senatorhung wrote:sprockitz wrote:Once a table is set, the only thing that matters for your Elo is your final position. It doesn't matter whether you beat a strong person and lose to a weak person or vice versa.
that is not my understanding.
take a 5.player 6 nimmt! game. knowing you finish 3rd of 5, you do NOT know whether you gain or lose ELO.
your ELO can be positive if the 2 players you beat have higher ELOs than you AND the players that beat you have higher EL0. (your ELO gains from the 4th and 5th players outweigh your ELO losses to the 1st and 2d)
if the 2 players you beat have higher ELO, but the 2 players that beat you have lower ELO ... you hover around the break even mark.
your ELO can be negative if the 2 players you beat have lower ELO and the 2 players that beat you have higher ELO. (ELO gains outweighed by ELO losses).
same situation applies to a 3.player takenoko game. if you have the highest ELO at the table .. you have to finish first to gain positive ELO. if you have the lowest ELO at the table, you pretty much have to finish last in order to lose ELO, unless the original ELO rank differences are slight.
but i do agree with your assertion that the higher ranked players on the prestige leaderboard tend to focus on 2 player games to minimize this sort of variance.
The Elo's of each person matter, but which opponents you beat and which ones you finish behind don't...only your position.
So losing to two players 200 ahead of you and beating two players with the same Elo results in the same net Elo as beating the two players 200 ahead andosing to the 2 players with the same Elo.
For a 5 player game (assuming the game's ideal number of players is 5 or more, and you've played at least 20 games), the number of points up for grabs (K) in each individual matchup is 20*5/(2*(5-1)) = 12.5
So to clearly show who you beat doesn't matter you can actually look at the Elo in this way. First subtract your expected win rate (x 12.5) against each player, then add 12.5 points for each player you beat.
The formula to determine your expected probability of winning is 1/(1+10^((Ra-Rb)/400)).
For simplicity say your Elo difference indicates a 75% chance to beat 2 of the players and a 50% chance to beat the other 2 your expected points earned is .75*12.5*2 + .5*12.5*2 = 31.25. This is the equivalent number of points lost if you don't beat anyone, then for every person you beat you do 12.5 points better than this.
Last place => -31.25 points
4th place => -31.25 + 12.5 = -18.75
3rd place => -31.25 + 25 = -6.25
2nd place => -31.25 + 37.5 = 6.25
1st place => -31.25 + 50 = 19.75
So you can determine your points won or lost without caring which player you beat and which you lost to.