Board Game Arena

Hello!!
I don't know how to apply the ELO formula on 3 players game.
eg. in a game like that
Can't Stop
1° - m3ru8 - 3
+34 1456
2° - bubbaxis - 2
+2 1443
3° - night_angel - 1
-36 1469
K=40*(3/2)=60 ?
m3ru8's score is 2?
bubbaxis's score is 0 ?
night's score is -2 ?

Can anyone explain me?

Thanks

Bubbaxis

I don't know the exact formulae, but from the BGA wiki, ELO in a multiplayer game is calculated as the sum of ELOs against all opponents. But, in general terms....

In this case, before the game started, the ELOs were
m3ru8 1422
bubaxis 1442
night_angel 1505
Looking at this, the outcome of the game should be night_angel 1st (by a reasonable margin), bubaxis 2nd, m3ru8 3rd (but just barely).

The outcome was reversed.
So, m3ru8 wins against bubaxis for a small amount (49.65% chance of winning), and against night_angel for a larger amount (48.58% chance of winning). Total, +34 points (Reasonable to assume about +14 and +20)
Bubaxix looses against m3ru8 for a small amount (50.35% chance of winning), and wins against night_angel for a medium amount (48.93% chance of winning). Total, +2 points (Reasonable to assume -14 and +16)
night_angel looses against m3ru8 for a larger amount(51.42%), and looses against bubaxis for a small/medium amount (51.07%). Total, -36 points (Reasonable to assume -20 and -16)

Sum of all playing = 0 points.

When looked at as 1v1 competition, it would be:
m3ru8 takes 14 points from bubaxix
m3ru8 takes 20 points from night_angel -- total, +34 points for m3ru8

bubaxis takes 16 points from night_angel
bubaxis loses 14 points to m3ru8 -- total +2 points for bubaxix

night_angel loses 20 points to m3ru8
night_angel loses 16 points to bubaxis -- total -36 points for night_angel

All players were reasonably evenly matched at the beginning, and the ELO change represents a 2.3% increase for m3ru8, and a 2.4% decrease for night_angel. Flipping a fair coin would have resulted in a similar outcome. Changes in ELO are normally not significant unless the outcomes are significantly different than expected -- a player with a high ELO losing to a player with a low ELO.

Again, I do not have access to the specific formulae used, so this answer may be incomplete and/or inaccurate.

The formula is K*(S-ES)

K=constant. (60 first 30 games, 40 afterwards) but for multiplayers game K = K*(N/2) where N=number of players. On this match K should be 60=40*1,5
S=score. (1 for winner, 0 for looser)
ES=expected scores. From ELO table m3ru8 vs bubba has -19 (rating differences) then ES=0,47 to win, m3ru8 vs night has -83(rating differences) then ES=0,39 to win.

apply on m3ru8
60*(1-0,47) vs bubba = 60*0,53 = 31,8 = 32 rounded
60*(1-0,39) vs night = 60*0,61 = 36,6 = 37 rounded
m3ru8 should gain 69?

there is anything not work, I lost anything on my research....
work for 2 players game but not for multiplayer

anyway thanks for your analisys!