Another complaint about ELO

[Meeplelowda]

Every system is flawed from some point of view.

Sorry, but that seems like a copout and could be used to defend some very stupid things.

Simple question: Why would you design a system that rewards the winner of a game that is undeniably harder to win less than you would a game that is easier to win.

Because that's what is happening. And basic math does, in fact, make the odds undeniably worse. In both the actual game played and the theoretical H2H game involving the winner of the first game and the player with the highest ELO, the winner has to beat that player. But in the actual game, that player's odds of winning are less, even if only a little, because of the inclusion of two additional players that they also have to beat. Even if these players, by virtue of their low ranking, only have a 5% chance of winning, that's still something that lowers the two higher rated player's chances of winning. So, it would be illogical to even make the payout the same, let alone less

I realize, if you want to reward 2nd place, the points have to come from somewhere (unless, as I suggested, you simply "reward" 2nd place by not taking any points away from them). Of course, another obvious place to find these points is to not compound the foolishness by also rewarding the player who finished 3rd out of 4.

It baffles me, honestly. That a bunch of people smart enough to run this site, once they realized their ranking system defied logic and basic math, didn't try to figure out a better solution.

You may be interested in this thread: View my actual Elo/Glicko-2 score?

[Silene]

Simple question: Why would you design a system that rewards the winner of a game that is undeniably harder to win less than you would a game that is easier to win.

That's a rethorical question. But does it really apply here?

Let's say your have 400 ELO and your opponnents have 600/0/0 ELO.

The 2 beginners don't stand a chance against either of you both. No matter if head-to-head or in a 4p game.

In head-to-head you might not stand a chance against the 600 ELO player or at least your chances are very low.
However in a 4p game with the 4 of you, you might have a better chance beating that strong opponent because of all the meddling the 2 beginners are doing.

This is just an extreme example, but it shows it is not necessarily less likely to win in 4p game than in 2p game because of all the additional random influence that more players unavoidably bring into a game with more players.

So that is the reason, why in games with more players, the system reduces every gain/loss vs all the opponents compared to if it was 3 separate head-to-head results.
Also don't forget that in case you get last, you would also lose fewer points (vs. each opponent) due to that effect. So it is not enough to look only at reward but also weight that against the possible loss, should the result be the other way around.

[detlefchef11]

Simple question: Why would you design a system that rewards the winner of a game that is undeniably harder to win less than you would a game that is easier to win.

Because with more players there's also more randomness. Suppose you play against same-rated opponents and you win exactly the amount of games you're expected to win, and evenly distributed. Suppose in a two-player game you get +10 when you win and -10 when you lose. Your elo would fluctuate with +10, -10, +10, -10, +10, -10, +10, -10...

Now if it were as you seem to suggest, in a 4-player game you'd get +30 when you're first, +10 when you're second, -10 when you're third and -30 when you're last. Your elo would now fluctuate with +30 +10 -10 -30 +30 +10 -10 -30 +30 +10 -10 -30... (or +40 -40 +40 -40 +40 -40...).

To avoid those large swings in multiplayer games, the K factor is modified by the number of players.

Finally, the elo score is not some kind of "reward" that you get for beating tough opponents. It's an estimation of your skill in the game, so there's nothing "fair" or "unfair" with it.

Actually, your representation go the 4 player game does not reflect what I would like to see. Ideally, in a four person game of equal ELO players, where 10 pts is the basis, the winner would get 30 and everyone else would lose 10. Because I don't think it should matter if you're 2nd out of 4. 2nd in a tournament? Sure, you should get a medal for that. 2nd in arena standings? Again, well done. Hell, top 10 in that is great. But out of 4? In a single game? Not so much.

What's worse would be that I'm guessing the reason why I only got 12 points for winning the game in question was because the "wrong" person got 2nd. Is it safe to assume that, had the highest rated player gotten 2nd and the two lower rated players finished 3rd and 4th, those 2 players wouldn't have bled as many ELO points and I would have gotten more than 12? Which invites all sorts of ugliness. Either a) this is something that I can't affect so should not alter my score or b) I ethically shouldn't try to affect. Because surely you don't want players trying to affect the chances of the rest of the competitors finishing 2nd or 3rd or 4th. Do you?

And, if it is your intention to have ELO reflect the skill level of players, then why do you penalize players for playing multi opponent games as compared to H2H. And the math supports that. If you need me to show you, I will.

[detlefchef11]

Simple question: Why would you design a system that rewards the winner of a game that is undeniably harder to win less than you would a game that is easier to win.

That's a rethorical question. But does it really apply here?

Let's say your have 400 ELO and your opponnents have 600/0/0 ELO.

The 2 beginners don't stand a chance against either of you both. No matter if head-to-head or in a 4p game.

In head-to-head you might not stand a chance against the 600 ELO player or at least your chances are very low.
However in a 4p game with the 4 of you, you might have a better chance beating that strong opponent because of all the meddling the 2 beginners are doing.

This is just an extreme example, but it shows it is not necessarily less likely to win in 4p game than in 2p game because of all the additional random influence that more players unavoidably bring into a game with more players.

So that is the reason, why in games with more players, the system reduces every gain/loss vs all the opponents compared to if it was 3 separate head-to-head results.
Also don't forget that in case you get last, you would also lose fewer points (vs. each opponent) due to that effect. So it is not enough to look only at reward but also weight that against the possible loss, should the result be the other way around.

Well, in this very real game, the lowest ranked player finished 2nd and put up the kind of score (91) that could have been enough to win a decent amount of games. After all, in the tournament this happened in, I won my 1st round game with a lower score than that. In the game this thread is about, I got great cards, so I was going to be hard to beat and the high ELO player had a bad game. But, had I gotten just so-so cards, the player who got 2nd could have easily won. So to say they have "no chance" of winning is a rather bold statement. And this doesn't take into account the players I described above who are new here but not new to the game and are therefor much better than their ELO would have you believe.

I've also played people who had low scores and weren't that good, but good enough to take advantage of the amazing luck they were getting.

And, while I get what you're saying about the lower ranked players POSSIBLY turning the game for me, that does seem very theoretical. Certainly nothing concrete enough to build a ranking system around. After all, they could just as easily turn the game towards the top player. So that is either a wash or something that moves the margin in a minuscule bit towards even, but not enough to offset the chances each of those players have to win in anything but the absurd example you gave.

Also, the high ELO player did lose 26 ELO points which I'm guessing is about as much as they would have lost to me had we played H2H, so that sort of shoots down your bit about risking less if you lose.

[Jellby]

Actually, your representation go the 4 player game does not reflect what I would like to see. Ideally, in a four person game of equal ELO players, where 10 pts is the basis, the winner would get 30 and everyone else would lose 10. Because I don't think it should matter if you're 2nd out of 4.

OK, then it would be +30, -10, -10, -10, +30, -10, -10 ,-10... Still, the point is that there are bigger swings with that scheme. Also, another argument is that it's easier to "not be the winner" in a 4-player game, so why should I "be penalised" the same as when I lose a 2-player game?

There is a difference between places because elo is a measure of skill, not a prize, and it takes different skill to be 2nd or 4th. There are other games where losers are not ranked, and they're classified as tied, but that's up to the game's developer/designer to decide. One could also argue that elo change should depend on the in-game scores, and not on the position (but there are games with no scores, and scores change a lot between games).

What's worse would be that I'm guessing the reason why I only got 12 points for winning the game in question was because the "wrong" person got 2nd.

Well, that's wrong. Your elo change depends only on who you win and lose against. It's not affected at all by the order between them. Actually, when you do the math, it turns out it doesn't even depend on who you win or lose against, but only on your final position (and on your elo of your opponents', of course).

And, if it is your intention to have ELO reflect the skill level of players, then why do you penalize players for playing multi opponent games as compared to H2H.

Again, it's no penalty, it's the "system" being more cautious because higher player counts are more difficult to evaluate, so elo changes are smaller.

If you consistently win against 400-elo opponents, and tie with 450-elo opponents, your elo will stabilize around 450, whether you play 2-player or 4-player games. The multi-player change does not affect your "final" elo, it only affects the speed at which you get there and the size of the fluctuations.

[detlefchef11]

Actually, your representation go the 4 player game does not reflect what I would like to see. Ideally, in a four person game of equal ELO players, where 10 pts is the basis, the winner would get 30 and everyone else would lose 10. Because I don't think it should matter if you're 2nd out of 4.

OK, then it would be +30, -10, -10, -10, +30, -10, -10 ,-10... Still, the point is that there are bigger swings with that scheme. Also, another argument is that it's easier to "not be the winner" in a 4-player game, so why should I "be penalised" the same as when I lose a 2-player game?

There is a difference between places because elo is a measure of skill, not a prize, and it takes different skill to be 2nd or 4th. There are other games where losers are not ranked, and they're classified as tied, but that's up to the game's developer/designer to decide. One could also argue that elo change should depend on the in-game scores, and not on the position (but there are games with no scores, and scores change a lot between games).

What's worse would be that I'm guessing the reason why I only got 12 points for winning the game in question was because the "wrong" person got 2nd.

Well, that's wrong. Your elo change depends only on who you win and lose against. It's not affected at all by the order between them. Actually, when you do the math, it turns out it doesn't even depend on who you win or lose against, but only on your final position (and on your elo of your opponents', of course).

And, if it is your intention to have ELO reflect the skill level of players, then why do you penalize players for playing multi opponent games as compared to H2H.

Again, it's no penalty, it's the "system" being more cautious because higher player counts are more difficult to evaluate, so elo changes are smaller.

If you consistently win against 400-elo opponents, and tie with 450-elo opponents, your elo will stabilize around 450, whether you play 2-player or 4-player games. The multi-player change does not affect your "final" elo, it only affects the speed at which you get there and the size of the fluctuations.

What's wrong with bigger swings? And you realize your attempt to avoid them comes at the expense of the player who won. After all, your examples assume a situation where one of the players of similar ELO is not just "passing through" that ranking en route to a higher one and, rather winning and losing as often as "they should".

I'm actually curious how the distribution of points go in the same example you're giving. In a four player game where everyone has the same ELO. Would you mind explaining that?

As for my mistake regarding the ultimate finishing order of my opponents. Thank you for clarifying that. So, in other words. In that game, against those opponents, I was destined to earn 12 ELO points for winning regardless? Surely the lower ranked players would get less (or zero or perhaps even lose points) for finishing 3rd and 4th but the high ranking player would have lost less points (and thus providing less points to be divided by the rest) for finishing 2nd?

And, you're also saying that it doesn't matter who I finish 2nd to? That I either win or lose the same points regardless of whether we finish in order of highest to lowest ELO or if the lowest ELO player wins it?

That, if you understand the formula, you can predict about how many points you win earn or lose for each finishing position given the ELO of everyone at the table?

[Silene]

As for my mistake regarding the ultimate finishing order of my opponents. Thank you for clarifying that. So, in other words. In that game, against those opponents, I was destined to earn 12 ELO points for winning regardless? Surely the lower ranked players would get less (or zero or perhaps even lose points) for finishing 3rd and 4th but the high ranking player would have lost less points (and thus providing less points to be divided by the rest) for finishing 2nd?

And, you're also saying that it doesn't matter who I finish 2nd to? That I either win or lose the same points regardless of whether we finish in order of highest to lowest ELO or if the lowest ELO player wins it?

That, if you understand the formula, you can predict about how many points you win earn or lose for each finishing position given the ELO of everyone at the table?

yes, yes and yes

[detlefchef11]

As for my mistake regarding the ultimate finishing order of my opponents. Thank you for clarifying that. So, in other words. In that game, against those opponents, I was destined to earn 12 ELO points for winning regardless? Surely the lower ranked players would get less (or zero or perhaps even lose points) for finishing 3rd and 4th but the high ranking player would have lost less points (and thus providing less points to be divided by the rest) for finishing 2nd?

And, you're also saying that it doesn't matter who I finish 2nd to? That I either win or lose the same points regardless of whether we finish in order of highest to lowest ELO or if the lowest ELO player wins it?

That, if you understand the formula, you can predict about how many points you win earn or lose for each finishing position given the ELO of everyone at the table?

yes, yes and yes

Well, I guess that is somewhat reassuring but it still seems like a system was invented that is needlessly complicated and results in inaccurate distribution of ELO for no good reason because they wanted it to work in absurdly extreme examples like the one you gave at the expense of far more realistic ones like the game I just played. Which is unfortunate, because it's a system that begs to be "gamed".

If you want to ascend to a higher ELO quickly (and for all the rhetoric about it not being a reward... spoiler alert: people see it that way. If they're "good", they want to achieve "strong". If they're "strong", they want to make "expert", etc. It's not at all like on other sites I've played games on, even if it's not portrayed that way. Other sites have things like military ranks, etc, but it's basically the same thing. I've had conversations with other players. Congratulating them on making expert, etc), you want to avoid multi-opponent games. Because you can either play games with a base win rate of 50% that earn you X for winning or play games with a base win rate of 25% that earn you x/2 for winning. And that just defies logic and basic math.

Another thing. If what I said and you confirmed is true, why did the 3rd place person get anything at all for finishing there? They had the 3rd highest ELO, so they finished "where they were supposed to". So, at best, they should have simply not lost anything, but they shouldn't have gained anything. They didn't do anything to warrant any increase in ELO.

Again, it apparently doesn't matter that they finished ahead of a higher ELO player, because they went into that game apparently knowing that, if they finished 3rd, they'd get 1 pt. regardless of where everyone else finished. Even though that was basically where the apparent skill levels of all players would dictate they should finish all things being equal. Which also doesn't make any sense at all.

[Jellby]

but it still seems like a system was invented that is needlessly complicated and results in inaccurate distribution of ELO for no good reason because they wanted it to work in absurdly extreme examples like the one you gave at the expense of far more realistic ones like the game I just played.

I think it's the opposite. The elo system was invented (for 2-player games) long ago. BGA just applies it to multiplayer games by adding up the results of all player pairs and adjusting the K factor (which was already present in elo).

That, if you understand the formula, you can predict about how many points you win earn or lose for each finishing position given the ELO of everyone at the table?

Yes, the formula is quite simple:

Take two players, A and B, with elo RA and RB. The probability of A winning is estimated as

pA = 1/(1+10^((RB-RA)/400))

and the change of elo for A is K*(1-pA) if they win, or -K*pA if they lose. That's all there is. And BGA didn't invent anything new.

And, you're also saying that it doesn't matter who I finish 2nd to? That I either win or lose the same points regardless of whether we finish in order of highest to lowest ELO or if the lowest ELO player wins it?

Right. That's not immediate from the math above, but if you work it out it turns out that the final outcome, for a given set of players, depends only on your final position, and not on the individual position of the opponents.

What's wrong with bigger swings? And you realize your attempt to avoid them comes at the expense of the player who won.

Bigger swings are wrong because ideally elo should converge to the "true" value, and not oscillate wildly. You can't keep everything "the same" with all player counts, and they chose to keep (or try to) oscillations the same, rather than maximum change, or rate of convergence, or average gain per match. It's not done at the expense of anyone because, again, elo is not a reward.

[Silene]

If you want to ascend to a higher ELO quickly (and for all the rhetoric about it not being a reward... spoiler alert: people see it that way. If they're "good", they want to achieve "strong". If they're "strong", they want to make "expert", etc. It's not at all like on other sites I've played games on, even if it's not portrayed that way. Other sites have things like military ranks, etc, but it's basically the same thing. I've had conversations with other players. Congratulating them on making expert, etc), you want to avoid multi-opponent games. Because you can either play games with a base win rate of 50% that earn you X for winning or play games with a base win rate of 25% that earn you x/2 for winning. And that just defies logic and basic math.

You're completely neglecting the potential loss you might face as well in your calculations. Also you forget that in 4p game with even (same rating as yours) opponnents, you'd also earn something for 2nd place.

Also your numbers are totally exaggerated. With even opponnents (same rating as yours) you do win more (!and definitely not half!) points if you are 1st in a 4-player game than if you are 1st in a 2 player game. You only gain less in that 4-player game, than if you had played 3 separate 2-player games vs. each of those opponnents.