On the wiki, I don't understand programming language, can this be translated to mathematical formulas?

http://www.vdiplomacy.com/wiki/index.php?title=Rating

Better now?

PS: Most of the math is taken from here:
http://en.wikipedia.org/wiki/Elo_rating_system#Theory

Yes, that is better, but I think there is a problem in this part:
Rr=SC1/(SC1 + SC2)
I don't know the exact problem yet, but I will look at it again later.

I'll have to look at the other two formula's later also.

Rr=SC1/(SC1 + SC2)
Describes the relation of your SCs to the SCs of your opponent.
If both have 10 SCs at the end of the game thats 0.5
If A has 5 and B has 15 it's 0.25...

Hmm... that might not be it, but there has to be something wrong in the formula, or the programming of it.

At the current ratings, and based on the formula, I have a .0000001% chance of beating Bozo. Ouch! I hope I don't have to play him 100 million times to get a win. Actually Bozo has a mathematical certainty of winning every game he plays against anyone.

Yeah, didn't you know Bozo cheats! (Just kidding Bozo!!)

Yes, that's what I was trying to say : that is certainly not an Elo rating because when you calculate an Elo, the result is 1 point for a victory, 1/2 for a draw and 0 for a defeat.

Here, in the formula 1, 1/2 or 0 are replaced by SC1 / (SC1+SC2) which is a mistake. I mean, you can calculate what you want but then, that is not an Elo rating.

Then again, an Elo rating can ONLY be used in 2 player-games.

Here is a little story that illustrates that an apparently nice and correct calculation can give erroneous results :

3 friends go to a bar and have a drink. They each give the waiter one 10 $ note. That's a total of 30 $, right ? The boss of the bar tells the waiter that the bill is 25 $. The waiter doesn't know how to share to 5 $ between the three customers and gives them back each 1 $ and keeps for himself 2 $ as a tip.
BUT then, each customer has finally paid 9 $, for a total of 27 $ and the waiter has kept 2 $. That's a total of 29 $ ! Indeed 3 x 9 + 2 = 29 ! WOW ! What happened to the 30th dollar ???

Not quite retillion:
Say its 3 players, one with an ELO of 100, one with 200 and one with 300.

If the map is 18 scs, then it is expected that:
Player A will get 3 scs
Player B will get 6 scs
Player C will get 9 scs

If Player A gets above 3, his rating will increase, if he gets below 3, his rating will decrease. For Player B its 6 and Player C its 9.

Elo works for more then just 1v1 game.

Also the $2 tip was because the cost of the drinks was $25 not $27 and so they paid $27 giving him the $2 tip. While humans can easily make that mistake, a computer will not. That said there is such think as typos in a code, a computer follows the rule of GIGO

Oli,

You are using similar, but not identical, terms as the wiki, and I think it caused you to miss some. I went back to the original wiki and re-wrote the formula's using the original terms, and added a missing formula. Try these:

Initial true strength:
RA=Player A true strength
RB= Player B true strength

Intermediate term used to simplify the math:
QA=10^(RA / 400)
QB=10^(RB / 400)

Expected Results: (you have only one of these)
EA=QA/(QA + QA)
EB=QB/(QB + QB)

Actual Results: (Not from the original wiki)
SA=SC1/(SC1+SC2)
SB=SC2/(SC1+SC2)

Revised true strength:
R'A=RA+32*(SA-EA)
R'B=RB+32*(SB-EB)

For points won, I think this would be the only change:

Actual Results: (Not from the original wiki)
SA=PW1/(PW1 + PW2)
SB=PW2/(PW1 + PW2)

For Win/Draw/Survive/Defeat, I think this would do it:

Check all combinations:
IF S1='Won' SA = 1; SB=0 (4 combinations possible)
IF S1='Drawn' AND S2='Drawn' SA = 0.5; SB=0
IF S1='Drawn' AND S2='Defeated' SA = 1; SB=0
IF S1='Survived' AND S2='Won' SA = 0; SB=1
IF S1='Survived' AND S2='Drawn' SA = 0; SB=1 (is this possible?)
IF S1='Survived' AND S2='Survived' SA = 0.5; SB=.5
IF S1='Survived' AND S2='Defeated' SA = 1; SB=0
IF S1='Defeated' AND S2 ='Defeated' SA = 0.5; SB=.5
IF S1='Defeated' AND S2<>'Survived' SA = 0; SB=1 (you had a typo here)
IF S1='Defeated' AND S2<>'Drawn' SA = 0; SB=1 (New combination)
IF S1='Defeated' AND S2<>'won' SA = 0; SB=1 (New combination)

Oh, and one more ...
IF player1= "Devonian" SA=1.

Devonian, I noticed a typo in your last post, for future reference its spelled Fasces349 not Devonian

@Retillion:The WIn/Draw/Lost-score is still strange but uses 1=win, 0.5=draw 0=loss formula.
There must be an error somewhere else...

To check the formula I'll rate only this game: gameID=12010 later today with every player has a base-rating of 1500 and check the results.

That would be good. How about also doing it with a game that ended in a draw.

Premise: I have read the related material
http://en.wikipedia.org/wiki/Elo_rating_system
https://sites.google.com/site/phpdiplomacytournaments/theghost-ratingslist
http://www.vdiplomacy.com/wiki/index.php?title=Rating

I do appreciate the work done/in progress, but I think we’re unnecessarily making it difficult.

The weak point here and source of countless discussion is the way the “Edif” is defined.
Compared to the game typology, it’s not clear what “expected result” and “real result” are supposed to represent. I understand the math, but not the logic behind those assumptions. Yet it’s not clear what those “result” concepts are in words definition. Translating those uncertain word definitions into algebraic definition looks to me as an hazardous mental operation. It’s not chess, where the word “result” is clear since we have either a victory, a loss or a fairly unlikely draw. In chess translating “result” in a number between 0 and 1 makes sense. In diplomacy there are thousands of possible game results.

I am still favorable to Devonian’s initial suggestion, which in retrospect is even simpler than the Ghostrating definition.
Because of this, I’m spending one more coin to sustain that proposal (Devonian, did you change your mind? Don’t waste this support!):
During each game, instead of an Elo-differential, we have a skill-pot to divide running in parallel to a Dpoints-pot.
The pot is composed by the sum of users’ bet, which is not arbitrary, being it a fixed % of the current skill rating (say 5%). This happens regardless the D-point arbitrary bet. So everyone pays in advance in proportion to the own measured skill…
…and we don’t need to elaborate a questionable “Edif” in order to split the pot. The pot is divided accordingly to the game style, PPSC or WTA, using the current pot distribution system.
What’s the cause why this thread was started? Dpoints are not an accurate measure of skill.
Why? The main reasons are because the game-bet is arbitrary, because currently beating a champion is worth the same as beating a noob and because the points are re-inflated when users drop below 100.
I think this system overcomes many problems of numerical interpretation, first of all the word “result”, either “real” or “expected”.
This system will reflect the skill distribution criteria that have actually been used by the players during past games.
This skill-distribution system is robust, simple and already exists... it’s the current one.
Nobody runs out of points, since the skill-bet each time is 5% of your skill-points. There’s no need for skill-points inflation.
If we use an Elo-based formulation we have to tune the coefficient 400, the coefficient 32, the formula of the “real result”.
Using this proposal instead the only coefficient we have to tune is the fixed skill %, assumed 5% each game: make it smaller if you want to slow down skill-rating change after a match; make it bigger if you want to speed up skill-rating change.

Decima,

"I am still favorable to Devonian’s initial suggestion, which in retrospect is even simpler than the Ghostrating definition.
Because of this, I’m spending one more coin to sustain that proposal (Devonian, did you change your mind? Don’t waste this support!): "

No, I didn't change my mind! I also think my original suggestion was much easier. And I thought that was going to be how it was implimented. I was sad to see that the first iteration was not how I suggested.

However, when it appeared that my suggestion was not the direction it was going, I figured I would at least make sure the math was right. I think the math behind it is complicated, and if done wrong, can give wrong results. It is also hard to conceptualize since it uses high level exponential calculations using fractions and simplified normal distributions.

If Oli is willing to go back to my original suggestion I would be very pleased! It is much simpler, it is easy for everyone to understand, and it makes sense. I also think it should be rather easy to program since the math is very basic.

One big advantage is that everyone will know exactly what they will risk by beginning a game. (Per your example, 5% of their skill-points). And, they can rather easily calculate their potential gain under various winning conditions.

For reference, my proposal was on 1-9-2013, and is on the first page of this thread.

I am a little confused about:
Algorithm:
Q1=10^(E1 / 400)
Q2=10^(E2 / 400)

Does that not mean that if I were E1, and someone with, say, 1600 Elo was E2, Q1 would be 10^10 whereas Q2 would be 10^4? Therefore, Q1/(Q1+Q2) would essentially just be Q1/Q1, as Q2 would be neglible in comparison...

Sorry if I've missed something here - I'm not in maths mode at the moment - but it seems a little odd.

Right.
Using 400 as coefficient means: "It then follows that for each 400 rating points of advantage over the opponent, the chance of winning is magnified ten times in comparison to the opponent's chance of winning."

Captain,
Yes. That is why the formula is wrong.

I did some test with a different k-Faktor.
As in the wiki stated I used a factor of 32, but it looks like most organisations actially use a k-factor of 10. Changing this to 10 gives the result you can see now...
(And I will give Devonians algorithm a try if I have some more time too)

BTW: Even now with the altered k-factor I think we can agree that a rating based on SC count at the end of the game is not that meaningful.
I like the Won=1, Draw=0.5, Lost=0 most (And this is what's used in the last row), as it's easy to understand too.

Spreading the rating based on pointsWon is roughly the same, but it's not that elegant.

Oli,

Did you change the formula's also? The formula's are the real problem.

With the new K-factor, I now have a 0.0002% chance at beating Bozo, which means I will need to play him 500,000 times to get a victory! At least Bozo does not have a mathmatical certainty of winning every game against every player, but his expected results are still too optimistic for him. (The reason the odds have changed is because the formula is adding less error in each calculation, but unless the formula is changed, there will still be error.)

Correction. Based on the expected results, he still does have a mathematical certainty of beating every player in every game he plays.

Question:

I fully admit I haven't followed much of this conversation once it got into algorithms and the like, but from what I gather, there's still issues with how the system is calculating things. Is this so?

Because if not, it seems odd that a player with 21 defeats, 5 wins, 18 draws, and 13 survives would be ahead of a player with 3 defeats, 4 wins, 22 draws, and 0 survives. 18 less defeats, 1 less draw, 4 more draws, and 13 less survives (which if I understand right are considered "losses") is a lower rank?