcome can't happen if the two players really are equal. I have never seen this accounted for when people cite statistics regarding outcomes of chess matches. But your first sentence can't be dismissed either. Imagine a hockey team is losing 2-0. There is a good chance they will lose 3-0, since they may pull their goalie in the final moments of play. A team that doesn't do this, and loses 2-0, is not better than one that does, and loses 3-0. The same issues are present in these matches, since the games are not random events, they are connected segments of a larger event. Shirov lost a game. He had to win one to make up for this, so he went for it and lost another one. I'm also ignoring differences in win percentage with white and black, which is probably a big deal, considering how much attention these players seem to pay to it. >I noticed another statistic which *is* significant: It's always the bad results >that are not significant. The good ones are accepted without question. I don't know or care which is better, so I'm not arguing anything based upon that. I just think the math is interesting. bruce > >Amir
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