Re: new ranking calculation

Horn G=E1bor wrote:
> Hi!
> i made some modifications to the script that generates the ranking due
> to the discussed things. Here is a short summary:
>=20
> 1, It examines if there were allies. If two player exchanged techs,
> they're counted as allies.=20
>=20
> 2, when calculates the new ranking, it doesn't use the (current ranking=
)
> point of the player, but adds all of his ally's point to it's as Pille
> suggested, and makes a virtual point for the game for every player.
> Let's see an example, we have 4 players, A(1200), B(1250), C(1000),
> D(1350), E(1400). They do the following alliances:
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> A allies B.
> A allies C.
> A allies D.
> B allies C.
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> With the current script all they are counted w/ their original points
> regardless of allies. W/ the new script every player gets a virtual
> score for the current game, and get measured w/ that:
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> A: 1200+1250+1000+1350=3D4800
> B: 1250+1200+1000=3D3450
> C: 1000+1200+1250=3D3450
> D: 1350+1200=3D2550
> E: 1400

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.)

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.

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).

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.


I also question whether alliances should be penalized in this way.  When=20
playing a team game, obviously each team should be counted as a unit -=20
but I don't think alliances are the same thing at all.  After all,=20
player E had the chance to join alliances as well; doesn't the fact that=20
he didn't do so mean he deserved to lose this game?  Of course he may=20
have had little choice in the matter, but in the long term a good=20
diplomatic ability will be rewarded with a higher ranking.

Diplomacy is as important or more important than civ-building or war.=20
This is true historically as well.  Why should the ranking system punish=20
diplomatic skill while the others are rewarded?

jason