ELO and Karma

[KDLadage]

As someone with a rather strong mathematics background (and as a person with a best friend who is a Doctor of Applied Mathematics), I would like to make two suggestions.

ELO
In games with more than 3 players, the adjustment for ELO should be the sum of the greatest gain and the greatest loss. So, if I am in a 5 player game and I some in third place, I would not have losses from two players and gains from two players. It should just be the greatest gain I have added to the greatest loss I have in that game.

The system, as it currently stands, creates swings that are way, way too large.

KARMA
The Karma system is alright, I suppose, but the fact remains that the system has a lot of down without a lot of up. I suggest something like this:

Base Karma is 50. Minimum is 0 and maximum is 100

The ranks of Karma could be:
[*] 0-10 --- Abysmal
[*] 11-20 --- Terrible
[*] 21-40 --- Poor
[*] 41-60 --- Fair
[*] 61-80 --- Good
[*] 81-90 --- Great
[*] 91-100 --- Superb

When you are between 21-80, each game in which you had no time issues grants you +2 Karma.
When you are above 80 or below 20, each game in which you had no time issues grants you +1 Karma.
Any game in which you had time issues without being expelled, you lose -1 Karma.
Any game in which you had time issues and were expelled, you lose -5 Karma.

Karma should not be seen as a percent -- it isn't.

That said, after the Karma rating, a Karma percent could be listed where that value is the percentage of games where you have had no time issues.

Thus, a good player might have something that reads: Karma 83 (99.3%) Great

[Meeplelowda]

Interesting idea on karma. I might vote for it if you submit it for consideration.

As for Elo, you begin with an argument from authority (including touting a friendship with a mathematician?!), and then provide zero content based on this purported expertise. You could very well have said "this works because I know math. Trust me bro." It probably won't surprise you that there are many people on BGA with rather strong mathematics backgrounds, including at least one professional mathematician. They will probably not be impressed if you don't show your work.

Given your rather strong mathematics background, you might be interested in this 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. ...

[FSKFSK]

Elo was designed for a game like chess, where a substantially stronger player wins almost all the time.

Elo is not suitable for luck-based games. There are games on BGA where a player who knows the basic strategy will win at least 45% of the time, and skill only affect the remaining 10%.

The karma system is awful. You can time out of a tournament game for -4 and then play a couple of quick regular games and recover the loss.

Tournament karma should be tracked separately from regular karma. If someone has a habit of running out of time in tournaments, there should be an option for tournament organizers to block them. For example, if someone has timed out for more than 3 tournament games in the past 3 months, I want to have an option to ban them from my tournaments. I would allow for forgiveness of one timeout for every 10 tournaments finished with zero timeouts. (tournaments, not individual games) Also, timeouts older than 3 months expire just like all other karma penalties, so a player always has a chance to recover their good standing.

[KDLadage]

"As for Elo, you begin with an argument from authority (including touting a friendship with a mathematician?!), and then provide zero content based on this purported expertise."

My apologies. The point in bringing these things up was not to begin with an argument from authority, but to explain why this is of interest. My friend (Mike) and I have discussed this a few times. I do not believe that the current ELO calculations need to change, just the additive nature of them.

If I came across as arrogant or truly arguing from authority, please accept my most humble appologies.

[Meeplelowda]

My apologies. The point in bringing these things up was not to begin with an argument from authority, but to explain why this is of interest.m authority, please accept my most humble appologies.

In that case, welcome to the fold.

One thing I need clarification on is what happens if you finish last in the 5-player example you mentioned? Do you only lose Elo for the matchup that produces the biggest change? If so, won't that negatively impact the use of Elo as a measure of skill? For example, if a high-rated player loses to four low-rated players, the adjustment from just that one matchup doesn't really capture what happened.

[KDLadage]

No, I do not believe it would negatively impact the ELO and its measure.

Consider: in the ELO system used for chess, an 8-point swing is a large shift from one game. In this system, as it is now, I have had 25+ point swings from a single game. In the chess system, the ELO rankings get into the thousands. Here, we are in the hundreds.

I think that if a high rated player looses to four low rated players, then this was likely a fluke and it should not result in some 30+ point shift in their rating.

But that is just my view.

[BarnardsStar]

Consider: in the ELO system used for chess, an 8-point swing is a large shift from one game. In this system, as it is now, I have had 25+ point swings from a single game. In the chess system, the ELO rankings get into the thousands. Here, we are in the hundreds.

Elo is a generalized system with a few parameters that need to be applied to get a specific instance. One of the most important parameters is the "k-factor" - the system says you had a 35% chance to win and you did win, so you get an Elo adjustment of 0.65*k. Around here, k is 20 unless you are in your first twenty(?) games on the site. Don't quote me but my recollection is, it's 60 for the first 10 games, 40 for the next ten games, and then you settle at 20. Something like that.

Whereas FIDE ratings use a k-factor of 40 for your first 30 competitive matches, 20 thereafter, unless your rating has ever exceeded 2400 in which case your k-factor is 10 (even if you drop below 2400 later). So between two grandmasters, yes, 8 is a very big swing. It would be the result of an upset between two players with an Elo diff of 240. Between two players who have never exceeded 2400, it would be the expected result between two players with an Elo diff of 70.

Whereas, yeah, you've had swings even bigger than 25 points, like here: https://boardgamearena.com/table?table=896968169 -- it was the 9th time you'd played the game, and so your k-factor was 60. Huge swing, but that's the point. The k-factor (both here and in FIDE) is higher to boost you quickly to the rough Elo range you should be at.

But do note that the Elo change isn't just unadulterated sums of the wins and loses. There is a reduction factor at play, and for a 4-player game of Love Letter it's ⅔ the Elo from each match that you would have gotten were it just a head-to-head. This is intended to address some of your very issues, but it still recognizes that beating 2 people is harder than beating 1. It's not twice as hard, but it is harder.

I think that if a high rated player looses to four low rated players, then this was likely a fluke and it should not result in some 30+ point shift in their rating.

Surely any loss to a low-rated player (more than, say, 300 Elo below you?) must be a fluke. Should we discount all "flukes"?

[Meeplelowda]

I think that if a high rated player looses to four low rated players, then this was likely a fluke and it should not result in some 30+ point shift in their rating.

Why do we assume that it is a fluke as opposed to the more natural interpretation that the high-rated player is simply overrated?

[KDLadage]

Ah. I see your points.

I will have to think about this for a bit. But this discussion has me feeling more comfortable with the way it works.

Thanks for engaging with the topic, and being patient with me. Very mush appreciated.