How does bga calculate multiplayer ELO?

[Meeplelowda]

I'm still confused, so let's use a concrete example.

Let's say 3 players play a game.

John, Sam, and Keith.

Each have an Elo of 200, and are past 21 games played for purposed of determining their individual k-factors.

John wins.
Sam finishes second.
Keith finishes 3rd.

What will each player's Elo be afterward?

John will again 2X Elo, 1X based on winning against each of Sam and Keith. Similarly, Keith will lose 2X Elo. Sam will gain 1X from the win against Keith, but lose 1X for the loss against John, and so will net 0.

We don't know what X is because the K-factor will not be 20. It will be something less than 20 that depends on the number of players. Someone tried to reverse engineer how they scale down the K-factor for multi-player games, but I can't find that thread quickly.

But there is this thread from a couple years ago where I link to an academic paper about multi-player Elo.

[FrankJones]

I think the k-factor for 3-player must be 5, because the example I gave was based on something that actually happened. All 3 players had identical Elo. The winner received 10 points, which would equate to a K-factor of 5.

So, winning a 3-player game gives the same Elo as winning a 2-player game. But it's more difficult to win a 3-player game. Seems odd to me.

[Meeplelowda]

I think the k-factor for 3-player must be 5, because the example I gave was based on something that actually happened. All 3 players had identical Elo. The winner received 10 points, which would equate to a K-factor of 5.

So, winning a 3-player game gives the same Elo as winning a 2-player game. But it's more difficult to win a 3-player game. Seems odd to me.

That's a K-factor of 10, but the point remains that the K-factor should maybe higher than 20, not lower, to account for it being harder to win.

But they may be thinking that it's harder to come in 1st out of 3 than 1st out of 2, but because in a three-player game you can beat third place by placing 1st or 2nd, then that particular win is "easier." I'm not sure that makes sense, but maybe that's their thinking. Regardless, Elo/Glicko wasn't designed for multi-player, so however you try to tweak it around the edges instead of using something completely different it's not going to make sense if you scrutinize it.

[FrankJones]

I think the k-factor for 3-player must be 5, because the example I gave was based on something that actually happened. All 3 players had identical Elo. The winner received 10 points, which would equate to a K-factor of 5.

So, winning a 3-player game gives the same Elo as winning a 2-player game. But it's more difficult to win a 3-player game. Seems odd to me.

That's a K-factor of 10, but the point remains that the K-factor should maybe higher than 20, not lower, to account for it being harder to win.

But they may be thinking that it's harder to come in 1st out of 3 than 1st out of 2, but because in a three-player game you can beat third place by placing 1st or 2nd, then that particular win is "easier." I'm not sure that makes sense, but maybe that's their thinking. Regardless, Elo/Glicko wasn't designed for multi-player, so however you try to tweak it around the edges instead of using something completely different it's not going to make sense if you scrutinize it.

Right, my fault.

What I was trying to say (and failed ) was that usually a win against an equally rated opponent would give 10 points, and in this case, it seemed that each of the 2 wins gave 5, such that the K-factor was half the usual, meaning 10, causing each win to give half the Elo as usual, meaning, 5.

Agreed on your other points.

[Jellby]

A "reasonable" formula would be dividing the normal 2-player k-factor by the number of opponents (so number of players minus 1), based on the fact that at the end every player will have that number of contributions to the final elo change. I don't know if that's actually what's done, and I don't know if it is any different for team games, probably not (cooperative games use a totally different per-game system).