I'm not sure I understand what you mean Fasces.

Do you mean that to beat someone rated 10 times better (on 1v1), should reward you as much as beating all players of inferior skill on a 11-player map? If so, I agree in princple. (Not necessarily the ratio's you suggest.) The ELO system rewards beating the 10 inferior players, 10x more than beating the highly skilled player.

Similarly, shouldn't beating a player with much greater skill (1v1) reward you more than beating a player with inferior skill?

The system I proposed addressed both these problems. It also addressed the problem of having players with only a few games have unreasonably high rankings.

I see some value in the ELO system, but it has significant drawbacks. I would like to see it alongside the system I proposed, if that would be possible.

Playdip just got a new ranking system. Someone could go over there and ask an admin nicely how it works.

Ditto Devonian. I'd like to see his bet 5% skill points idea implemented as well.

Anyone followed up on goldfinger's suggestion? I don't have an account there so I'd be a noob asking the question and be less likely to get a serious answer.

Could the current ranking system be updated? I have just drawn 4 games in short succession and I would be interested in seeing how much of an effect it has had.

*Current ranks, even. That is to say, the algorithm run again so it takes into account more recent games.

CM, it's a draft. A preliminary algorithm...

I know, but I would like to see how the scores adjust with time. It would be handy for everyone to know how much they adjust in case this is (and also to decide whether this is) the system that gets implemented.

Ok, it’s been a boring rainy sunday, so it’s time for an algebraic post:

I’ve kept the Elo-based structure and expanded it into a multiplayer one. I got rid of the “decomposition into duels” idea, which I think is ill-posed. This way we can avoid to enter in debatable comparisons like “IF S1='Survived' AND S2='Defeated' Rr =…” and so on. For example, a classic game is treated as a single 7 players game, not as a matchup of 21 duels.

With this algorithm each player has 1 single expected result, 1 single real result, 1 single equation in order to evaluate the net gain.

I update the formulas here: http://imgur.com/pBFu0Lv
It may look complicated at first glance, but actually it’s not.

I’ve separated the real results criteria whether the game is WTA or PPSC. I think that keeping this distinction is important, especially if we’re going to make a retrospective skill rating.

In order to keep the analogy with the system proposed by Oli, the k constant is to be set k=15 and the function f(n)=(n-1). I’ve added an optional g(players’ average skill rating) function, value around unity, in order to take into account the average skill per player inside a game: however, I’m not sure if this last g function makes sense in an Elo-based algorithm.

Devonian,
don’t worry, I’m not abandoning you. I still have the suspect that your formulation is better; especially when we’ll have to discuss how to handle exceptions like CD, take-over, concede and so on…

Nice. I'll check this asap.

One question: Does 1 equation mean if you are rated 1000 and are playing against a 500 and a 1500 player your chances are 0.5? Because that's clearly not the case.

In the meantime I did some experiments with the survives (if there is a winner) to take the SCs gained into account. Win-> 1.0 against all
Draw -> 0.5 with each draw, 1 against all other
Survived -> 0.X (where X is the SC-difference) with all survived, 1 against Defeated/Resigned
Defeated/Resigned -> 0.5 with all Defeated/Resigned.

This makes a 2-way draw worth more than a 4-way draw, and a high SC-count in survived better than a low.

To Oli’s question:

Per hypothesis: 3 players equally rated -> each one has expected result of 0.333.

In your example: 3 players rated a500, b1000 and c1500 (that means an absolute noob, a normal person and a diplomacy genius in a 3 players game) gives as expected results:
Ea = 0.003
Eb = 0.053
Ec = 0.944

Oli -

Does this: Survived -> 0.X (where X is the SC-difference) with all survived, 1 against Defeated/Resigned

apply to all games? Or just PPSC games? Or how would it work? Because obviously in WTA games, a survive = defeat. IMO a survive should always equal a loss since you let someone else win, but I can see how in PPSC games you can make the argument that it's better than a loss.

A question then: PPSC Classic game. Final count: 18, 15, 1. Winner gets 1, 1 against the other two. Player with 15 gets what against the player with 1? Is it capped at <0.5? Because shouldn't a survive always be worth less than a draw?

I think Decimas equation is the best suggestion so far

I'm noting that with the current ranking method, I don't rank in the top 150, and what I seem to lack that the top 150 have is sheer number of wins (most of which, many top 150 members have accrued by playing 1v1 games with other top 150 members which would, as I expect, inflate their rankings by sheer number of games they have played with other top 150 members). Once again, I'm not sure with the wide range of number of players we have across variants that Elo's system adapted for multiplayer would work well here to compare across play styles. Larger multiplayer games seem to inadvertently be penalized more heavily. Since I play primarily large variants and have only ever played one 1v1 game. Imo, my play preference shouldn't compromise my ranking as is apparently the case.

Also are the 'by variant type' rankings working? Is it possible to have an option to sort by all non-1v1 games for comparison (and confirmation of my suspicions)?

@Fasces,
I think not :-)
my suggestion solves the 1vs1 matchup oddities, but has still several problems to overcome.

@Leif.
The problem with the “1vs1 matchup” formulation, is that even with a survived result in a multiplayer game, you can score multiple “separated victories” or multiple “separated draws” compared to other players in the game. Even with a defeat you still can score “separated draws” compared to any other defeated player.
So it’s possible, if you had the misfortune to be defeated in a couple of WWIV games, that you’ve been overly penalised.

Leif,

It's not that it penalizes players of large games, it {over} emphasizes wins. For example, Grace and Retillion are ranked high with only large games.

A win is also defined as getting a draw vs another player who gets a defeat. However, between the drawing players, a draw may translate into a win or a loss depending on the relative skill of the players. So, your 44% draw rate (which implies high skill) translates into fewer wins, and lower ranking. So, I agree that this might be an issue.

Also, the logic about playing top 150 members is not entirely accurate, since one top 150 would decline an equal amount as the other increases. It would push one higher, but the other lower, which it should do. But, again, the emphasis is on winning.

I like it more because it solves the difference in play balance respect to map size.

I note that selecting a variant in the drop down list for ratings doesn't change anything...

@DC:
What does the f(n) in "k * f(n) * [Ra->Ee]" mean?
or the g(WDLi) in the next function?

I tried your formula. Another question:
Example:
Player1: Rating: 2000
Player2-4: Rating:1500
In PPSC PlayerA should take 85% of all SCs to _not_ loose any points, but the game is over after he reaches 50% (Winning condition).

PS: The list is useless at the moment. It does represent random values.

You can check my Excel here: https://dl.dropbox.com/u/86746736/Rating-Tests.xls

constant k=15, “n” is the players number and function f(n)=(n-1)

In order to keep the analogy (total points distributed) with your previous formulation: on a player perspective a duel can move +/- 15 , a classic can move +/- 90 , a WWIV can move +/- 510 .
Those point ranges are the mathematical theorical limits. Actually using common sense user ratings those limits are significantly reduced.
The function g(ratings) … forget it. I don’t think there’s the need of that further function

Oli… Bingo!
The biggest problem between PPSC Diplomacy and an Elo-based formulation (yours included if you try to include PPSC awards) is the Real Result contradiction: in most of cases the standard win condition is just above 50% of SC possession…. While IF a great player faces a small number of poor opponents, the great player’s Expected Result can be above 50%... so in this case the great player has no way to outperform his expected score through his Real Result.

This happens when the skill difference between the most skilled player and ALL the others players in-game is high, so, most likely, in small maps.

Yes, we could avoid PPSC for duels, but the problem remains for 3-4-5 players variants.

A negative net gain is not certainly what we expect from a solo… on the other hand, I wonder what skills a 2000-ranked player can learn playing with a bunch of 1500-ranked players: I remind that +500 mean 12.5 TIMES more skilled.

This reminds me on the GhostRating.
In fact a percentage of 85% does not mean he should get 85% of all SCs, but has a chance of 85% to get the SCs necessary to win (eg. 18).
Another problem is the end result.
A player rated 1500 playing 3 1800 players and getting 2nd
1st. 18SC, 2nd=13SC, 3rd=8SC 4th=0SC
The 2nd gains 3 . Thats the same result as is he lost to a 1800 rated player 18 to 13 SC in a duel.
(I've updated the Excel)

PS: Sorry, did see your explanation of the f(n) too late. This would change my example a bit. (it didn't use the f(n) to change the k-value)

nevermind. the essence is the same. Nevertheless it's just a multiplicative factor.
We may substitute what I called "SC%", board SC % possession, with "VC%" , victory condition % possession. Maybe this would work better. I still have to think at it. We may have problems with the final "zero sum", though.

Did you check the GR? It really looks like what you want to accomplish.
https://sites.google.com/site/phpdiplomacytournaments/theghost-ratingslist

I'll talk to Alderian (host of the GR over at webdip) and zultar later this week.

Yes I studied it when it was mentioned at the beginning of this thread, but some passages are not clear to me. Apparently they don't use the exponential formulation. And apparently there's a contraddiction in the "V" funcion intent.

*function*