Author: Dann Corbit
Date: 13:26:51 10/27/99
Go up one level in this thread
On October 27, 1999 at 15:02:01, James B. Shearer wrote: [snip] > This is just wrong. > First you ignored the point of Hyatts post. The Elo system assumes >ratings are real numbers but on ICC they are rounded to the nearest integer. >This introduces a bias particularly for opponents with very different ratings. >Suppose for example you are playing someone 800 points below you. Suppose you >should be getting .4 rating points for every win and losing 31.6 rating points >for every loss, 15.6 rating points for every draw (these are not the actual >exact values). However because ICC rounds ratings to the nearest integer you >will in fact gain 0 points for a win and lose 32 points for a loss, 16 points >for a draw. So in effect you are unjustly losing .4 rating points every time >you play this guy. In such a case, the rating system is broken, and you should simply noplay people who are so far under that you can't win points (if you are concerned about rating, that is). > Second you are ignoring the fact that the ELO system is based on a >model of chess strength which is just an approximation of reality. For example >the ELO system predicts that if A beats B 2/3 of the time and if B beats C 2/3 >of the time then A will beat C 4/5 of the time. There is no theoretical reason >for this to be the case, it is just an empirical approximation. You could use a >model which predicted A would beat C 3/4 of the time or 5/6 of the time and >derive a different rating system based on it. To the extent that a win >probability model differs from reality a rating system based on it will have >systematic anomalies where the actual win probability for certain rating >differences differs from the predicted win probability since it will be >impossible to get the win probabilities right for all rating differences. These >anomalies are likely to be particularly apparent at large rating differences >since the ratings will adjust to try to get the common (fairly small rating >difference) cases more nearly correct at the expense of the rare cases. If the model is broken, then it is broken for the real players in real tournaments. The fact is that win expectency is very close to reality in the long run. In any case, if it is broken, it is broken everywhere, so it at least has the same meaning.
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