Re: new ranking calculation

On Thu, Oct 09, 2003 at 01:38:24PM -0400, Jason Short wrote:
> Paul Zastoupil wrote:
> >On Thu, Oct 09, 2003 at 05:39:30AM -0400, Jason Short wrote:
> >
> >>Horn G=E1bor wrote:
> >
> ><snip all of Horn's ideas> 
> >
> >>Where to begin?
> >>
> >>My understanding of the ranking system is that it is similar to ELO, 
> >>but=20
> >>simpler.  You may want to consider the mathematics behind it before=20
> >>proposing any change.  (Actually, since the ranking system is a=20
> >>simplification of ELO I'm not sure there is any mathematical basis for=20
> >>it.  You might do better to rework it from scratch.)
> >
> >
> >It is Elo.  It has only been modified to allow for multiplayer.
> 
> Hmm.  The modifications looked significant and non-mathematically-sound, 
> although I haven't studied closely.  I know that ELO can be extended to 
> multi-player in a mathematically sound way (I have done this before; 
> http://ggz.sf.net/), but it requires going back to the original 
> principles and working things out from scratch.

Well, the most recent modifications I can't speak to, I haven't looked
at the actual system in a while.

> 
> >>To add two rankings together is mathematically worthless.  The ranking=20
> >>scores have no absolute frame of reference; they only have worth in=20
> >>relation to each other.  So instead of rankings of 1200, 1250, 1400 
> >>they=20
> >>could just as easily be 200, 250, 400 - obviously this would give 
> >>vastly=20
> >>different results when added together.  Or they could be -800, 750,=20
> >>-600...in which case the alliance would actually be considered weaker=20
> >>than the single player.  My point is that adding the rankings is an=20
> >>awful idea.
> >
> >
> >Actually he IS doing the right thing, IMO.  I don't have a proof handy
> >(it wont fit in the margin here ;) but negative isn't possible.  The
> >actual numbers are significant (at least within the system).
> 
> Only because you choose to try to keep it on an absolute scale; this 
> isn't a part of ELO.
> 
> What would happen if players got better over time?  Their ELO rankings 
> wouldn't go up (because you normalize the rankings), but they would be 
> better.  Of course, this is problematic in ELO at all since there is no 
> absolute frame of reference...

I don't see a problem here, but maybe I'm missing something.  The
scoring system is a relative scale between players.  If everyone in the
system gets better at the game, the scores are still valid because
someone with a score of 1200 is still 100 points better than someone at
1100.  Even if they are now both way better than they used to be.

> 
> >>What you can do is average scores, and you can add on fixed-scale=20
> >>amounts if you think it's appropriate.  These are ad hoc additions to=20
> >>the system, though - to get something accurate you should go back to 
> >>the=20
> >>basics and work the math out from scratch with the concept of teams=20
> >>already in place (or at least try).
> >
> >
> >This will destroy the system.  Points are conserved.  I haven't run it
> >in a while but I have a script that adds up the score of the whole
> >database and divides by the number of rows.  Its usually off less than
> >.1 from 1000 due to rounding.
> 
> I disagree.  Even if points are conserved, using a willy-nilly method of 
> determining alliance rankings won't harm the system.  Because in 
> calculating the change in points, all that is taken into account is the 
> difference in scores, and *it is symmetrical between all the players of 
> the game*.

I must have misunderstood you here.  That is correct.

-- 
Paul Zastoupil