Why do I not win as much ELO as I lose?

[purefct]

It appears to me that on a regular basis I am unable to win as much ELO as I lose. Granted, I tend to win more than I lose and as such I'm gaining ELO.

For example I won a 3 player game:
Me 310 + 13 = 323
P2 414 - 8 = 406
P3 100 - 0 = 100

I beat a player with significantly more ELO but I didnt get much of an ELO increase. I sort of understand why P3 didn't lose ELO, he has a lot less than me and P2

Here I won a 2 player game:
Me 181 + 15 = 196
P2 407 - 16 = 391

Again, a player with twice my ELO and I basically gain what they lost

I haven't lost recently in a 2 player game where P2 had lower ELO, primarily because I now avoid lower ELO when I can. But sometimes I lose twice the ELO the other player gains, or they gain twice the amount that I lose. Why is that, especially when I am the lower ELO player, the gain/loss is very similar?

Here I took last in a 3 player game:
P1 343 + 9 = 352
P2 103 + 9 = 112
Me 292 - 18 = 274

In my examples of my most recent play, it almost looks like ELO is redistributed among the players. But when I lose to a lower ELO player in 2 player, and also when in 3/4 player most opponents are lower ELO, I sometimes lose up to twice the gain of the other players... yet when I win against higher ELO I don't receive a similar benefit.

Why is this?

[Ehronde]

Here is a short article how ELO is calculated:

https://boardgamearena.com/faq?anchor=faq_account_elo

[Jellby]

It appears to me that on a regular basis I am unable to win as much ELO as I lose. Granted, I tend to win more than I lose and as such I'm gaining ELO.

Which is exactly why you lose more than you gain. Your ELO is supposed to stabilize around your "true" skill level. Once there, you should gain as much as you lose in total, that is, if you win more games than you lose, each game you lose will cost you more points, that are recovered by all the games that you win.

For example I won a 3 player game:
Me 310 + 13 = 323
P2 414 - 8 = 406
P3 100 - 0 = 100

I beat a player with significantly more ELO but I didnt get much of an ELO increase. I sort of understand why P3 didn't lose ELO, he has a lot less than me and P2

I'd say you gained a lot. P3 didn't lose anything because in BGA you never lose below 100. Otherwise they'd have lost 5, because 13 = 8 + 5.

Here I won a 2 player game:
Me 181 + 15 = 196
P2 407 - 16 = 391

Again, a player with twice my ELO and I basically gain what they lost

Exactly what they lost. It only looks different because of rounding. ELO should be zero-sum (except for the 100 thing), what you lose or gain is what the the others gain or lose. If the other player had won, he would have gained (and you lost) much less.

I haven't lost recently in a 2 player game where P2 had lower ELO, primarily because I now avoid lower ELO when I can. But sometimes I lose twice the ELO the other player gains, or they gain twice the amount that I lose. Why is that, especially when I am the lower ELO player, the gain/loss is very similar?

Here I took last in a 3 player game:
P1 343 + 9 = 352
P2 103 + 9 = 112
Me 292 - 18 = 274

You lost against 2 players, P2 won against you and lost against P1, so you did worse. And P2 had lower ELO than both of you, so they gained. If they had something in between, they would have gained around 0. In total, again, 18 = 9+9, so what you lose is what the others gain.

In my examples of my most recent play, it almost looks like ELO is redistributed among the players. But when I lose to a lower ELO player in 2 player, and also when in 3/4 player most opponents are lower ELO, I sometimes lose up to twice the gain of the other players...

That could happen during your first few (around 20?) matches in a particular game, then your ELO change (gained or lost) is multiplied by some factor. After those first few matches, the factor will be effectively 1. But if you play against someone who's still in their first few matches, their gain or loss will be multiplied by some factor, so it could look uneven too.

[Romain672]

To take an extreme example: https://boardgamearena.com/gamestats?pl ... finished=0

You can see (bottom right) that each victory gave me 0 to 2 elo. The 0 is because I gained 0.62 elo, which was rounded to 0 since my starting elo was 814.82. And 814.82+0.62<815.5 .
And one defeat gave me -19 elo.

And it's normal, since my elo is way higher I'm supposed to win a lot more than losing.
If you open a game and put your mouse on my elo you can see thing similar to 'Probability of a win: 94%'.

That mean against that player, I'm supposed to win 94% of my games to win and lose the same amount of elo.

[purefct]

It appears to me that on a regular basis I am unable to win as much ELO as I lose. Granted, I tend to win more than I lose and as such I'm gaining ELO.

Which is exactly why you lose more than you gain. Your ELO is supposed to stabilize around your "true" skill level. Once there, you should gain as much as you lose in total, that is, if you win more games than you lose, each game you lose will cost you more points, that are recovered by all the games that you win.

For example I won a 3 player game:
Me 310 + 13 = 323
P2 414 - 8 = 406
P3 100 - 0 = 100

I beat a player with significantly more ELO but I didnt get much of an ELO increase. I sort of understand why P3 didn't lose ELO, he has a lot less than me and P2

I'd say you gained a lot. P3 didn't lose anything because in BGA you never lose below 100. Otherwise they'd have lost 5, because 13 = 8 + 5.

Here I won a 2 player game:
Me 181 + 15 = 196
P2 407 - 16 = 391

Again, a player with twice my ELO and I basically gain what they lost

Exactly what they lost. It only looks different because of rounding. ELO should be zero-sum (except for the 100 thing), what you lose or gain is what the the others gain or lose. If the other player had won, he would have gained (and you lost) much less.

I haven't lost recently in a 2 player game where P2 had lower ELO, primarily because I now avoid lower ELO when I can. But sometimes I lose twice the ELO the other player gains, or they gain twice the amount that I lose. Why is that, especially when I am the lower ELO player, the gain/loss is very similar?

Here I took last in a 3 player game:
P1 343 + 9 = 352
P2 103 + 9 = 112
Me 292 - 18 = 274

You lost against 2 players, P2 won against you and lost against P1, so you did worse. And P2 had lower ELO than both of you, so they gained. If they had something in between, they would have gained around 0. In total, again, 18 = 9+9, so what you lose is what the others gain.

In my examples of my most recent play, it almost looks like ELO is redistributed among the players. But when I lose to a lower ELO player in 2 player, and also when in 3/4 player most opponents are lower ELO, I sometimes lose up to twice the gain of the other players...

That could happen during your first few (around 20?) matches in a particular game, then your ELO change (gained or lost) is multiplied by some factor. After those first few matches, the factor will be effectively 1. But if you play against someone who's still in their first few matches, their gain or loss will be multiplied by some factor, so it could look uneven too.

I don't know about your reasoning... I just lost a chess game and there is no "balance" between our ELO gain/loss

Him 207 + 18 = 225
Me 182 - 10 = 172

This guy had a slightly higher ELO yet his win gave him almost double the ELO I lost

Then there is this 5 player game I won... Fine, I was highest ELO but two players were close to my ELO and I only received a fraction of their lost ELO

Me 321 + 16 = 337
P2 151 + 17 = 168
P3 303 - 3 = 301
P4 201 - 18 = 183
P5 309 - 48 = 271

I mean sx@t, P5 alone should have boosted me more. And merely beating 4 other players should have as well.

[purefct]

To take an extreme example: https://boardgamearena.com/gamestats?pl ... finished=0

You can see (bottom right) that each victory gave me 0 to 2 elo. The 0 is because I gained 0.62 elo, which was rounded to 0 since my starting elo was 814.82. And 814.82+0.62<815.5 .
And one defeat gave me -19 elo.

And it's normal, since my elo is way higher I'm supposed to win a lot more than losing.
If you open a game and put your mouse on my elo you can see thing similar to 'Probability of a win: 94%'.

That mean against that player, I'm supposed to win 94% of my games to win and lose the same amount of elo.

Dude, you usually gain 1 or 2 ELO against Nymeria3 who has 300 ELO or less, and he usually loses 0. But on January 31 he won. He gained 19 and you lost 19. THIS I could understand. But if I were playing, it would be more like the lower ELO winner getting 19 and me losing 40, or the winner getting 40 and me losing 19. This is my point, and heck... your ELO difference is huge but there isn't a large imbalance in the ELO lost/won. There are large ELO imbalances when I lose against players with ELO similar to mine.

[Silene]

read the last section of your quoted post of Jellby again. it has the answer to your observations. your opponnent didn't play many games yet, so his gain was doubled.

[purefct]

Here is a short article how ELO is calculated:

https://boardgamearena.com/faq?anchor=faq_account_elo

This "probability of a victory" must be screwing me...

p(D) is the probability of victory considering the previous difference

[Silene]

Here is a short article how ELO is calculated:

https://boardgamearena.com/faq?anchor=faq_account_elo

This "probability of a victory" must be screwing me...

p(D) is the probability of victory considering the previous difference

How so? I think it was calculated as said there.

You can see the p(D) in the mouse-over when hovering over the calculation on the game-end-screen.

[JackNapis]

I don't know about your reasoning... I just lost a chess game and there is no "balance" between our ELO gain/loss

Him 207 + 18 = 225
Me 182 - 10 = 172

This guy had a slightly higher ELO yet his win gave him almost double the ELO I lost

I checked the results for that game. The other player got +18.55 ELO (rounded down to +18), and you got -9.27 ELO (rounded down to -10), so before rounding, they received exactly double the ELO you lost. This is because their K factor is 40, while yours is 20. Your K factor is based on the number of times you've played that game; it goes down as you play more games. I hope that helps!