Auction, Player Status, other changes & Plans

We were thinking to implement a standard ELO system.

The ELO system is based on this formula K x (W - p(D)) where:

• W is the result of the game: 1 for a victory, 0 for a defeat, 0.5 for a tie;
• D is the difference of ELO between you and your opponent;
• p(D) is the probability of victory considering the D difference
• K is the 'elasticity factor'. It has a value that depends on the number of games you have played. Other platforms are using 60 for your first 10 games, 40 between your 10th and 20th games, and then 20.

The ELO system is for two player games while most board games are multiplayer game. This is dealt with by considering each N player match as consisting of (N/2)*(N-1) separate two player matches between each pair of players.

We aren't planning to do a live ELO system using also on the factions, like in terra.snellman.net. The reason is that we think that the impact of faction can be mitigated by the auction system that we introduced yesterday.

Regarding how to manage dropping players. We've introduced the karma system, which should help to motivate people to finish what they decided to start ;) We already have the ability to select a "sleeping period", which is stoping the timer. This should help players to commit on games that are "compatible" with their zones. But still, if someone is dropping, we have two options:

1. we don't update the ELO for anyone in the game;
2. we do something like the 3way tie against the dropping person.

We are open to your feedback and suggestions!

I had just finished writing about the problem of dropping players that the karma system popped out of nowhere... everything moves so fast, we do really live in the future.

Thanks, this is brilliant, I think it'll really contribute to solve the problem. I still think it would be better not to factor games where someone has dropped in the ELO, but maybe other people who already have experience in this type of ranking system know better than me.

I also think it'd be nice to have something like average final score or average final position for each player. I mean, in GP many different outcomes are possible, sometimes you score 190 and you're still second, maybe by only 2-3 points, sometimes you're last at 120 and the first player overscored you by 80 points. I imagine it would be difficult to create an ELO system that is able to account for all these differences - that'd involve some complex maths I guess - but maybe show average scores or average position independently from the ELO? Don't know. Just an idea.

@Molfo The score difference impacting the ELO change is a good point!!

Since unlike Chess, we have an objective measure of "how close" the match is.

It's especially true in four players games, for example if the scores are 130 167 168 200, the impact of player 2 "losing" to player 3 should be lessened.

The higher precision also can make people reaching their target ELO faster, which is important with games like GP that last a long time.

The new formula can be something like: K x (W - p(D)) x S(|δ|), where δ is the score difference between two players and S is a sigmoid function that for an average δ returns 1.

Edit:

Thinking about it,changing W makes much more sense.

Something like: K * (W(δ) - p(D))

An example function W(x) = 0.5 + 0.5 * sgn(x) * sqrt(|x| / μ), where μ is the average score difference between players (μ would change depending on if we are in a 2, 3 or 4 player game).

An interesting side effect in that scenario is that if a high ELO player wins against a much lower ELO player and the score difference is very small, the high ELO player would actually lose a few points, and the low ELO player would win a few points.

honestly i think that points difference impacting ELO makes sense only in auction based games because in normal faction selection, assuming everybody is at the same level, someone can end up in a very advantaged/disadvantaged position from the get go through no merit/fault of his own. So even though this is true in theory and in the reality of things probably skill matters a lot more, I'm not sure how fair it would be to have score difference impacting ELO

Regarding the possibility to implement different ELOs for 2-3-4 player game. Do you think this is mandatory or not?

@Babbuc49 I agree that in the "normal" setup, the difference in points shouldn't impact the ELO.

This is great news!!! I don't have an opinion related to ELO calculations, since every system has both advantages and disadvantages... but... ...since you're planning an ELO system... do you think in the future it could be possible to implement teams/clans/groups of grudgeful, competing nerds as well?

Sorry to abuse of your listening to us, but me and others would love this, so I tried to ask :innocent:

@El-Temblo : you are not abusing. We love to hear your feedback, suggestions, and ideas! Could you please elaborate more on groups?

@zuli the only reason for having different ELOs for different player counts is that once there's a ranking system and people start to care about it, someone that only plays 4p with other equally ranked players could complain about somebody else who only plays 2p and mainly plays weaker opponents therefore easily getting a very high ELO through less effort and puttin himself through a lot less risk. I've seen a lot of people complaining anout this on BGA. But still it's not of vital importance anyway, also another solution would be organizing season based tourneys since in that case competitive players would probably value a trophy more than their ELO ranking.

@coyotte508 i'm afraid you lost me at "sigmoid function", but you look like you know what you're doing so, i'll trust you on the subject. thank you as you usuale for you feedback!

as for the difference between auctioned/non-auctioned games, as babbuc knows I strongly dislike auctions in gaia poject. i'm planning to open a separate conversation to discuss the subject with whomever is interested in the topic, but in general, i don't think that the two types of games should be treated differently, ELO-wise.

PS: sorry, i forgot. I agree with el temblo, clans would be fun :D

My opinions on Elo:

• There should be one value, not separated by player count. Separating it will mean lower game counts in each category and so values will be less accurate/useful
• K value should be smaller at higher player counts (you should gain more for winning 3 2-player games than 1 4-player game)
• It should not take score difference into consideration (much easier to abuse, some setups and player counts naturally give higher overall scores than others). Also, auctions might cause bigger swings if people are bad at judging value.
• I think it's ok to have it for both auctions and not. Everyone's on equal footing in both types, so there's no reason your skill rank would be skewed in one case.

@trojanrabbit Sorry but I really don't get your second point, why should you gain more ELO when winning in lower player counts? since it's a lot harder to win a 4p game than a 2p it seems to me more fair the other way around, also that would incentivize even more what i said above about people only playing 2p games against weaker opponents just to skyrocket their ELO

@Babbuc49 said in Auction, Player Status, other changes & Plans:

@trojanrabbit Sorry but I really don't get your second point, why should you gain more ELO when winning in lower player counts? since it's a lot harder to win a 4p game than a 2p it seems to me more fair the other way around, also that would incentivize even more what i said above about people only playing 2p games against weaker opponents just to skyrocket their ELO

What I mean is that when you treat the Elo gains from a 4p game as 6 separate matches between all possible pairs of opponents, you should modify the K value to be slightly smaller. If you keep K the same then you'll gain 3x for winning a 4p game since you'll gain against each of your opponents. I've actually done a lot of research in this area and studied multiplayer ranking systems a lot. If K is 60 for 2p games, then it should be about 45 in 3p and 35 for 4p. For example, if everyone was evenly matched, you would gain 30 Elo points from winning a 2p game, 45 for winning 3p, and 53 for winning 4p. If you don't reduce the K you would get 30/60/90 which overvalues 4p games.

@trojanrabbit said in Auction, Player Status, other changes & Plans:

@Babbuc49 said in Auction, Player Status, other changes & Plans:

@trojanrabbit Sorry but I really don't get your second point, why should you gain more ELO when winning in lower player counts? since it's a lot harder to win a 4p game than a 2p it seems to me more fair the other way around, also that would incentivize even more what i said above about people only playing 2p games against weaker opponents just to skyrocket their ELO

What I mean is that when you treat the Elo gains from a 4p game as 6 separate matches between all possible pairs of opponents, you should modify the K value to be slightly smaller. If you keep K the same then you'll gain 3x for winning a 4p game since you'll gain against each of your opponents. I've actually done a lot of research in this area and studied multiplayer ranking systems a lot. If K is 60 for 2p games, then it should be about 45 in 3p and 35 for 4p. For example, if everyone was evenly matched, you would gain 30 Elo points from winning a 2p game, 45 for winning 3p, and 53 for winning 4p. If you don't reduce the K you would get 30/60/90 which overvalues 4p games.

I like Trojan's approach to setting up a balanced ELO rating. Why cant there also be more data/stats? I discussed this w my game group when we were talking about setting up a tournament.

The stats I would like to have (as well as ELO) would be:

4 Player game

• 12 points for 1st, 8 points for 2nd, 4 points for 3rd and 0 points for 4th

3 Player game

• 8 points for 1st, 4 points for 2nd and 0 points for 3rd

2 Player game

• 4 points for 1st, 0 points for 2nd (ties add points together and divide by # of players who tied)

Stats of avg points/game

Winning positions with each faction

Avg time taken/game

Win to loss ratio of games (and with each faction)

There are probably more but none come to mind atm

@trojanrabbit said in Auction, Player Status, other changes & Plans:

@Babbuc49 said in Auction, Player Status, other changes & Plans:

@trojanrabbit Sorry but I really don't get your second point, why should you gain more ELO when winning in lower player counts? since it's a lot harder to win a 4p game than a 2p it seems to me more fair the other way around, also that would incentivize even more what i said above about people only playing 2p games against weaker opponents just to skyrocket their ELO

What I mean is that when you treat the Elo gains from a 4p game as 6 separate matches between all possible pairs of opponents, you should modify the K value to be slightly smaller. If you keep K the same then you'll gain 3x for winning a 4p game since you'll gain against each of your opponents. I've actually done a lot of research in this area and studied multiplayer ranking systems a lot. If K is 60 for 2p games, then it should be about 45 in 3p and 35 for 4p. For example, if everyone was evenly matched, you would gain 30 Elo points from winning a 2p game, 45 for winning 3p, and 53 for winning 4p. If you don't reduce the K you would get 30/60/90 which overvalues 4p games.

Usually 4P games are treated like a 2P game against an average ELO of your opponents, so there's no need to apply different K or repeat Elo formulas multiple times for multiplayer games.

Anyway, no matter which system you use you should enforce activity for top rated players or they will no longer be motivated to play games in order to risk losing Elo. So you should decrement Elo of players with rating above a certain number if they don't finish a game within X days/months.

If the activity problem does come up, we can use a "decay" mechanism: displayed ELO in profile / ranking is reduced by X% depending on lack of recent activity, but the underlying ELO (used in formulas) would not be decreased.

The decay would be completely removed after a few games

I'm not sure how fair it is to drop someone's ELO for inactivity, I mean there are reasons that may cause someone to stay away from the game for some time other than just wanting to sit on top of the ranking ( also it would mean that that someone will stop playing a game he/she really likes just for that reason which seems a bit weird).

Anyway ELO ranking is very volatile by nature, so I still think that the most rewarding thing for competitive players would be to organize tournaments!

@Babbuc49 said in Auction, Player Status, other changes & Plans:

I'm not sure how fair it is to drop someone's ELO for inactivity, I mean there are reasons that may cause someone to stay away from the game for some time other than just wanting to sit on top of the ranking ( also it would mean that that someone will stop playing a game he/she really likes just for that reason which seems a bit weird).

Anyway ELO ranking is very volatile by nature, so I still think that the most rewarding thing for competitive players would be to organize tournaments!

I agree with @Babbuc49 on this.

Also, I think many of the proposals that @Robert-Shepherd was making are worth considering. Separate rankings for 4/3/2p games, and a ranking that takes into account the final position (1st, 2nd, etc.).

@zuli said in Auction, Player Status, other changes & Plans:

@El-Temblo : you are not abusing. We love to hear your feedback, suggestions, and ideas! Could you please elaborate more on groups?

Well, thanks; I'm not a true expert on clans and such, but a simple system to create and join teams would be fun (stuff like displaying [your team name] in square brackets before your nick, your know); there could be a parallel ranking for clans, nothing too complicated, a simple sum of all ELOs or an average, or whatever you want. Most important, this opens the way to a loto of different possibilities for the future.

I'd listen to trojanrabbit on ELO stuff 100%.

My only doubt is, if you have a single ranking which makes no distinction between 2/3/4p games, isn't it automatic that somebody who really likes 2p games and plays a lot of those will get a higher ELO? (simply because, on average, you should have a win ratio of around 50% when playing 2p).

@Molfo said in Auction, Player Status, other changes & Plans:

My only doubt is, if you have a single ranking which makes no distinction between 2/3/4p games, isn't it automatic that somebody who really likes 2p games and plays a lot of those will get a higher ELO? (simply because, on average, you should have a win ratio of around 50% when playing 2p).

Not necessarily, the values W and p(D) in the formula Zuli posted are usually adjusted accordingly to the number of players at the table.

What do you think about option for players to add the description of the game? For example: 'please - don't join if you make only 1-3 moves per day' 'only Friday and Monday - speed live game' etc...

I know, is not a perfect concep... But some persons don't want play with players who make 1 move / day.

@ariallito : Do you think that the time settings are not enough to understand your commitment to the game?

@zuli Thanks for reply. Right, it's enough. For you, for me... but not for all. Peoples use their telephones, they have 'online' status... and nothing. Maybe the "description" will help them to understand that this is just a game, not a date with Rihanna.

@ariallito :rolling_on_the_floor_laughing:

@trojanrabbit Do you have a more generic formula, for games with 5, 6, ... 10 players?

Maybe something like K = K * 3 / (N + 1), where N is the number of players? That would give the winner a global K of K * 3 * (N - 1) / (N + 1), tending towards a max of 3 times the elo gain. (It fits with your example: 60 for 2p -> 45 for 3p -> 36 for 4p).

@coyotte508 said in Auction, Player Status, other changes & Plans:

@trojanrabbit Do you have a more generic formula, for games with 5, 6, ... 10 players?

Maybe something like K = K * 3 / (N + 1), where N is the number of players? That would give the winner a global K of K * 3 * (N - 1) / (N + 1), tending towards a max of 3 times the elo gain. (It fits with your example: 60 for 2p -> 45 for 3p -> 36 for 4p).

Yes, that is the formula I use. It's a pretty good fit up to 5 players. Haven't done experiments with more than that.