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Subject: Scoring in a multi-player board game "tournament" rss

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Dimitris Metafas
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I am using a number of tables to present the scores in our unofficial tournament. The case is to calculate the scores with the following assumptions:
1) multi-player games
2) sporadic participation of the players
3) only the winner (or the winners in the case of a draw) get points (this is not necessary but I decide to do it in this way)

The details are presented in

The simplest way to calculate the scores is the Cumulative Weighted Points vs Sessions

Cumulative Weighted Points vs Sessions Graph

The score is cumulative (it depends on the number of games you played).

A better way to represent the scores, I think, is the Cumulative Zero-sum Weighted Normalized Points vs Session-Records

Cumulative Zero-sum Weighted Normalized Points vs Session-Records Graph

This score is also cumulative, but it is zero-sum. The winners get the points from the losers.

I conclude that the best way to represent scores is the Player vs Player (PvP) Tables and especially the PvP Tables per Game.

PvP Table

The numbers in the rows denote how many points the Player-of-the-Row has scored vs the Player-of-the-Column.

PvP Table per Game: i.e. our PvP table for Dominion

I found interesting the way to calculate the results for draws in a multi-player game.
I had to transform the basic table to a new one.

Meetings Basic Table

The basic table from which all other tables are calculated.
The necessary info is
Game (the name of the game)
Game session weight (it may differ from the standard weight of a game usually because of the version of the game played (basic, advanced) or the use of an expansion)
list of players and score (an indication of a win, a lose, a draw, or no-participation)

Meetings Session-Records Table

The transformation of the "Meetings Basic Table" to this one is necessary for the calculation of the PvP and zero-sum tables.
In this table a draw of Nw players generates multiple records (Nw records). In each record everyone of the N-1 players loses 1/Nw points. The winner gets a total of (N-1)*1/Nw points. Adding the records of the same game each winners finally gets (N-1)*1/Nw - (Nw-1)*1/Nw and each loser a -Nw*1/Nw = -1
E.g. In a game of 5 players where two players share a draw, each loser gets a -2*1/2 = -1 while each winners gets a 4*1/2 - 1*1/2 = 3/2.
It is Zero-sum as the winners get the points from the losers.

For the Zero-sum Normalized Points calculation, the winners share one point and the losers share a minus one point. It is produced from the previous table as x/(N-Nw) (i.e. normalization). For the same example each loser gets -1/3 points and each winner gets 1/2 points.

I think it is the equivalent of a chess score of a draw 1/2 - 1/2 instead of 0 - 0, in the case of multi-player games.
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