Author: Graham Laight
Date: 07:32:18 05/15/01
Go up one level in this thread
On May 15, 2001 at 09:49:24, Robert Hyatt wrote: >On May 15, 2001 at 07:56:49, Graham Laight wrote: > >>On May 15, 2001 at 06:26:14, Ralf Elvsén wrote: >> >>>On May 15, 2001 at 06:03:11, Graham Laight wrote: >>> >>>I still say it's quicker and easier to draw a graph of strength of players >>>plotted against proportion of draws. >>> >>>Since I don't have a copy of chessbase, the graph below is based on guesswork >>>rather than actual study - but here's a quick example of what it would probably >>>look like: >>> >>>Percentage Of Draws >>> >>> >>>100 | * >>> | * >>> | * >>> | * >>> | * >>>75 | * >>> | * >>> | * >>> | * >>> | * >>>50 | * >>> | * >>> | * >>> | * >>> | * >>>25 | * >>> |* >>> | >>> | >>> | >>>0 | >>> ------------------------------------------------------ >>> 1000 1500 2000 2500 3000 3500 >>> >>> Elo Rating >>> >>> >> >>Check out this: >> >>http://math.bu.edu/people/mg/ratings/Draws.jpg >> >> >>Ralf, >> >>Thanks very much for drawing this work to my attention! >> >>Since it's done by the chairman of the USCF (home page = >>http://math.bu.edu/people/mg/ ), I think we can assume that it's a good quality >>study. >> >>The exciting thing (from the point of view of "solving chess" or "playing >>perfect chess") point of view is that, above 2200 Elo, the proportion of draws >>shoots up very sharply above 2200 Elo - implying that the limits of chess are >>being approached quite rapidly now. >> >>Just to describe the graph (which you can see for yourself by following Ralf's >>link above) approximately, the draw proportion starts at 15% (presumably because >>players are unable to obtain a win), drops to 8% at 650 Elo, rises steadily from >>there to 25% at 2200 Elo, then shoots up rapidly to 48% at 2700 Elo. >> >>This would imply that the limit of chess is less than 3700 (because the graph is >>rising sharply at the end) - so my original guess (2 posts back) of 3500 was not >>too bad! >> >>-g > > >I think the conclusion is wrong. Draws are offered and accepted for reasons >beyond "this position is known or proven to be a draw." The higher your rating, >the more likely you are to win an event before the last round, then offer a >quick draw to take the money and run... Or in a match, to save mental energy >in a drawish-looking opening. > >I'll bet there are more draws (at the 2600+ level) that are 30 moves are less >than there are draws of 31 moves and longer. Which means the conclusion about >2600+ players nearly playing perfect is badly flawed. I'm not in a position to disprove this - but there is one thing I can say with absolute certainty: Any player who takes draws in positions in which they could win is likely to have a lower Elo rating than they otherwise would have. This effect would automatically skew the curve towards players below the top level - which would negate the argument that this effect is increasing the proportion of draws at the top. -g
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