

Elo ranking for more than two players games - showagel

Does anyone know a good way to rank the participants of an endless tournament (as it happens, a darts tournament) ?<p>- The total number of participant in infinite<p>- The number of players may vary in each game, but is finite<p>- Each player can participate to an infinite number of games<p>- Each game as only one winner<p>We use quite a rudimentary system right now compiling the number of victory balanced by the number of players in each game but there is a huge bias : the more you play, the more you earn points.
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fsk
Your system can be summarized as the ACBL masterpoints system, where people
earn points for winning but never lose points for losing. Then, the rating
just measures how often you play, with better players needed to play fewer
games for the same points.

How elo works:

\- Each player contributes points to a pool (based on their relative ranking)
and the winner gets all the points.

So you can generalize:

\- Each player contributes points to a pool (based on their relative ranking)
and the winner gets all the points.

This guarantees that "average sum of all ratings" remains constant over time.

However, no matter what system you pick, it will have flaws. If people try to
maximize their rating, then they will choose to play or not play based on who
are the other players. For example, if the method you pick penalizes you for
playing with weaker players, then people who want to maximize their rating
will refuse to play against weaker players.

You will always have a situation where the points a player contributes won't
correlate to his actual chance of winning.

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dragonwriter
A simple way would be treat it exactly like your favorite two-player,
win/lose-only Elo system. In each game, each player is either the single
winner (in which case, they are treated as winning against every other player)
or a loser (in which case they are treated as losing against the winner only.)

If you have a ranking of players within the game and not just a single winner
and everyone else a not-winner (which would be the case with games where
everyone who completes the game has a score, and the high score wins), you can
treat each game as a pairwise contest between each pair of players, with a
win, lose, or draw between the pair based on their ranking within the game.

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allendoerfer
So what you describing is an FFA (free for all) game.

I would let the points the winner gets equal the points the losers lose and
spread the lost points across the losers according to their ELO ranking.

To prevent inflation, you could decay player's points, when they have not
played for a while and you could add a winning tax according to the inflation
rate.

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showagel
Thanks, so you propose that every player starts with a stack of points.

I do not really understand the way you propose to apportion the points among
the players, could give an example ?

I do not want to check inflation, since I want to figure out who is the best
player, not who is the most implicated.

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allendoerfer
>>Thanks, so you propose that every player starts with a stack of points.

Isn't that essential to the ELO system?

Let's say you have a game with four players with these levels: a=1, b=2, c=2,
d=3

Player b wins. So player a loses 1 point, player c loses 2 points and player d
loses 3 points. Player b gets 6 points. If you add a tax, 1 point gets lost
and Player b gets 5 points.

Well, you are not responsible for the inflation. The inflation is created
through new players, who get their starting value.

If you do not want to decay the points of inactive players, you could add the
mentioned tax, so that the new points added to the system each day are equal
to the points eaten by the tax on each game of a day.

