Another complaint about ELO

[detlefchef11]

I just won a 4 player game that included a player that had an ELO that was nearly 200 higher than mine and I'm about certain that I got less ELO points than I would have had I simply beaten that person head to head. Which is silly because the base odds dictate that it's harder to win a game against three other people than it is against one. That's two more people who could get better cards than you, better luck with the dice than you, etc.

Of course, the other two people (who finished 2nd and 3rd) had much lower ELO than either of us, but that meant the 2nd place person got as many points as I did and even the third place person got a point. For finishing third. Out of four. But they got a point.

Just seems like it would be so much easier and more equitable to have it be winner take all and simply level the playing field by dividing the respective rankings of the players and multiplying that by 20. So, higher ranking players risk more and gain less when facing lower ranked players. But, if you win a game with more players in it, you're not given less points than you do for a H2H game.

[RobertBr]

Do you understand the systems you are discussing?

You say 'they got a point' which doesn't sound like a reference to Elo, but you title the post as if it is. Different parts of the site use several different systems, including Elo, and Arena and the main site track two seperate Elo ratings for you.

In multi-player competitive games (coops work differently) the site calculates your Elo as a series of match ups, between you and each other player at the table based on where you finished. If you ranked higher than an opponent you 'won' that match up, if you ranked lower you 'lost'. The k factor for those matchups can vary (the most common reason being less experienced players get higher k factors).

[detlefchef11]

Do you understand the systems you are discussing?

You say 'they got a point' which doesn't sound like a reference to Elo, but you title the post as if it is. Different parts of the site use several different systems, including Elo, and Arena and the main site track two seperate Elo ratings for you.

In multi-player competitive games (coops work differently) the site calculates your Elo as a series of match ups, between you and each other player at the table based on where you finished. If you ranked higher than an opponent you 'won' that match up, if you ranked lower you 'lost'. The k factor for those matchups can vary (the most common reason being less experienced players get higher k factors).

They got an ELO point. The highest ranking person (535 at least at the start of the game) came in 4th and lost 26 pts, that person (who I recall was around 180) got 1 pt for finishing 3rd. The 2nd place person was the lowest ranking (low 100s) and got 12. And I (about 350) got12 for winning.

And, no. I don't understand how they figure out ELO, though I've been told that it's based on how chess rankings are determined. Which, if true, seems strange given that chess is always a H2H game. In fact, the ELO in H2H games I've played (mostly Wingspan) seems fine and logical. It's just in multi opponent games where it seems to lose its way.

Again. Had I beaten the person with the 535 ELO H2H, I would have certainly gotten more than 12 "points" for the effort. But, you add two players. Two more people who have a chance of winning (thereby decreasing my odds of victory at least somewhat), and now I get LESS reward for winning?

It makes no sense at all. I suppose if they want to continue this misguided practice of rewarding someone for coming in 2nd, you could make 2nd place (in games with 4 or more players) just not gain or lose any points and the winner just gets them from the 3rd and 4th place players (adjusted, of course, by a ratio that takes into account each players ELO).

But, once they realized that winning a 4 player game got a player a lower ELO than they would have had they played a H2H against one of the same people in that game, they should have certainly gone back to the drawing board and figured that one out.

[detlefchef11]

There are a lot of ways this could work and make significantly more sense than how it is done.

1) winner take all. You divide the respective ELO numbers of all the people who didn't win into the winners and multiply that by 20. Then, each person who didn't win loses that amount and the winner gets the sum of those amounts. Super easy.

2) winner takes most. In games with at least 4 players, it works the same as above only 2nd place is removed from the equation. So, they break even and the winner gets the points from 3rd, 4th, 5th, etc based on the same fraction x 20 that is used in scenario 1

3) winner takes most with another twist. In addition to factoring the respective ELOs x20, you also apply a fraction based on how you finish. So, 2nd place has their points lost reduced by .75. Third place just loses the core number. 4th place loses their core points multiplied by 1.25. There could be different discount factors based on 3 player, 4 player, 5 player, etc.

Mostly, however, 2nd place should not be rewarded as much as it is right now. Finishing 2nd is great. If you finish 2nd in the Olympics, it means you're the 2nd best person in the world at something. Which is very impressive. Heck, finishing 2nd in a tournament here that had like 100 or more people in it. Very cool. Finishing 2nd among 4 people in one game... not so much.

[Jellby]

I believe you're referring to this game: https://boardgamearena.com/table?table=451030890 (it would have helped if you provided the link from the beginning). You can the win probability and the elo variation per match-up if you hover on the elo. Note also that (https://boardgamearena.com/faq?anchor=faq_account_elo): "the K factor is adjusted depending on the total number of players to make sure ELO variation is not too important (or too unimportant)"

The second player earned more or less the same amount as you because they are much lower rated, and it is roughly as "unlikely" for them to be second as for you to be first. The 3rd player still got some positive result, because their beating a much higher-rated player more than compensates the somewhat expected loss against you and a similarly-rated player.

[detlefchef11]

I believe you're referring to this game: https://boardgamearena.com/table?table=451030890 (it would have helped if you provided the link from the beginning). You can the win probability and the elo variation per match-up if you hover on the elo. Note also that (https://boardgamearena.com/faq?anchor=faq_account_elo): "the K factor is adjusted depending on the total number of players to make sure ELO variation is not too important (or too unimportant)"

The second player earned more or less the same amount as you because they are much lower rated, and it is roughly as "unlikely" for them to be second as for you to be first. The 3rd player still got some positive result, because their beating a much higher-rated player more than compensates the somewhat expected loss against you and a similarly-rated player.

I realize what happened. I realize that the 2nd place person got more points than they would have had they been ranked higher. What I'm saying is that the system is flawed. Regardless of what their ELO is, their inclusion in the game reduces EVERYONE'S odds of winning the game. It's just basic math. Even if they have a small chance of winning, they still are one more person that you have to beat. They may not be very good but could get lucky. They could actually be a very good player and simply be new to the site. I mean, I had played a ton before I joined here and won my first 8 or so games. So, I was a guy with a 85 ELO or a 125 ELO that was not playing like a novice. I've played similar players here. You see your opponent has a 125, but by the end of round 1, it's bloody clear that they know exactly what they're doing.

If you have a system where the winner of a H2H game against a certain player would reward them, say 20 points, but that same winner in a game against that same opponent but also includes 2 other players rewards them only 12, then you need to recognize that your system is flawed.

[Jellby]

Every system is flawed from some point of view.

[detlefchef11]

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.

[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.

I understand your frustration. I (and many others) agree that the currently implemented multi-player ELO system is not ideal. However, this has been debated ad nauseum in other threads.

[Jellby]

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.