Author: Joseph Ciarrochi
Date: 15:10:56 01/17/06
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Dan, as i'm sure you know, chessbase tries to work out how well an opening is performing, independently of the strength of the players. I am not sure what they heck they do. Is there a strict mathematical relationship between elo rating and liklihood of winning? e.g., Prob win = b1*your elo - b2* oponent elo + E Where B1 and B2 indicate strength of relationship, and E is error, or all the stuff we don't immiediately explain including opening differences. If there is not a precise mathametical relationship, we could easily induce the relationship with a huge data base (maybe 1 to 10 million games). We would enter your elo and oponents elo and use it to predict probablility of winning Once we have estimates of B1 and B2, we can then look at specific openings and see if they are discrepant from what you would expect from your elo and your openents elo. thus, based on this formula , we might predict that a particular form of the roy lopez in our 10 million game data base should have won 54%. If it only wins 51%, then it is doing 3 % worse than what you would expect based purely on the strength of the players. Another way to say this is, we can statistically remove the effects of player strength. Remaining differences in the openings would then be do to the opening itself and random factors. This of course assumes a number of things, including that B1 and B2 would be constant across opening types and player level, which is probably not true (and i therefore have have no idea how chessbase makes this estimate). For example, B1 and B2 might be smaller for drawish openings (meaning ELO differences may have somewhat less of an effect). Or B1 and B2 might be bigger amongst weaker players (meaning that a difference of 50 ELO points amongst 1300 players might be more significant than a 50 point difference between 2700 players) We could test this empirically. If anybody could get me a large data set of elos and game outcomes, I could certainly do it. I just need a million or so games in the following format opening white elo black elo outcome c32 2300 2250 1 On January 17, 2006 at 16:20:49, Dann Corbit wrote: >On January 17, 2006 at 05:41:22, Joseph Ciarrochi wrote: > >>Another issue is that players may vary in how variable their play is, and more >>variable players would have larger standard errors for a given n size >> >>I used a stat package to generate the following statistical output. player 1 and >>2 have the same mean level of points and the same N, but player 1 tends to win >>and lose alot, wherease player 2 tends to draw alot. AS you can see, standard >>error is bigger for player 1. >> >>This sort of analysis assumes that the variable "mean" is contionous, though >>really we have three categories(win, draw, loss). Still, with large samples, it >>is probably ok. I guess I could just use the formula for confidence intervals >>around means. >> >>The formula you suggest is useful in that it does give you the confidence >>interval for win verus everything else, which is an important statistic >> >> >> >>PLAYER Mean N Std. Deviation Std. Error of Mean >>1.00 .5000 300 .48385 .02794 >>2.00 .5000 300 .40893 .02361 >>Total .5000 600 .44759 .01827 > >I think that the following study would be interesting (it will require that at >least 30 people have chosen the move): > >Figure out if a move really improves on expectancy. It sounds simple, but it >must also take into account the Elo of the player, whether they are playing >black or white, and the Elo of the opponent. > >We must also take the entire game into account. > >My notion is to classify openings [or parts of openings] as underperforming, >average performing, or overperforming. > >In other words, a player with a higher Elo and who is also playing white has TWO >advantages. We would expect that a certain percentage of the time they should >win against someone with a lower Elo or someone with an equal Elo playing black. > And then, we may have a slightly higher Elo playing black. So who "should" >have the advantage becomes complicated. > >After working out the initial theory, we could make some measurements with >actual data and see how well the prediction fits the model for the entire >database. Once the model has been corrected to give good results, we could then >figure out how good moves "turn out" as a function of how they "ought to turn >out" and the strength of the players and other advantages they may have.
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