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## Re: [Bug-gnubg] Ratings as random walks

**From**: |
Joern Thyssen |

**Subject**: |
Re: [Bug-gnubg] Ratings as random walks |

**Date**: |
Sun, 15 Jun 2003 14:23:16 +0000 |

**User-agent**: |
Mutt/1.4.1i |

On Sun, Jun 15, 2003 at 06:54:09AM -0700, Rod Roark wrote
>* Joern, I'm realizing that the standard deviation of a FIBS*
>* rating increases with the number of matches played, so it's*
>* not going to be meaningful to publish it in isolation.*
>* *
>* For some theory behind this, consider that the rating is a*
>* type of one-dimensional random walk[1], since each new rating*
>* must be close to the previous one. There's some academic*
>* discussion at http://www.chm.uri.edu/urichm/chm531/walk/walk.html,*
>* and in particular the statement:*
>* *
>* Equation (35) implies that the standard deviation of*
>* the random walk probability distribution function grows*
>* as the square root of the number of steps.*
Yes, but to get the 95% confidence interval you should devide by the
square root of the number of steps (following the discussion last week).
>* And the latest numbers, in case you are interested:*
>* *
>* Number of samples : 1245*
>* Lowest : 1945.040000*
>* Highest : 2116.510000*
>* Mean : 2029.861751*
>* Standard Deviation : 29.786614*
Hence the 95% confidence interval is around 1.7.
Jørn

**[Bug-gnubg] GnuBG Rocks!**, *Rod Roark*, `2003/06/02`
**Re: [Bug-gnubg] GnuBG Rocks!**, *Joern Thyssen*, `2003/06/03`
**Re: [Bug-gnubg] GnuBG Rocks!**, *Rod Roark*, `2003/06/03`
**Re: [Bug-gnubg] GnuBG Rocks!**, *Joern Thyssen*, `2003/06/04`
**Re: [Bug-gnubg] GnuBG Rocks!**, *Rod Roark*, `2003/06/04`
**Re: [Bug-gnubg] GnuBG Rocks!**, *Rod Roark*, `2003/06/08`
**Re: [Bug-gnubg] GnuBG Rocks!**, *Rod Roark*, `2003/06/12`
**Re: [Bug-gnubg] GnuBG Rocks!**, *Joern Thyssen*, `2003/06/12`
**[Bug-gnubg] Ratings as random walks**, *Rod Roark*, `2003/06/15`
**Re: [Bug-gnubg] Ratings as random walks**,
*Joern Thyssen* **<=**
**Re: [Bug-gnubg] Ratings as random walks**, *Douglas Zare*, `2003/06/15`
**Re: [Bug-gnubg] Ratings as random walks**, *Joern Thyssen*, `2003/06/15`
**Re: [Bug-gnubg] Ratings as random walks**, *Rod Roark*, `2003/06/15`
**Re: [Bug-gnubg] Ratings as random walks**, *Nis Jorgensen*, `2003/06/16`