Re: new ranking calculation

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.

> 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).

> 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.

> 
> One idea would be
> 
>    ranking(team) =3D average(rankings of players) + 100 * (size of team)
> 
> where the size of the team is the number of players in the team, not=20
> counting the first.  The value of 100 may be high, though, and it seems=20
> there are diminishing returns from added allies.  So maybe:
> 
>    ranking(team) =3D average(rankings of players) + 50 * sqrt(size of tea=
> m)
> 
> would be better.  You may want to determine this emperically, although=20
> this would take a lot of work.

These ideas completely break the system.

> 
<snip diplomacy stuff>

-- 
Paul Zastoupil