View my actual Elo/Glicko-2 score?

[Fromper]

Of course, that's how it's implemented, but it's not what it's designed for. If it were actually designed for multi-player games, it would account for the estimated probability of finishing 2 out 3, or last out of 4, etc. When calculating rating change between 2nd and 3rd place finishers, they use exactly the same formula as if the 2nd and 3rd place player were playing a two-player game, which cannot possibly trend toward an equilibrium that estimates the actual probability of finishing *anywhere* above the 3rd place player, including 1st and 4th, 2nd and 4th, etc.

But it's good enough and better than nothing if you care about those kinds of things.

That is good enough. No need to overcomplicate things. There is no ideal metric to calculate a probability of winning as most board games have a randomness/luck factor.

If you take each pair of players and calculate each one's probability of winning over each other, and then add them all together, you will get a quite good final result about how much each player's elo should change after the game ends.

What actually should matter to me is only winning. So 2nd vs 3rd place is worthless. I'd change that only 1st player vs losers is the calculation.

I disagree. The current system incentivizes best play even if you know you're losing, to try and finish as high as possible. If it only mattered who was first, then someone who has no chance of winning might play kingmaker just to "get it over with" and end the game. Under the current system, they should still compete fairly to try and get 2nd instead of 3rd or whatever.

[Stroom]

Of course, that's how it's implemented, but it's not what it's designed for. If it were actually designed for multi-player games, it would account for the estimated probability of finishing 2 out 3, or last out of 4, etc. When calculating rating change between 2nd and 3rd place finishers, they use exactly the same formula as if the 2nd and 3rd place player were playing a two-player game, which cannot possibly trend toward an equilibrium that estimates the actual probability of finishing *anywhere* above the 3rd place player, including 1st and 4th, 2nd and 4th, etc.

But it's good enough and better than nothing if you care about those kinds of things.

That is good enough. No need to overcomplicate things. There is no ideal metric to calculate a probability of winning as most board games have a randomness/luck factor.

If you take each pair of players and calculate each one's probability of winning over each other, and then add them all together, you will get a quite good final result about how much each player's elo should change after the game ends.

What actually should matter to me is only winning. So 2nd vs 3rd place is worthless. I'd change that only 1st player vs losers is the calculation.

I disagree. The current system incentivizes best play even if you know you're losing, to try and finish as high as possible. If it only mattered who was first, then someone who has no chance of winning might play kingmaker just to "get it over with" and end the game. Under the current system, they should still compete fairly to try and get 2nd instead of 3rd or whatever.

And I disagree with that. Playing for 2nd place can also cause you to play a kingmaker in order NOT to lose 2nd place. Only winning really matters and players who throw the game for whatever silly reason, deserve to be red-thumbed. 2nd place does not matter. But sure, you can use it for elo calculation as it should not be taken seriously anyway. If people only play for elo gain or loss then they completely miss the reason why we play board games.

[ufm]

And I disagree with that. Playing for 2nd place can also cause you to play a kingmaker in order NOT to lose 2nd place. Only winning really matters and players who throw the game for whatever silly reason, deserve to be red-thumbed. 2nd place does not matter. But sure, you can use it for elo calculation as it should not be taken seriously anyway. If people only play for elo gain or loss then they completely miss the reason why we play board games.

This is incorrect, as a usual solution of kingmaking scenario is incentivizing non-first places:
https://en.wikipedia.org/wiki/Kingmaker ... n_practice
Kingmaking happens when the choice becomes irrelevant to the final result. 'Only winning matters' policy just worsens it.

[Stroom]

And I disagree with that. Playing for 2nd place can also cause you to play a kingmaker in order NOT to lose 2nd place. Only winning really matters and players who throw the game for whatever silly reason, deserve to be red-thumbed. 2nd place does not matter. But sure, you can use it for elo calculation as it should not be taken seriously anyway. If people only play for elo gain or loss then they completely miss the reason why we play board games.

This is incorrect, as a usual solution of kingmaking scenario is incentivizing non-first places:
https://en.wikipedia.org/wiki/Kingmaker ... n_practice
Kingmaking happens when the choice becomes irrelevant to the final result. 'Only winning matters' policy just worsens it.

I explained how playing for 2nd can just mean that you make the leader win faster. This especially works for the current elo calculation. You make the 1st place win, retaining 2nd place and 3rd, 4th etc do not have a chance. You still won vs 3rd and 4th, it doesn't matter if 1st place had 10 points, you had 4 points and 3rd, 4th had 2 points.

It definitely depends on the game but overall, you should always play to win in every game. No need to incentivize any kind of behavior. With any kind of system, players will try to abuse it.

And in your link, one of the examples was "penalties greater than match loss (for example, ostracism, disqualification)—questionable or unsportsmanlike conduct geared toward effecting a kingmaker scenario." - so the player gets red thumbed and can't play with higher skilled player if he plays like that.

[Jellby]

I explained how playing for 2nd can just mean that you make the leader win faster.

And how is that different if losers are not ranked? A "kingmaker" will still make questionable moves to make the leader win faster and get it over with. The difference is with ranked losers the questionable moves are still benefitting the player.

[pjt33]

Elo for multiplayer games is OK as it is. Nothing wrong with it.

This is very much a case of "If you only have a hammer, every problem is a nail". Elo designed his system using a specific model of what player strength means. It's a tool specifically for two-player games with no luck. It can be abused for multiplayer games or games with luck, but it's not really correct to claim that there's nothing wrong with doing that. If we meet in a four-player game then the probability that I finish higher than you is not dependent solely on my skill and your skill, so the preconditions for Elo to be the right tool are not met.

[Stroom]

I explained how playing for 2nd can just mean that you make the leader win faster.

And how is that different if losers are not ranked? A "kingmaker" will still make questionable moves to make the leader win faster and get it over with. The difference is with ranked losers the questionable moves are still benefitting the player.

If you have 2nd place and losing makes you lose either way... you might try to still bash the leader and become first. Which is the main goal for most games. Playing for 2nd is like giving up on trying to me. Making the game end sooner and not trying is red-thumb-worthy to me. Any kind of kingmaking is. So, in case of 2nd place always losing is more of an incentive for all players to try and win.

[Stroom]

Elo for multiplayer games is OK as it is. Nothing wrong with it.

This is very much a case of "If you only have a hammer, every problem is a nail". Elo designed his system using a specific model of what player strength means. It's a tool specifically for two-player games with no luck. It can be abused for multiplayer games or games with luck, but it's not really correct to claim that there's nothing wrong with doing that. If we meet in a four-player game then the probability that I finish higher than you is not dependent solely on my skill and your skill, so the preconditions for Elo to be the right tool are not met.

You could say it about any kind of ranking system. Elo is used for all kinds of games with minor modifications. It generally still works based on the way things are calculated. Winning probability differences defines how much points trade hands. Seems like you are suggesting that we have a ranking system perfectly tailored for each game based on all aspects. And that is just ridiculous when you look at how many games there are.

Randomness and player interaction will clearly influence the elo calculation anyway. It is most beneficial for you to make the player with highest score to lose as you get more points out of him. You can't negate that in any kind of system. But the general idea of elo calculation is still reasonable for multiplayer games. The one with highest score does win more often on average. The more randomness and player interaction there is, the more the score will fluctuate. But that's not a real issue. Someone at 770 is not necessarily better than someone with 750. One game can influence your score a lot. It's just a general estimation. Any kind of system can be gambled. The current system is good enough. You can't make a system that is considerably better than we have now.

[ufm]

I explained how playing for 2nd can just mean that you make the leader win faster. This especially works for the current elo calculation. You make the 1st place win, retaining 2nd place and 3rd, 4th etc do not have a chance. You still won vs 3rd and 4th, it doesn't matter if 1st place had 10 points, you had 4 points and 3rd, 4th had 2 points.

It definitely depends on the game but overall, you should always play to win in every game. No need to incentivize any kind of behavior. With any kind of system, players will try to abuse it.

If you have 2nd place and losing makes you lose either way... you might try to still bash the leader and become first. Which is the main goal for most games. Playing for 2nd is like giving up on trying to me. Making the game end sooner and not trying is red-thumb-worthy to me. Any kind of kingmaking is. So, in case of 2nd place always losing is more of an incentive for all players to try and win.

Overall maybe, but scores are not always tight. Tons of games end up with runaway leaders or clear winners.
Again, enforcing 'only winning matters' regardless of the situation only worsens kingmaking.
There is a reason why BGA and many other sites adopted this approach rather than yours.

And in your link, one of the examples was "penalties greater than match loss (for example, ostracism, disqualification)—questionable or unsportsmanlike conduct geared toward effecting a kingmaker scenario." - so the player gets red thumbed and can't play with higher skilled player if he plays like that.

I'd say securing second/third/or whatever place when the chance to get the first place is slim a strategic move to cut the losses.
You may red thumb freely though.

[Tulivuori]

It is most beneficial for you to make the player with highest score to lose as you get more points out of him. You can't negate that in any kind of system

This is not true. You get the same amount of points for same position, regardless of whether you beat the highest scored and lose to lowest score, or the opposite.