[Freeciv] Re: new ranking calculation

[Jason Short <jshort@xxxxxxxxxxxxxx>]

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.

>>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...

>>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*.

jason