New players' Ghostrating=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)=(1Ap)*(A1*Ap/(1A1)+A2*Ap/(1A2)+A3*Ap/(1A3)+A4*Ap/(1A4)+A5*Ap/(1A5)+A6*Ap/(1A5))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*(ResultExpected 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*(ResultExpected 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)=(1Ap)*(A1*Ap/(1A1)+A2*Ap/(1A2)+A3*Ap/(1A3)+A4*Ap/(1A4)+A5*Ap/(1A5)+A6*Ap/(1A5)) 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*(ResultExpected 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*(ResultExpected 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.
