Board Game Arena

Hi,

It seems I noticed discrepancy in ELO calculation and what is stated in FAQ on that. Please, correct me, if I misunderstand concept or miss something.

According to the F.A.Q.:
"When you play with more than 1 opponent, we consider that you win against each opponent who scores lower than you during this game, and lose against each opponent who scores higher than you. For example, if you place 2nd in a 4 player game, you gain ELO points as if you won against the 3rd and 4th players, and lost against the 1st."
But currently that's FALSE.

Let's see a simple example: https://boardgamearena.com/table?table=170981668
Here I ("JackKey") won against "calexico" with the same rating and had to score +9.98 from that.
See the screenshot: https://imgur.com/a/Sjdy9xB
That's correct according to the ELO formula. The same is fair for the tie with "LoLo93" and the defeat to "CollyLeslie".

Expected behaviour: all these results (+9.98, -4.09, -13.91) are summed and applied to the ELO rating.
151.85 + 9.98 - 4.09 - 13.91 = 143.83

Achieved behaviour: these results were averaged, not summed. Do you agree on that is a bug?
151.85 + (9.98 - 4.09 - 13.91) / 3 * 2 = 151.85 - 5.34 = 146.51

This bug leads to the fact: it's better to play against 3 opponents 1 by 1, rather than all together (in games where you can vary the number of opponents, of course, e.g. "Railroad Ink").
Another example: https://boardgamearena.com/table?table=170784289
See screenshot: https://imgur.com/a/IDbe8wJ
Winning against two opponents I score less points (+1.18) than I would score playing against only one of them (e.g. Johanna1968 would bring +1.32); while the chances to win against many players is always less than against one of them (e.g. the chance to roll "6" on D6 twice (1/36) is always less than the chance roll it once (1/6)).
I would expect to get +2.36 to the rating (both +1.32 and +1.04) rather than +1.18.

I have created the bug report on that, so if you agree, you are welcome to vote for that: https://boardgamearena.com/bug?id=40798

it's not a bug in the Elo calculation. If anything you can consider it a display bug. The formula accounts for the number of players in a match so you will swap less points against players in a multiplayer game with N opponents than you would in N 2 player games.

This: https://boardgamearena.com/forum/viewto ... =9&t=15950
Elo change depends on game and player number. (And yes, the FAQ is misleading here!)

dschingis27 wrote: ↑11 May 2021, 17:24 This: https://boardgamearena.com/forum/viewto ... =9&t=15950
Elo change depends on game and player number. (And yes, the FAQ is misleading here!)

Thank you for the input, I didn't know that.
Anyway, I do not see any good logic behind having the c-factor different from 1.
If it was made intentionally, then it is not a bug report, but a suggestion to change that for something more reasonable (e.g. c is always 1).

The logic is that playing a single game with n opponents is quite different from playing n individual games. Winning n individual games is a lot harder than winning a single game with many opponents, and as such players should receive less reward for winning large multiplayer games.