The ELO (rating) system is far, far too fluid.

[ChiefPointThief]

I agree with FSKFSK. The first thing that would need to be done though is having a better rating system for the games. The players should set the rating rather than the dev because there are a lot of games that have inaccurate ratings.

The probability calculations for team games isn't realistic either. It treats it as head to head match ups and disregards what the teams are.

[FSKFSK]

It would possible to do it by data mining. For example, only look at games where both players have 300+ elo, and see how often the better player wins based on elo difference. Use that to determine the cap.

Someone else complained about "elo volatility", which probably means the K factor should also be lower for games with a substantial luck component.

[h_illes]

(You always get +2 for a win, no matter how much lower rated the loser is.) For some games, the cap should be 70% or even 55%.

You don't always get +2 ELO change; example: https://boardgamearena.com/table?table=574720452

For example, Elo as implemented here caps out where the better player has a 90% chance of winning.

It's not capped, but that doesn't make sense, since always getting +2 for a win would result in strong players getting more ELO for wins against weak players than they currently get, working AGAINST any sort of cap.

[Jellby]

Any system giving +x for a victory and -x for a defeat would result in all players with more than 50% win rate having an unlimited ELO (i.e. 8700 or whatever the current maximum is) and all players with less than 50% win rate having 100 ELO.

[h_illes]

I believe (and I could be wrong) that those who are focusing on the fact that some (most?) games have elements of luck, kingmaking, and the like.

That is not the issue (best I can tell).

The issue is that the calculations for ELO adjustment are so fluid as to exacerbate the issue of luck, kingmaking, and so on.

If the ELO adjustment calculations were not as volatile as they are, this would not be such an issue. So reign them in.

My suggestion above might be too extreme for some. So what about something like this: if your ELO score at the start of a game is less than 200, then do not change anything. If it is 200-299, then divide all adjustments by 2 and round toward 0. If it is 300-399, then divide all adjustments by 3 and round toward 0. If it is 400-499, then divide all adjustments by 4 and round toward 0. And so on...

Just something -- anything -- to stabilize it a bit. Make it harder to reach each +100 points, and stabilize things when you get there.

Anyway. This is just my thoughts. I can see that there are a lot of thoughts when it comes to how the ELO is calculated, and they are far from a consensus. So I will relax and say no more on this topic.

In chess, they use something similar (a smaller K-factor for higher ratings). That said, proper scaling is subjective, and might also depend on the actual game, so it's definitely not a straightforward fix.

[FSKFSK]

Any system giving +x for a victory and -x for a defeat would result in all players with more than 50% win rate having an unlimited ELO (i.e. 8700 or whatever the current maximum is) and all players with less than 50% win rate having 100 ELO.

No, because a +2 cap would mean +2 on a victory and -18 on a defeat. I thought there was a cap, but I guess I didn't see any games where the rating difference was that big.

[Jellby]

+2 and -18 is not +x and -x, it's +x and -y

Anyway, +2 and -18 would give a unlimited ELO to anyone winning more than 90% of their games. Even if they only play against newbies.

[ChiefPointThief]

More importantly than some form of cap is that win probabilities shouldn't be calculated the same for all games. The luckier the game the closer to 50% the calculations should be. In the current system if player a has 100 more elo than player b they are about 65% win prob. If a game has a luck rating of 5 then this % should probably be like 51/52. For luck rating of 3 somewhere in between that etc.

"The ELO (rating) system is far, far too fluid." It is even worse for luck games in arena which has double the k factor. You can have a win% which equates to being in the top 1% of players and still fall below subpar players instantly if you catch a bad streak.

[KDLadage]

After some time to reflect on this (and to study more carefully how BGA handles the ELO scores), I have determined:

1. I was wrong about the calculations. Those are fine.
2. The issue is with the fact that, in multi-player games, the ELO adjustments are calculated for every opponent and added together.

If I am playing in a 4-player game, my ELO calculation might look like this: +12, +8, -3 for a sum adjustment of +17. What should be happening here (in order to normalize the adjustments), is to take the ELO calculation of me vs. the opponent with the highest rating I defeated plus the ELO calculation of me vs. the opponent with the lowest rating I was defeated by. Thus, in the above example, my adjustment would not be +17, it would be (+12 and -3) +9. The current system truly exacerbates the impact of winning such a game. If I had won above, and had +12, +8, and +5 (for example), my ELO goes up +25... when, what I am suggesting would mean an adjustment of +12.

For ELO to be meaningful, it needs to ebb and flow. If, instead, it jumps up and down like like an ADHD child on a sugar high, it becomes meaningless as it moves from 200 to 400 to 200 again in the matter of a week. As far as those thinking that the calculation should take luck into account... if you stabilize the ratings as I have suggested, luck is taken into account! Luck will average out in the ratings as the normalization causes it to cease to be such an issue.

Anyway, this is my proposal. So thanks for reading.

[Meeplelowda]

After some time to reflect on this (and to study more carefully how BGA handles the ELO scores), I have determined:

1. I was wrong about the calculations. Those are fine.
2. The issue is with the fact that, in multi-player games, the ELO adjustments are calculated for every opponent and added together.

If I am playing in a 4-player game, my ELO calculation might look like this: +12, +8, -3 for a sum adjustment of +17. What should be happening here (in order to normalize the adjustments), is to take the ELO calculation of me vs. the opponent with the highest rating I defeated plus the ELO calculation of me vs. the opponent with the lowest rating I was defeated by. Thus, in the above example, my adjustment would not be +17, it would be (+12 and -3) +9. The current system truly exacerbates the impact of winning such a game. If I had won above, and had +12, +8, and +5 (for example), my ELO goes up +25... when, what I am suggesting would mean an adjustment of +12.

For ELO to be meaningful, it needs to ebb and flow. If, instead, it jumps up and down like like an ADHD child on a sugar high, it becomes meaningless as it moves from 200 to 400 to 200 again in the matter of a week. As far as those thinking that the calculation should take luck into account... if you stabilize the ratings as I have suggested, luck is taken into account! Luck will average out in the ratings as the normalization causes it to cease to be such an issue.

Anyway, this is my proposal. So thanks for reading.

ELO wasn't designed for multi-player scenarios, which is part of the reason why it doesn't really work in those scenarios. Rating systems for multi-player games have actually been academically studied. I've linked to such an article in another one of the dozens of ELO threads.

For the curious, here is a research paper* detailing a proposal for an Elo system actually designed for multi-player contests.

Generalizing the Elo Rating System for Multiplayer Games and Races

Abstract: We introduce a non-standard generalization of the Elo rating system for competitions involving two or more participants. The new system can be understood as an on-line estimation algorithm for the parameters of a Plackett-Luce model which can be used to make probabilistic forecasts for the results of future competitions. ...

*Note that this is self-published, i.e., not peer-reviewed.