Re: [pbmserv-dev] Solitaire game scoring

[Cameron Browne <cameronb@optusnet.com.au>]

A rolling average for solitaire game ratings has been tested using the 
following formula (N = 10):

> Once  totalplayed >= N, then it becomes a rolling average of the last
> N games played
>
>                    ((N-1) * oldrating) + currentscore
>     newrating = ----------------------------------------------
>                               N

This works pretty well. One problem is that values are stored as integers 
so some pretty hideous rounding occurs during the calculation.

It turns out that the user's rating changes by 1 pt for every N pts their 
score differs from their current average. For instance, if the user's score 
is less than 10 pts different from their current average there is no 
change, if it is 73 pts different then the average changes by 7 etc.

This becomes obvious if we substitute "currentscore = oldrating + difference":

>                   ((N-1) * oldrating) + (oldrating + difference)
>     newrating =  ------------------------------------------------
>                               N

>                    N * oldrating + difference
>     newrating =  -----------------------------
>                               N

>     newrating =  oldrating + difference/N

and integer rounding makes this a pretty chunky increment.