Author: Christophe Theron
Date: 14:50:51 03/30/04
Go up one level in this thread
On March 30, 2004 at 13:28:36, Pierre Chevalier wrote:
>An important subject on this site has been the number of games necessary
>for a result to be statistically meaningful. My question is whether
>Kasparov and Karpov have played enough games against one another or if
>Kasparov's margin of victory has been large enough to be statistically
>meaningful? Most chessplayers only play one another maybe ten times
>but K and K played each other in 144 championship level games. Anyone
>can answer but Theron and Utzinger I know have expertise on this matter.
Here are the tables that I use. Grab a calculator and draw your own conclusion.
(sorry about the bad formatting, the tables have been formatted to look good on
proportional fonts on my Palm)
Reliability of chess matches
(assuming each opponent has 1/3 chances to win, 1/3 to loose and 1/3 to draw)
90% confidence
Games %err+/- elo+/-
10 20 140pts
20 15 105pts
25 14 98pts
30 12 63pts
40 10 70pts
50 9 56pts
100 6.5 35pts
200 4.72 33pts
400 3.34 23pts
600 2.66 19pts
800 2.39 17pts
1000 2.12 15pts
1200 2.00 14pts
1400 1.81 13pts
1600 1.66 12pts
2000 ~1.50 11pts
80% confidence
Games %err+/- elo+/-
10 15 105pts
20 11 77pts
25 10 70pts
30 9 63pts
40 8 56pts
50 7 49pts
100 5.0 35pts
200 3.75 26pts
400 2.60 18pts
600 2.15 15pts
800 1.86 13pts
1000 1.66 12pts
1200 1.46 10pts
1400 1.40 10pts
1600 1.34 9pts
70% confidence
Games %err+/- elo+/-
10 15 105pts
20 10 70pts
25 8 56pts
30 8 56pts
40 6.3 44pts
50 6.0 42pts
100 4.0 28pts
200 3.0 21pts
400 2.2 15pts
600 1.7 12pts
800 1.5 11pts
1000 1.3 9pts
1200 1.24 9pts
1400 1.14 8pts
1600 1.04 7pts
400 games:
err=+/-2% conf=68% elo=+/-14
err=+/-1% conf=38% elo=+/-7
err=+/-0.5% conf=22% elo=+/-4
800 games:
err=+/-2% conf=84% elo=+/-14
err=+/-1.5% conf=71% elo=+/-11
err=+/-1% conf=52% elo=+/-7
err=+/-0.5% conf=28% elo=+/-4
General rule: when the number of games is multiplied by 4, the error margin is
divided by 2.
Official elo formula:
elodiff=-400*log10(1/wp-1)
(wp is the winning percentage)
Christophe
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