ELO calculation: the more players in a game the less ELO points gained/lost?

[Storm Giant]

The more players in a game, the less Elo points the winner would gain for defeating all the other opponents compared to if the game had fewer opponents. Likewise, the loser would lose less points for losing to more opponents. How could this be correct?

For example, in 7 Wonders the total Elo gain/lost (total Elo variation) is multiplied by the following factor:
3 players: 75%
4 players: 66%
5 players: 50%
6 players: 44%
7 players: 33%

Here, the absurd effect is the winner gains less Elo points the more players that winner defeats in a game. It's harder to win against all 6 other players than it is to win against just 2 players and yet, you get the opposite in the Elo point gain. Other games I looked at (Sushi Go, For Sale) show the same bias against higher player counts, though with different but lower multiplier factor.

[sprockitz]

The more players in a game, the less Elo points the winner would gain for defeating all the other opponents compared to if the game had fewer opponents. Likewise, the loser would lose less points for losing to more opponents. How could this be correct?

For example, in 7 Wonders the total Elo gain/lost (total Elo variation) is multiplied by the following factor:
3 players: 75%
4 players: 66%
5 players: 50%
6 players: 44%
7 players: 33%

Here, the absurd effect is the winner gains less Elo points the more players that winner defeats in a game. It's harder to win against all 6 other players than it is to win against just 2 players and yet, you get the opposite in the Elo point gain. Other games I looked at (Sushi Go, For Sale) show the same bias against higher player counts, though with different but lower multiplier factor.

these are multipliers per person so your final statement isn't true. you still gain more total Elo the more players you have (up to the recommended number of players, after which it is equal)

3p = .75*2 = 1.5
4p = .66*3 = 2.0
5p = .50*4 = 2.0
6p = .44*5 = 2.2 (should be 2.0, think you have the wrong percentage here...should be 40%)
7p = .33*6 = 2.0

since game is recommended with 4p, the net multiplier does not go up when you increase players above 4.

[PandeNacho]

What the hell? This is an absurd system, which leads to situations like these that I've gotten into -

https://imgur.com/a/30w5oip

https://imgur.com/a/pVIFUGi

Both times I won the game or placed higher, but got fewer elo points than the person below me. How is that fair? It seems like I should aim to beat fewer players? What sense does this make?

Edit: Here it is again. This time, it's even crazier, and I cannot make head or tails of this system. 4 players had their elo changes divided by 2, while one player suffered the full elo loss. It seems completely random what factor people get applied to their total elo score.

https://imgur.com/a/2TFUHt8

[dschingis27]

What the hell? This is an absurd system, which leads to situations like these that I've gotten into -

https://imgur.com/a/30w5oip

https://imgur.com/a/pVIFUGi

Both times I won the game or placed higher, but got fewer elo points than the person below me. How is that fair? It seems like I should aim to beat fewer players? What sense does this make?

Edit: Here it is again. This time, it's even crazier, and I cannot make head or tails of this system. 4 players had their elo changes divided by 2, while one player suffered the full elo loss. It seems completely random what factor people get applied to their total elo score.

https://imgur.com/a/2TFUHt8

First, if you haven't already, please read https://boardgamearena.com/faq?anchor=faq_account_elo

You found a bug in the ELO computation display of the K factor. Let's take the third example. For Kleverok777, the person with the big elo loss, it was just his 14th game of 7Wonders, so his K factor is 40 according to the FAQ and computation was right. But the displayed K factor was 20 which is just wrong (and apparently not used in the computation). We could make a bug report if there isn't one already.

I think all of your examples can be explained by this. So nothing wrong with the compuation, just with the display of the K factor.

However, unrelatedly, if you want better elo calculation, please vote: https://boardgamearena.com/bug?id=14455
(And if you like to play to accumulate points, then play Arena mode. )

[augustjologs]

@Pandenacho,
The two issues you mentioned are unrelated to the original post. In the first issue, where you won but got fewer points than the second placer, is not abnormal, especially if you are rated higher than the other players and the second placer beat higher rated players. For example, you are a good player, and you beat a beginner who beat an apprentice. You won't gain much points because you just beat players you are expected to beat (they are lower rated). But the beginner who beat an apprentice (unexpected victory, ie, lower probability of winning) would probably get more points than you did. There is a misconception that the winner should get the most points, even if he beat a bunch of beginners. Not so, it depends on your relative ratings.

The second case, where one player got full points deducted, usually happens when that player had played fewer than 20 times of that game. This is just the rating taking into consideration that it's harder to estimate the true Elo rating of a new player. What is surprising is that even with new players, the K factor, which is supposed to limit the gains/losses of Elo points for the game played is not followed. In that game, the K factor was 20, yet the new player (Kleverok777) having played only his 14th 7Wonders game, still lost 39.97 points.

these are multipliers per person so your final statement isn't true. you still gain more total Elo the more players you have (up to the recommended number of players, after which it is equal)

3p = .75*2 = 1.5
4p = .66*3 = 2.0
5p = .50*4 = 2.0
6p = .44*5 = 2.2 (should be 2.0, think you have the wrong percentage here...should be 40%)
7p = .33*6 = 2.0

since game is recommended with 4p, the net multiplier does not go up when you increase players above 4.

Yes, it's true that you still gain more total Elo the more players you have but the Elo calculator reduces the total gains by multiplying them with reducing factor (with the more players, the bigger the reduction). Why reduce the total Elo gained with more players? Because the game exceeded the recommended number of players? The Elo rating measures the skill of the player, not how nice the game was played based on some arbitrary boardgamegeek poll of what players think is the 'best number of players' in the game.

[KlaatuBaradaNicough]

In the first issue, where you won but got fewer points than the second placer, is not abnormal, especially if you are rated higher than the other players and the second placer beat higher rated players. For example, you are a good player, and you beat a beginner who beat an apprentice. You won't gain much points because you just beat players you are expected to beat (they are lower rated). But the beginner who beat an apprentice (unexpected victory, ie, lower probability of winning) would probably get more points than you did

But the beginner here didn't beat the apprentice, the beginner lost the game as well. Unless it was a race of some sort or the game / tournament rules specify partial wins or finishing order.

[PandeNacho]

Okay, having read your responses, @dschingis27 and @augustjologs, the situation has become a lot clearer, and yes you're correct that a lot of stuff can be explained by the K-factor display bug. Still, a couple of things I disagree with.

In the first game, if you see my (2nd place) starting ELO compared to the 3rd place's starting ELO, mine is actually lower than theirs - 167 vs 173. My ELO gain at the end of the game was divided by 3, while their ELO gain was kept at the original value. I went back and counted the number of games they had played at that time, and the one in question was their 9th game. This definitely explains the situation as their K-factor was actually 60, compared to my 20. So this is another one that can be attributed to the K-factor display bug.

The same phenomenon explains the 2nd game as well, while the 3rd game is a bit harder to explain as to why the person who came last lost full ELO points compared to significantly lower gains and losses among the other players.

I think I get what the system is at this point, and I do want to apologize for my outraged tone earlier - I was ignorant of the real situation/calculations, and was struggling to find answers anywhere. Now I get the process, even though I'm still not a huge fan lol - I did go and vote for the proposed system though. Thanks for all your help!

As for the Arena mode, I do like to accumulate points, but I guess I still wanted to play without any stress so I haven't given that a shot. I probably will sometime in the future, though!

[augustjologs]

This looks more than just a display bug. There were games were I lost more than the K factor (not my first few games).

In my 132nd 7W game, I lost 30 Elo points (K factor 20). Table# 57555281 https://imgur.com/wLxCU06

In my 135th 7W game, I lost 24 Elo points (K factor 20). Table# 49202116 https://imgur.com/RZnzCZV

I seem to recall some games I played first time and won (K factor displayed 20, but FAQ says 60) and gained more than 60 Elo points. Isn't the K factor suppose to limit the gain/loss of Elo?

Is this a bug or something else?

[dschingis27]

Isn't the K factor suppose to limit the gain/loss of Elo?

That would be correct in a 2p game. However, as pointed out by sprockitz in this thread, you can gain or loose more Elo than the K factor in 3p+ games.

[Tulivuori]

https://boardgamearena.com/bug?id=18212

I made a bug of this. I hope it helps and someone finally documents how it works.