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 Post subject: Ghost-rating
PostPosted: Wed Feb 04, 2009 7:35 pm 
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Joined: Tue Aug 26, 2008 8:46 pm
Posts: 249
I am making an attempt to finally finish the Ghost-rating system, getting everything actually right.

The method I am using at the moment is by no means a long way off what I will be settling upon, so I have written it up, and am positing it here for checking. I am at present just checking that the system makes sense in terms of accuracy, and cannot be improved in that. Then, when I am happy that the formula is right, and we understand what it does with ratings, we can start discussing its suitability for the site.


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 Post subject: Re: Ghost-rating
PostPosted: Wed Feb 04, 2009 7:35 pm 
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Joined: Tue Aug 26, 2008 8:46 pm
Posts: 249
New players' Ghost-rating=100 This is arbitrary, but a power of 10 as the starting point is neat, and any higher and the ratings start being too long to easily remember, any lower and you would need decimal places to give a proper rating

To Calculate New ghost rating of player p against players 1, 2, 3, 4, 5, & 6:

1.When player p joins the game:
a) New Game:
T,Mp,M1,M2,M3,M4,M5,M6,Sp,S1,S2,S3,S4,S5,S6=0,1,1,1,1,1,1,1,0,0,0,0,0,0,0

b) CD takeover:
Mi= SCi*7/34, Where SCi= Number of SCs held by player I, for all I (ie i=p,1,2,3,4,5,6)
T,Sp,S1,S2,S3,S4,S5,S6=0,0,0,0,0,0,0,0
T= Number of turns, Mi= Multiplier for player i (so a weak CD would give a multiplier of less than 1, so that the expected result is lowered), Si is the Sum of the ratings of player i for each diplomacy season (so that Si/T is the average rating)

2. Each "Diplomacy" turn/season
T=T+1
Si=Si+Ci, for all i, Where Ci= Current rating of player i. Ci=0 if player is in CD.
This is just maintaining T and Si as described above

3. On falling into CD:
a) PPSC
Result=(SCp/34)-1
This is essentially the strength of the position (SCp/34), minus a penalty for CD (-1)
Put Ri=Mi*Si/T Effective rating, or, in other words, rating adjusted for the position given.
Put Ai= Ri/(Rp+R1+R2+R3+R4+R5+R6) Gives a relative rating, simpler for calculation
Put (Bp;1,2,3,4,5,6)=(1-Ap)*(A1*Ap/(1-A1)+A2*Ap/(1-A2)+A3*Ap/(1-A3)+A4*Ap/(1-A4)+A5*Ap/(1-A5)+A6*Ap/(1-A5))Notation to simplify the expected result formula
Expected Result= (18*Ap + 16*(Bp;1,2,3,4,5,6)/((Bp;1,2,3,4,5,6)+(B1;p,2,3,4,5,6)+(B2;p,1,3,4,5,6)+(B3;p,1,2,4,5,6)+(B4;p,1,2,3,5,6)+(B5;p,1,2,3,4,6)+(B6;p,1,2,3,4,5))/34The expected result= (18*Chance of winning (in accordance with WTA)+ 16*Expected Result for second place)/34
Delta Rating = (Sp+S1+S2+S3+S4+S5+S6)/17.5T*(Result-Expected Result)(Sp+S1+S2+S3+S4+S5+S6)/17.5T Gives us the value of V in our equation. The /17.5 keeps the average game's V as 40, which is what I have used since the first tests. There is room for a debate as to whether V should be higher or lower than this, which is one I would want to have, because it is very much a social factor. We have this to make sure that top players don't have to play hundreds of games to get a realistic rating. It also means that no matter who you play, the expected change in rating (given a certain "real skill" and certain rating) will be pretty even, in accordance to the models. I have another justification, but it is pretty messy to write up. I might be able to make a very much more complicated one, tailored specifically to PPSC, but it would only make life more confusing/difficult.

b) WTA
Result=(SCp/34)-1
Put Ri=Mi*Si/T
Expected Result= Rp/(Rp+R1+R2+R3+R4+R5+R6)
Delta Rating=(Sp+S1+S2+S3+S4+S5+S6)/17.5T*(Result-Expected Result)
Result idea is the same as with above, because it is not yet the end of the game, obviously, so we are looking a strength of position rather than actual result. Penalty as before. Expected result is the standard I have always used, and New rating formula is the same as for PPSC.

4. On completeion of game
a) PPSC
Result= 1/n for n way draw, SCp/34
Put Ri=Mi*Si/T
Put Ai= Ri/(Rp+R1+R2+R3+R4+R5+R6)
Put (Bp;1,2,3,4,5,6)=(1-Ap)*(A1*Ap/(1-A1)+A2*Ap/(1-A2)+A3*Ap/(1-A3)+A4*Ap/(1-A4)+A5*Ap/(1-A5)+A6*Ap/(1-A5))
Expected Result= (18*Ap + 16*(Bp;1,2,3,4,5,6)/((Bp;1,2,3,4,5,6)+(B1;p,2,3,4,5,6)+(B2;p,1,3,4,5,6)+(B3;p,1,2,4,5,6)+(B4;p,1,2,3,5,6)+(B5;p,1,2,3,4,6)+(B6;p,1,2,3,4,5))/34
Delta Rating = (Sp+S1+S2+S3+S4+S5+S6)/17.5T*(Result-Expected Result)
Result is as currently used, the Expected result is the same as PPSC with CD, for the same reasons, Similarly for New rating formula.

b) WTA
Result = 0 for loss, 1 for win, 1/n for nway draw
Put Ri=Mi*Si/T
Expected Result= Rp/(Rp+R1+R2+R3+R4+R5+R6)
Delta Rating = (Sp+S1+S2+S3+S4+S5+S6)/17.5T*(Result-Expected Result)
Result is as currently used, the Expected result is the same as WTA with CD, for the same reasons, Similarly for New rating formula.

EDITS: Adding justifications.
Edits: 05/07/09 Changing to give the Delta Rating, to be added to the current rating.


Last edited by TheGhostmaker on Sun Jul 05, 2009 8:10 am, edited 6 times in total.

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 Post subject: Re: Ghost-rating
PostPosted: Wed Feb 04, 2009 11:23 pm 
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Joined: Sat Sep 27, 2008 12:00 am
Posts: 44
If you have time, It would greatly help if you would comment your pseudo-code at least explaining what is the goal you tried to achieve in each section as - while one can surely make the effort to follow the flow of calculations - it is not always clear what is the "logic" behind them. :)


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 Post subject: Re: Ghost-rating
PostPosted: Sat Feb 07, 2009 9:38 am 
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Joined: Wed Jan 28, 2009 3:08 pm
Posts: 6
Shouldn't V change depending on the rating of the players? I mean, the weaker the player the easier it is for him to improve, so his rating should change more than that of an expert player.


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 Post subject: Re: Ghost-rating
PostPosted: Sat Feb 07, 2009 11:51 am 
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Joined: Tue Aug 26, 2008 8:46 pm
Posts: 249
I have made the formula for V as it is so that if you have a player with rating x, skill equivalent to a rating r, against players whose ratings sum to k, on average the new rating is the same.

This formula for V makes it so that the better players get roughly the same % change as the weaker players, whilst remaining zero sum.

As for weaker players changing more than stronger players, they do indeed gain more from winning a game than a stronger player, because of the expected result part.


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 Post subject: Re: Ghost-rating
PostPosted: Sat Feb 07, 2009 3:18 pm 
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Joined: Wed Jan 28, 2009 3:08 pm
Posts: 6
I see; what do you mean exactly with zero sum? That the sum of the ratings of the players after a game is the same as before?


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 Post subject: Re: Ghost-rating
PostPosted: Sat Feb 07, 2009 3:34 pm 
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Joined: Tue Aug 26, 2008 8:46 pm
Posts: 249
That exactly. Being zero sum makes sure that there is no inflation/deflation, and so avoids penalising players who play more/less or started earlier/later or did/didn't have breaks for holidays/exams etc.


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 Post subject: Re: Ghost-rating
PostPosted: Sun Feb 08, 2009 1:21 am 
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Joined: Wed Jan 28, 2009 3:08 pm
Posts: 6
If it's zero sum there is inflation. New players = inflation, as they get 100 points. It could be interesting to find out the growth curve and add some deflation to compensate at least a bit.


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 Post subject: Re: Ghost-rating
PostPosted: Sun Feb 08, 2009 9:06 am 
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Joined: Tue Aug 26, 2008 8:46 pm
Posts: 249
Inflation occurs when the average number of points increases, rather than just the total number of points.


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 Post subject: Re: Ghost-rating
PostPosted: Sun Feb 08, 2009 2:30 pm 
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Joined: Wed Jan 28, 2009 3:08 pm
Posts: 6
Sorry, you're right.

I still have a remark. Weaker players improve with time, so we should expect all the ratings to approach the starting value over time, shouldn't we try to avoid this?


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