Re: [Bug-gnubg] Player Records Overall ratings

[Joern Thyssen]

On Wed, Mar 19, 2003 at 10:00:05AM -0300, Albert Silver wrote
> Hi,
> 
> I sent this a few days ago but had no reply neither to this nor
> to two other messages sent to the mailing list. This has made me wonder
> whether they were received by others.

The mails did reach us, but there is no guaranteed turn-around time for
incoming mails.

> I'm a bit confused by the overall rating given in the Player Records. I
> began entering games but the overall rating seems weird. One record
> looks like this:
> 
> Record #1
> 
> Total games:  52
> 
> Checker total:        -0.0148 Expert
> Cube total:           -0.0081 World Class
> 
> Overall:              -0.0139 Expert
> 
> --------------------------------------
> 
> Another looks like this:
> 
> Record #2
> 
> Total games:  18
> 
> Checker total:        -0.0136 Expert
> Cube total:           -0.0008 Supernatural
> 
> Overall:              -0.0161 Advanced
> 
> 
> I don't understand why the second record's overall rating is Advanced if
> the average checker play is Expert and the cube decisions are
> Supernatural. 

I really can't explain what's going on, but the relationship between the
total chequer, the total cube, and overall error rate is not linear.

However, the total EPM (error rate per move) must be smaller (or equal
to) the sum of the cube and chequer EPM.

                E(cube) + E(chequer)
EPM(overall)= ----------------------------
              moves(cube) + moves(chequer)
             
                       E(cube)                        E(chequer)
            = ---------------------------- +  ----------------------------
              moves(cube) + moves(chequer)    moves(cube) + moves(chequer)
             

                E(cube)       E(chequer)
           <= ------------ +  --------------
              moves(cube)     moves(chequer)
             
            = EPM(cube) + EPM(chequer)

Since this inequality holds for all EPMs, it also holds for the average
shown in the players's records, hence something is obviously wrong with
record #2. 

If you have the individual games saved that consitute record #2 I would
very much like to see them!

Jørn