Re: [pbmserv-dev] multiplayer wish list

[Yves Rutschle <pbm@rutschle.net>]

On Fri, Sep 24, 2004 at 12:27:21PM -0700, Mark Ballinger
wrote:
> > > What  the "perudo  scoring"  above does  solve is  the
> > > variable  number of  players. If  karen beats  camb at
> > > perudo  6 times,  and  Eric beats  5  others 2  times,
> > > didn't Eric do better?
> > If karen and  camb play together, and Eric  plays with 5
> > *others*, you have  no way of comparing  karen and camb,
> > *ever*.
> Assuming Eric's  five opponents  and camb have  all played
> perudo together  many many times, and  they are determined
> to be equally  adept at the game and as  it turns out have
> equal rating scores. If Karen  now joins in play, but only
> against  camb, and  scores 6  wins, she'll  rocket up  the
> charts. If  Eric challenges  two games  against the  5 and
> wins both, he'll move up far less.

Ah ok, that's not the  same as what you originally specified
now is it? :-)

Thing is, a *perfect* rating system must also have a measure
of certitude in  the rating, which depends  precisely on the
number of players and type  of results involved to find that
rating.  For example,  if camb  has 1720  points, and  Karen
beats  him 6  times, it's  reasonable to  place Karen  above
camb, but you can not tell *how much* above. Karen will need
to lose some  games against someone in the group  to be able
to place  her accurately. Even  if she played  everyone, and
won all  the time, you could  really only say she  is "above
all", but not "20% better".

That   said,  I   think   only   the  internatinal   Othello
ratings  follow  a  model  that includes  "accuracy  of  the
rating",  probably because  Othello  is played  by too  many
mathematicians  while  most  of us  probably  wouldn't  care
enough and just spend more time playing instead :-)

Y.