Scoring Systems

Fractional System

by Anthony Simons

The scoring system I would adopt took a great deal of thought for something so simple. I call it the fractional system. Because the groups I play in tend to play different games in variable numbers, I decided I wanted to use a system that would allow direct comparison between different games. Such a system will never be failsafe by any means, but then the metagame of a league table is asking for trouble.

Many systems reward the winner a greater score in comparison to placings; but this means the winning score needs to be altered with respect to different numbers of players. This meant that to compare, say, a 3 player game to a 6 player game would often result in more points for a player beating more players. This also meant that a losing player in second place could do better (or almost as good as) a winner of a 3 player game. Naturally it depends on the game in question, but often the winner of a game with more players doesn't get there solely on his own, so awarding more points for the winner did not make sense to me.

After various options, I decided the best way of scoring was to keep the winner's score constant and merely alter the score for placings. For this reason I came up with a fractional system. At the end of a game, award points as follows:

S = P/N
or better yet as was suggested to me
S = (P - 1)/(N - 1)
where S = score
P = position
N = number of players
Position P will equal N for first place, N-1 for second place and so on.

The scores will of course always be 1 or less, but by referencing scores to the winner rather than the loser there are several benefits to offset the mathematical difficulties:

1. The scoring discourages players from taking the king-making option, because they will where possible maximize their score in the endgame (or at worst attack the player nearest to them - depending on the game of course this can be a bad thing).

2. More players means more points for placings; effectively players are being rewarded for the number of players they defeat.

3. Last place benefits more in a game with less players; but of course the last place in a 2-player game is 2nd place. This encourages a variety of games played, with varying numbers of players (hopefully).

4. There is only direct translation of positions. This means any game in which position can be measured can be used. Unfortunately this means games without discernable position are more difficult to score. My solution is to assign joint last place to the losers in such a game (e.g. Attika), of course this depends on the game.


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© Copyright 2004 by George Phillies.
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