Another complaint about ELO

[detlefchef11]

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.

You keep saying it's not a reward, but that goes against human nature. People either don't care what their ELO is or they want it to be higher. Well, I recall a friend here who was bummed that his expert ELO kept him out of a tourney I was in, but that's a very unique case. Essentially, everyone who cares at all about it, "wants" to be ranked as highly as they can be. If they're at 295, they WANT to get over 300 and earn the rank of "strong player". If they're at 495, they want to make "expert". It's human nature in a competitive arena.

So, what follows, is that people get annoyed when they win a game that, statistically is harder to win but advance slower along the ranking system than they would by winning a game that is statistically easier to win. And to what end? To avoid "wild swings"? Well, the loser in my game lost 26 points. That's a pretty "wild" swing. So you didn't actually avoid that, did you? All you did manage to do is increase one players ranking by about 10% for not actually winning a game and increase another players rank, even if only barely, for finishing 3rd in a game where he was the 3rd highest ranked player so finished "where he was supposed to".

[Silene]

So, what follows, is that people get annoyed when they win a game that, statistically is harder to win but advance slower along the ranking system than they would by winning a game that is statistically easier to win. And to what end? To avoid "wild swings"? Well, the loser in my game lost 26 points. That's a pretty "wild" swing. So you didn't actually avoid that, did you?

He would've lost way more, if the 4p-modification (that's giving you reduced ELO compared to 3 separate games) wasn't in place. He lost so much, because he underperformed big time by losing to very low-ELO-players. If it had happened to him in 3 separate games vs. the 3 of you, his loss would be even bigger than 26 points.
And he wouldn't have lost that much if he had only lost to you and came in 2nd.

Obviously it is a flaw of the system, that new players who might be much better than their ELO says, give you such a big hit and so little gain. But that problem is independent of the decision to dampen down gains/losses in a 4p game compared to 3 separate games.

[Jellby]

The K-factor adjustment is the same for all players. In this particular case it changed from 20 (2-player game) to 10 (4-player game). It means you won half the elo you would have won with three separate victories. But it also means every other player won or lost half as much as they would have with three individual matches with the same outcome. In particular, the 4th player would have lost more than 50 points without the adjustment.

[detlefchef11]

So, what follows, is that people get annoyed when they win a game that, statistically is harder to win but advance slower along the ranking system than they would by winning a game that is statistically easier to win. And to what end? To avoid "wild swings"? Well, the loser in my game lost 26 points. That's a pretty "wild" swing. So you didn't actually avoid that, did you?

He would've lost way more, if the 4p-modification (that's giving you reduced ELO compared to 3 separate games) wasn't in place. He lost so much, because he underperformed big time by losing to very low-ELO-players. If it had happened to him in 3 separate games vs. the 3 of you, his loss would be even bigger than 26 points.
And he wouldn't have lost that much if he had only lost to you and came in 2nd.

Obviously it is a flaw of the system, that new players who might be much better than their ELO says, give you such a big hit and so little gain. But that problem is independent of the decision to dampen down gains/losses in a 4p game compared to 3 separate games.

Would they have lost much more? In the very simple yet extremely effective system I'm proposing, they would have lost the base number multiplied by the ratio of mine and their rankings. And, if 20 is the base number, they would have lost 30 points to me (535/350*20), so not much more than the 26 they lost. The player who finished 3rd would have lost about 10 points to me (180/350*20), and the 2nd place player would have lost about 6. Or, in the modification that I proposed where the 2nd place person just breaks even, they would just gain zero and I would have my ELO increased by the sum of what the 3rd and 4th place players lost.

[Silene]

Would they have lost much more? In the very simple yet extremely effective system I'm proposing, they would have lost the base number multiplied by the ratio of mine and their rankings. And, if 20 is the base number, they would have lost 30 points to me (535/350*20), so not much more than the 26 they lost. The player who finished 3rd would have lost about 10 points to me (180/350*20), and the 2nd place player would have lost about 6. Or, in the modification that I proposed where the 2nd place person just breaks even, they would just gain zero and I would have my ELO increased by the sum of what the 3rd and 4th place players lost.

Winner takes all of course makes it possible to gain many points while your losses are limited (but still severe even if you reach 2nd place). It will lead to a different gameplay with everyone targeting the leader and hopelessness if one can't win anymore, possibly leading to more erratic decisions. It can lead to a better or worse gameplay - depending on the game and the players.

I think it's better for the feeling of the players, when even if you cannot be first anymore, you might still have something to fight for. Especially for players who aren't exactly the best players in general and are barely ever winning in a 4-player-game. They would usually be happy to come in 2nd, if they succeed with that. I think it's good for the ELO to reflect that.

[detlefchef11]

Would they have lost much more? In the very simple yet extremely effective system I'm proposing, they would have lost the base number multiplied by the ratio of mine and their rankings. And, if 20 is the base number, they would have lost 30 points to me (535/350*20), so not much more than the 26 they lost. The player who finished 3rd would have lost about 10 points to me (180/350*20), and the 2nd place player would have lost about 6. Or, in the modification that I proposed where the 2nd place person just breaks even, they would just gain zero and I would have my ELO increased by the sum of what the 3rd and 4th place players lost.

Winner takes all of course makes it possible to gain many points while your losses are limited (but still severe even if you reach 2nd place). It will lead to a different gameplay with everyone targeting the leader and hopelessness if one can't win anymore, possibly leading to more erratic decisions. It can lead to a better or worse gameplay - depending on the game and the players.

I think it's better for the feeling of the players, when even if you cannot be first anymore, you might still have something to fight for. Especially for players who aren't exactly the best players in general and are barely ever winning in a 4-player-game. They would usually be happy to come in 2nd, if they succeed with that. I think it's good for the ELO to reflect that.

Which would be accomplished if you had a "winner take all, 2nd place doesn't pay", set up. Winner gets more than they would by beating either of the last two places H2H, because he gets paid by both of them. There's still incentive to finish 2nd because you at least don't lose anything. And it's a far simpler metric.

It also doesn't run the risk of awarding the person who finished 3rd out of 4 any ELO points, which is basically inane. And, again, according to you had NOTHING to do with the fact that the person who finished 3rd finished ahead of the highest ranked player at the table. It was predetermined that finishing 3rd out of 4 would result in an increase in ELO for them, despite that being the spot that everyone's ELO suggested was the natural finishing spot.

[Jellby]

It was predetermined that finishing 3rd out of 4 would result in an increase in ELO for them, despite that being the spot that everyone's ELO suggested was the natural finishing spot.

When you win, in 2- or more player games, you get an elo increase too, even if you had the highest elo at the table. Are you suggesting you shouldn't?

[detlefchef11]

It was predetermined that finishing 3rd out of 4 would result in an increase in ELO for them, despite that being the spot that everyone's ELO suggested was the natural finishing spot.

When you win, in 2- or more player games, you get an elo increase too, even if you had the highest elo at the table. Are you suggesting you shouldn't?

No I'm not. I actually think they should either get points from everyone or at least everyone but the 2nd place player. I don't think 3rd place should ever get anything and should lose something.

I was just pointing out the particular absurdity of the 3rd place person, who happened to have the 3rd highest ELO, getting points.

[detlefchef11]

So, I realize that the "winner gets points from 3rd and 4th (and so on) and 2nd gets a free pass" scenario sets up the unfortunate situation where the winner could get more or less points depending on who finishes 2nd. And that is less than ideal. Of course, I would say to that, "just make it truly winner take all".

If, however, we're dead set of throwing 2nd a bone, there are some ways to work around it. First off, the ELO doesn't need to be a net zero sum affair and, I believe already sometimes isn't. Correct me if I'm wrong, but if you beat a 100 ELO player H2H, you get something but they don't lose anything. Right? And if that's the case, that ship has sailed.

At any rate, the ELO award for the first place player could be determined by factoring what all the losing players would give them, dividing by a fraction depending on how many losing players there are (2/3 in a 4 player game, 3/4 in a 5 player game, etc). And giving that to the winner, then the 3rd place players and beyond lose exactly what they would have lost to them based on the ratio of their respective ELOs to the winner x the base number. And, of course, 2nd place just loses nothing.

That would of course end up with it not adding up to zero. It would either be more points awarded to the winner than was lost by the 3rd and 4th place players if the 2nd place finisher had either the most or second most ELO, OR would result in more ELO being lost by the 3rd and 4th place finishers than gained by the winner if either (or both) of the 2 high rated players finish in the last 2 spots. However, I don't think it would amount to much of delta in all but very extreme examples.

[Jellby]

You'd probably be happier if you ignore elo and look only at the victory percentage. Only the winner gets a "victory" and a rate increase, all other players just get a rate decrease; also, victories in multi-player games count more than in 2-player games (that's why you can have more than 100% in some cases).