Biased ELO scoring for multi-player games

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Phoxtrot
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Joined: 03 January 2012, 20:55

Biased ELO scoring for multi-player games

Post by Phoxtrot »

https://boardgamearena.com/bug?id=49929

To be 100% clear: this has nothing to do with the k factor

When a game is played with more players than "normal", there is a hidden factor that reduces the ELO gains and losses.
This makes sense on principle.

One problem is that this factor is hidden, it should be displayed.

A bigger problem is that this factor should be the same for every player at the table.

A consequence of that is that statistical expectancy for total ELO gain at tables is not 0 (bias) and there can be a significant net gain or net loss of ELO at the table even if everyone has the same K factor and is well above 100 ELO.
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ufm
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Re: Biased ELO scoring for multi-player games

Post by ufm »

I think K display in multiplayers is weird as hell...
It does not factor in [N/(2 * (N-1)) → (recommeded N)/(2 * (N-1))] and initial 10/20 games multiplier correctly.
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Silene
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Re: Biased ELO scoring for multi-player games

Post by Silene »

Looks weird indeed.
My guess would be that extreme positions are damped down so that no too crazy elo-changes for 1st/last player are awarded/lost while keeping it interesting in the middle. That would be consistent with your first example in the bug report.
I don't know if this is the case but i feel like an effect like that might be desirable. So I don't think the "hidden multiplayer factor" must be the same for all players on the table as you state there.
Anyway - seeing a description on how it's done would definitely be interesting.
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Romain672
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Re: Biased ELO scoring for multi-player games

Post by Romain672 »

So. I didn't read any of the post.

Sum of gain loss is really yeah.
The loss of X vs Y is always equal to the gain of Y vs X.
The multiplicator hidden of the game is because of number of players is x0.25 for the first palyer. So the elo gained/lost is multiplicated by that value. So here is the comparaison on the value I calculate, and the value displayed:
sum of elo gain => multiply by x0.25 => gain/loss of elo
32.57 => 8.4125 => 8.41
-3.57 => -0.8925 => -0.89
4.89 => 2.445 => 4.89
-5.7 => -2.85 => -5.7
-14.23 => -7.115 => -14.23

So that mean the two first players got a factor of x0.25 of their elo. And the three last a factor of x0.5. And it's exactly.

If the two first players have >50 games, and the three last <40 games, that can be coherent, let me check the profile:
1100 games
800 games
20 games
22 games
23 games

So yeah it's totally coherent.

SO: I confirm what was said more up: the display of K-factor is wrong (it should be 40 for the 3rd, 4th, 5th player of this game), but only the display is: the gain and loss is right.
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Romain672
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Re: Biased ELO scoring for multi-player games

Post by Romain672 »

You said exactly that on your post of the bug.
For players in position 1 and 2, the factor is 0.25 : they only win/lose a quarter of the "normal" elo gain/loss
But for players in position 3,4 and 5, the factor is 0.5
This is not fair.

As a result, even though everyone has the same K, the table has a total loss of 7 ELO points, more than can be justified by rounding display issues.
I disagree with the fact it is not fair, but you give no reason for why on this bug report or this post on the forum.

In chess, the K-factor is always identical I believe.
In online gaming, that's hidden, so I have no idea, but since it's hidden, I would bet they got different K-factor. League of legend has two ranking of elo: one to tell which level you are at (your elo), and one which tell against which player you will play next game (your mmr) which move way faster. That way, if you win three times on a row, you will be against more powerful players, to try to gain even more. This doesn't mean 'k-factor' is identical or different but that look like a complete mess.
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sprockitz
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Re: Biased ELO scoring for multi-player games

Post by sprockitz »

It isn’t a bug for Elobut for display of the k factor. Later places had double the k factor. Net Elo gain or loss (without k factor and minimum of 100 factors) is always 0.
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Phoxtrot
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Re: Biased ELO scoring for multi-player games

Post by Phoxtrot »

The k factor is displayed, and it my first example, it was 20 for everyone one.

Now maybe the problem is indeed that the displayed k is wrong.

With more data I should at some point be able to see if indeed the problem is that the displayed K is wrong and/or if there is an unbalance in the multi-player factor.

Now, having a multiplayer factor that is not symmetrical around the middle would clearly be wrong as it would induce an average loss or gain of ELO over the table.

On the other hand, a multi-player factor that is not the same for all players but symmetrical (say 0.5 for 1st and 4th but 1.0 for second and third) can be defended but I think it's still not a good idea in my opinion. The reason is that any player that is high ELO enough compared to the other players to pretty much always be 1st or second and certainly almost never last would be screwed. He is already "paying" for being high ELO in the standard elo calculation that makes him win very little ELO point for beating someone to the point that he loses ELO for being 2nd of 4 or even for being 2nd of 6 players but now that is compounded by making his first places be worth half as much as his second places. That's pushing high ranked people away from playing tables with many players and that is not good.

The point of a multi-player factor, as I see it, is that because there are many 1 to 1 comparisons in a multi-player game, you need to scale it down so that those multi-payer games don't end up being so much more important than 2 players games. How much you scale the ELO variation down for say a 6-players game might logically take into account how long a 6-players game of that particular game takes in average compared to a 2-players game and it might take into account how much more (or less) "chaotic/based on luck" such a game. If you make the scaling depending on the position at the end of the game then you introduce a bias that is correlated to how "good/bad" each player is which is already taken into account in the basic ELO computation.
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Romain672
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Re: Biased ELO scoring for multi-player games

Post by Romain672 »

Phoxtrot wrote: 04 October 2021, 21:52any player that is high ELO enough compared to the other players to pretty much always be 1st or second and certainly almost never last would be screwed. He is already "paying" for being high ELO in the standard elo calculation that makes him win very little ELO point for beating someone to the point that he loses ELO for being 2nd of 4 or even for being 2nd of 6 players but now that is compounded by making his first places be worth half as much as his second places. That's pushing high ranked people away from playing tables with many players and that is not good.
No, if I understood you correctly, that's completely wrong.
Each person will have I will call it a 'score' which would work like chess elo, so where the sum of each 'score' on every game is always 0.
Then, the K-factor arrive, and multiply by 2 the elo gained/loss by the player who got few games.
So don't consider is elo is worth half as much, consider the person who got few games gain twice their elo.

There is some problem about that, when a player which got few games gain lots of games in a row (so btw, being able to reduce their K-factor to 20 when they reach top 20 would be a great idea), but form what I have seen, that work well otherwise.


The point of a multi-player factor, as I see it, is that because there are many 1 to 1 comparisons in a multi-player game, you need to scale it down so that those multi-payer games don't end up being so much more important than 2 players games. How much you scale the ELO variation down for say a 6-players game might logically take into account how long a 6-players game of that particular game takes in average compared to a 2-players game and it might take into account how much more (or less) "chaotic/based on luck" such a game. If you make the scaling depending on the position at the end of the game then you introduce a bias that is correlated to how "good/bad" each player is which is already taken into account in the basic ELO computation.
Again, the scaling does not depend of position. It depend of the number of games played by each person. You can see on my post 'If the two first players have >50 games, and the three last <40 games, that can be coherent, let me check the profile:' this was because these three players got <40games. And that caused their gain of elo of the three last players were halved, and not because they were in the second half of the game.

For the rest of your post, yeah this system isn't good, but the elo system need to not be too complicated if possible, and be able to classify player in a lot of range of differents games, and differents numbers of players. (Creating distinct ranking risk to split the community.)
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Silene
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Re: Biased ELO scoring for multi-player games

Post by Silene »

But his post makes perfect sense if you don't cut off the "On the other hand, a multi-player factor that is not the same for all players but symmetrical (say 0.5 for 1st and 4th but 1.0 for second and third) can be defended but I think it's still not a good idea in my opinion. The reason is that ..."-part ;)
He wasn't stating facts but arguments for this opinion ^^
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Romain672
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Re: Biased ELO scoring for multi-player games

Post by Romain672 »

Still don't get it if I missunderstood. Langage barrier is too high this time :(
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