Elo changes with luck rating

[Romain672]

tldr: take the luck rating of each game in the elo calculation, to make make high elo can't stop players win more and lose less against low elo players. Same for elite on arena.


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Hello,
A commun complain about games like can't stop is that the game is too much random, and to have an high elo or to win the arena, you need to be lucky and stop playing after a good streak.
You can see in the game information part: https://boardgamearena.com/gamepanel?game=cantstop that we got a luck rating which is at 4/5 in can't stop, so let's try to get a new elo formula with that rating that we will name the 'luck-factor'.


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Firstly, let's assume that 2/5 luck rating give the actual elo changes so luck-factor would be equal to 1.
Then a 3/5 luck rating would give a luck-factor of 0.9, which mean that any gain and loss of elo would be multiplied by 0.9 . That mean the elos will be closer from each other, and so an higher elo player playing against a lower elo player will gain more elo in case of a win (compared to atm), and will lose less elo in case of a loss. Since the game is more random, that's what we want.
Then a 4/5 luck rating would get 0.81 luck-factor.
A 5/5 would get 0.73 luck-factor.
A 1/5 would get 1.1, which mean that you incentive high elo players to play against other high elo player.
A 0/5 would get 1.21.

And to me that look pretty nice.


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Then secondly, let's talk about interaction.
Another problem I have seen in the forum and for playing 3p games with very high elo, is that when someone got two similar choices, and need to help one player or another, I will by default not be chosen because i'm more a threat which make total sense. But that's not counted in the elo calculation.
So let's add an interaction-cursor.

This interaction-cursor is not a change of the elo factor. That cursor will before all calculations multiply all the elo by that amount, and will after the calculations divide all the elo by that amount. (maybe there is a better solution than that)
This has consequence when that value is inferior to 1, to make the higher elo player win more elo in case of a win, and lose less elo in case of a loss.

In 2p games, that interaction-cursor is 1: you can't focus another player.
If interaction is 0/5 then that interaction-cursor is 1: it's extremely hard to focus another player. You could decide to make decisions to have more chance to be in front of player A compared to B, even in games like Yahtzee, but that look minor and extremely rare.

Then I guess for each point of interaction above 0 and each player above 2, you add a x0.98 to that interaction-cursor.
And so a 2/5 interaction with 3 players will give ~x0.94.
A 4/5 interaction with 5 players will give ~x0.87.


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All the value displayed here is an example of what is possible, I try to put right value, but I have no idea how much they should change. It's possible per example for one arena season to start at x0.98 to see how it goes, if that work try x0.95, then if that work try x0.9.
The big downside is that it complexify a lot the calculation of elo changes.

I have talked by the past on some of those ideas in others posts, but now that idea got their own post

[ufm]

1. Parameters are not reliable. The developer decides it, but each parameter does not have a firm standard.
For example, if I were the dev, I would have set the luck rating to 5/5 instead of 4/5.

2. Why should high ELO players win more and lose less against low ELO players in luck-based games, after all?
They voluntarily chose games of chances. They have to take the risk as well.

[Ceaseless]

Either I'm wildly misreading what you're proposing, or this is really flawed. I'll tell you what I see and hopefully you can clear up any misunderstanding.
 

Firstly, let's assume that 2/5 luck rating give the actual elo changes so luck-factor would be equal to 1.
Then a 3/5 luck rating would give a luck-factor of 0.9, which mean that any gain and loss of elo would be multiplied by 0.8 . That mean the elos will be closer from each other, and so an higher elo player playing against a lower elo player will gain more elo in case of a win (compared to atm), and will lose less elo in case of a loss. Since the game is more random, that's what we want.

Multiplying all ratings by a constant will result in no changes to that rating. It just becomes a unit conversion. 3 feet is still 36 inches, even if 3 feet is 3 units and 36 inches is 36 units (the units in this case just happen to be different even if both of them are called units.) If you don't reset the ratings afterwards and keep all current ratings you get the weird effect of everyone's ratings at that moment being inflated or deflated, depending on if the nonnegative constant was less than or greater than 1, accelerated by how high their rating was.

It should really stand out as new accounts come in having only dealt with the new calculations. This would actually have the opposite effect to what you were aiming for in your example. With the .8 multiplier, the higher rated players now have inflated ratings and should be getting pulled down with more games accordingly. The lower numerical ratings of their opposition without a corresponding reduction in their skill means the higher rated players would end up losing more points as a result, as their performance against what was once a 200 is now their performance against a 160, 400 to 320, etc.

With 1.1, if you didn't reset the ratings, you'd probably want to make a new account to take advantage of the k factor. In general, you'd want to play more games since you're underrated even if you didn't make a new account though. You would prefer not playing against anyone who had a high rating prior to the change because they are underrated and aim for the newer accounts stabilizing at those same numbers because of the new change.

This interaction-cursor is not a change of the elo factor. That cursor will before all calculations multiply all the elo by that amount, and will after the calculations divide all the elo by that amount. (maybe there is a better solution than that)
This has consequence when that value is inferior to 1, to make the higher elo player win more elo in case of a win, and lose less elo in case of a loss.

If I have X rating, multiply it by a constant A, add rating B, then divided by constant A again, I'd have (AX+B)/A, or X + B/A. In other words, you just proposed dividing the changes by the number instead of multiplying, which is just multiplying by the reciprocal value anyways.

[Romain672]

Did not expect 2 answers on that subforum Ty for answering.

2. Why should high ELO players win more and lose less against low ELO players in luck-based games, after all?

Because a part of their game will be lost by chance.
And by doing that, you compensate slightly those loss.

Either I'm wildly misreading what you're proposing, or this is really flawed. I'll tell you what I see and hopefully you can clear up any misunderstanding.

There was a typo, changed 0.8 by 0.9 on my first post.Yeah it's totally probable, I said what I think was right, but I'm not confident on it.

Multiplying all ratings by a constant will result in no changes to that rating. It just becomes a unit conversion. 3 feet is still 36 inches, even if 3 feet is 3 units and 36 inches is 36 units (the units in this case just happen to be different even if both of them are called units.) If you don't reset the ratings afterwards and keep all current ratings you get the weird effect of everyone's ratings at that moment being inflated or deflated, depending on if the nonnegative constant was less than or greater than 1, accelerated by how high their rating was.

Let's see two games. Game A got usual ratings. Game B got 50% of ratings.
Let's take two players Alice who got 200elo in game A, and Bob who got 100elo in game A.
I think in game B we can start by putting 100elo to Alice, and 50 elo to BoB.
But when the two will play together, both game will not have the same difference of rating, and so Alice is less or more favorite than Bob depending of the game, no?


But yeah I didn't propose anything to compensate the current ranking. Arena got a lot of reset, so that should be fine for it.

[Romain672]

I did an excel to see better the potential changes: https://docs.google.com/spreadsheets/d/ ... id=0#gid=0 (it's not an exact replication, but should be close)

With k-factor 20 you got Alice at 159,97elo, Bob at 166,26elo, and Cathy at 273,77elo.
If you put a k-factor at 30 (so like putting luck-factor at 1.5), you got Alice at 126,14elo, Bob at 164,97elo, and Cathy at 308,89elo.
And if you put k-factor at 13,3 (so like putting luck-factor at 0.67), you got Alice at 179,65elo, Bob at 172,29elo, and Cathy at 248,05elo.

And so on my third example, the bad streak of Alice was less detrimental at the end, they even goes above Bob in elo.

A3=B3=C3=200,0
FG columns are 1,2 five times, then 2,1 twice, then 1,3 thrice, then 3,1 six times.

[ufm]

2. Why should high ELO players win more and lose less against low ELO players in luck-based games, after all?

Because a part of their game will be lost by chance.
And by doing that, you compensate slightly those loss.

Applying that in all games sounds like a common excuse: "I won because of my skill, but I lost by chance/kingmaking/etc.".
If you want a revised rating system which factors luck elements and/or multiplayer aspects in, you should consult mathematicians instead.
For example: https://arxiv.org/abs/2104.05422

[ChiefPointThief]

2. Why should high ELO players win more and lose less against low ELO players in luck-based games, after all?

Because a part of their game will be lost by chance.
And by doing that, you compensate slightly those loss.

Applying that in all games sounds like a common excuse: "I won because of my skill, but I lost by chance/kingmaking/etc.".
If you want a revised rating system which factors luck elements and/or multiplayer aspects in, you should consult mathematicians instead.
For example: https://arxiv.org/abs/2104.05422

In sobek 2p the pirouges are random, the corruption tiles are random, the tile distribution is random, and the special tiles/characters are face down. W/ all of these added factors there should still be the same win probabilities as 2 ppl playing chess?

Are you saying that we should find a mathematician that agrees that having the same win probabilities for all games is faulty and then bga would consider changing it instead of addressing this issue to bga? I didn't understand that part.

[ufm]

Are you saying that we should find a mathematician that agrees that having the same win probabilities for all games is faulty and then bga would consider changing it instead of addressing this issue to bga? I didn't understand that part.

ELO is used in BGA not because of its precision but simplicity.
If you want a strictly better general rating system which can be applied to >1000 different games, you should consult mathematicians instead of BGA.

[ChiefPointThief]

Are you saying that we should find a mathematician that agrees that having the same win probabilities for all games is faulty and then bga would consider changing it instead of addressing this issue to bga? I didn't understand that part.

ELO is used in BGA not because of its precision but simplicity.
If you want a strictly better general rating system which can be applied to >1000 different games, you should consult mathematicians instead of BGA.

Adjusting for luck factor doesn't have to be overly complicated.
https://boardgamearena.com/table?table=573268657
Captain flip has a luck rating of 4. Im world elo leader and have a win rate of 68% but my probability vs this top 30 player is 69%. This is unrealistic for this game.
You wouldn't need 1000 different rating systems. For every .5 on the luck rating system the formula could be adjusted to lower the win probability based on players elo.

[ufm]

Again, that luck rating purely depends on the developer's whim.
For example, BGA Checkers has the luck rating of 1.
Also, simple adjustments cannot solve this whole 'ELO is flawed' debate.
There are tons of games with variants and different setups which change the impact of luck factors.

In short, the luck rating of metadata is not reliable as you expect.
And this will cause more needless confusion, like ELO 'updates' introduced in the last year.