No, yebellz. That only affects the distrobution of the pot. Ypu still contribute the same amount as you would in WTA: 2/35th of your curremt GR.

So in your new rating system where would I be compared to where I am now. On the fun-o-meter I use I'm #$%+1

The way you describe the CD takeover bonus seems broken to me. Surely the starting SCs and the # of other people in the game should be taken to account?

@TMOW, I'm not exactly sure what you are saying. Let's say a game has a 10 center country that is in civil disorder. If you buy into that position, you are putting in enough dip points that you'll have contributed 10/34ths of the pot. If you then get a three way draw, you'll get 1/3rd of the pot which is slightly more than 10/34ths.

But the ghost rating calculation doesn't know that you bought into a 10 center position. It thinks you started out with the 3 or 4 centers that countries start with. So even though you had little risk, assuming you bought in knowing no one would be able to solo, you get full credit for a 3 way draw.

@yebellz, I was not looking at the code earlier, but have it in front of me now. (Unsurprisingly it looks like the memorized version I have in my head.)

The perl code provided to me by Ghost did not implement a maximum result of 18/34ths, so my java version does not either. I do not know if that maximum was lost on the conversion from Excel to perl done by who I can't remember now, or if it was never actually implemented.

In any case, even with "chance of winning" + "chance of surviving" being less than 1, it is still possible for it to be more than 18/34ths. (But only on Classic if you are MadMarx playing a bunch of new players.)

If I get a chance, I'll run the numbers on what someone's expected result is whose rating is 700 when playing six players whose ratings are 100 each.

From those of us who are merely mathematically competent, let us state our admiration for those of you who were probably damaged in the womb and are freekin' mathematically and technologically brilliant. Hopefully you are lacking in some other skill set to balance it all out. At any rate, thanks for creating this community :)

I enjoyed mathematics to some extent in school, but logic is my passion. That's why I'm a computer programmer and not an accountant.

If it helps, yes, with my passion for logic, you can guess that I'm not so great with women. Or men for that matter. Or dogs. Cats are good though.

@Draugnar, yes, (as I mentioned earlier) for WTA games, the GR simplifies to down to:
1) Each player pays 2/35th of the GR into a pot.
2) That pot is split according to the WTA rules (a winner would get all of it or each d-way drawer gets 1/d of it, and losers get nothing).

The way the calculations are presented instead casts this as:
change in rating = V*(actual result - expected result), but when you simplify the equations for WTA you get the above described behavior, since V = (sum of initial ratings)*(2/35), and expected result = initial rating/(sum of initial ratings) . Hence, each players change in rating simplifies to:
change = (sum of initial ratings)*(2/35)*(actual result) - (initial rating)*(2/35)
so it's equivalent to each player contributing (initial rating)*(2/35) into a pot, and then splitting that pot according to the WTA rules (where actual result is equal one for a solo, 1/d for a d-way draw, and 0 for a defeat or survive).

However, Alderian and I were specifically talking about the PPSC solo adjustments, wherein I was making the point that the formulas, as explained on the webpage:
http://tournaments.webdiplomacy.net/theghost-ratingslist
would imply that with the way expected result is calculated, no player can lose points for winning.

For PPSC games that involve a solo, one does not simply contribute 2/35th of one's GR into a pot that is split according to PPSC rules, since doing so would result in conditions wherein a player with a ridiculously high ranking could actually lose points when winning against players with much lower rating, because the actual result is at most 18/34 (for classic) which could be less than the relative fraction of the pot that the highest ranked player has contributed. Apparently, Alderian has confirmed that the current GR code actually does not max it out at 18/34, which would allow players to needlessly extend a game in order to go for overkill (taking more than 18 SCs at the point of victory) in order to maximize their SC gain from a win. The lack of a maximum would seem to contradict what is stated on the Ghost Rating page and what I remember from chatting with Ghost along time ago, where I believe he specifically stated that the intent was to max it out at 18 to avoid needlessly extending games and abuse.

Ok, the max result for PPSC being limited to a value less than one, a bunch of messy formulas (which I don't fully agree with the philosophy behind, but that's a whole separate issue to get into later) were developed to prevent the expected result from ever being larger than 18/34 in order to ensure that a person winning a PPSC game wouldn't ever lose rating. I specifically remember Ghost explaining that this was the intent when chatting with him a long time ago.

Here is why the PPSC expected result is always less than 18/34:
Note: I'm going off of the formulas from this page:
http://tournaments.webdiplomacy.net/theghost-ratingslist
which may be different than what the code actually does.

Ok, for player i, his expect result is given by:
E[i] = (18/34)*("chance of i winning") + (16/34)*("expected success for i in non-victory")

"chance of i winning" = R[i] / ( SUM )
where "SUM" = sum{all k} R[k]
(the sum of all initial ratings over all players)

"expected success for i in non-victory" = sum_{k != i} ( (R[k] / SUM) * (R[i] / (SUM - R[k]) ) )
where "sum_{k != i}" denotes the sum over all terms where k does not equal i.
Note that the term value (R[i] / (SUM - R[k]) ) is less than one, hence
"expected success for i in non-victory" < sum_{k != i} (R[k] / SUM)

Hence, "chance of i winning" + "expected success for i in non-victory" < R[i] / ( SUM ) + sum_{k != i} (R[k] / SUM) = SUM/SUM = 1

Further, E[i] < (18/34) * ("chance of i winning" + "expected success for i in non-victory") < (18/34) * 1.

Therefore, E[i] < (18/34).

Going back to the equation:
change in rating = V*(actual result - expected result)
since the "expect result for player i" (that is E[i]) is less than 18/34, and a PPSC winner would have an actual result (at least) (18/34), you can see that the "change in rating" for the winner is always positive.

just read the last posts. it is actually interesting as I am working on this for real life questions…

suppose we have only 2 possible outcomes, winning (W) and surviving (S). This implies that probability Pr(S) = 1-Pr(W). Let p be Pr(W). Logically, Pr(S) = 1-p.

Let each of these outcomes be associated to a utility value given in SCs. Following the max-min principle as I understood it is implemented (too lazy to read the details), W = 18, S = 16.

The expected utility for a given player is the summed value of each outcome weighted by its probability:

EU = p*W + (1-p)*S.

Plugging in the values for W and S, we get:

EU = p*18 + (1-p)*16.

Isolating p:

EU = p*(18-16) + 16.

Simplifying

EU = 2*p + 16

Remember that p is a probability term and only defined for P = [0;1]. Hence:

argmin(EU) = EU(p=0), and argmax(EU) = EU(p = 1),

where p = 0 implies certainty of losing, and p = 1 certainty of winning (or near certainty, for geeks).

From this follows quite simply:

EUmax = 18, EUmin = 16.

Normalising these results by the total of available SCs, we get:

EUmax = 18/34, which corresponds to the maximal expectation.

QED.

Unless the does not max out at 18 SCs, Alderian is disproven. Logically :)

^addendum: I admit that strictly speaking, p only approximates 0 or 1, and hence EUmax ≤ 18 or 18/34. Therefore, it is ALWAYS lower than 18/34.

Agreed, with Indybroughton, much respect for you guys! I can sort of follow the posts on the calculations, but I feel more like a spectator of the Superbowl than a participant.

What I meant on the CDs is that I find it strange (and inbalanced) to calculate GR on the basis of the original starting position, when the actual position is so different. Since GR goes up if more people are eliminated, it should (at least) take the number of still playing people into account. If I walk into a CD where there are only three countries left on board, I contribute 2/35th GR. But if I draw the second I walk in, I leave with 1/3rd (oversimplified, I know, but you get the point). I think that's unbalanced.

It makes much more sense to me to include the # SCs and # remaining players into the 'expected result', rather than start from scratch. But how to do this?

Alderian,

Would you be willing to post your Java code (say on codepad, github, or whatever else you find convenient)? I would love to see the nuts and bolts of exactly how GR is currently being calculated, and I'm sure others in the community would be interested as well.

I actually have quite a bit of experience with coding in Java, and an ulterior motive in that I would like work on an alternative to the Ghost Rating system, which by working off your codebase would surely streamline.

I would really love to at least be able to see the current GR code.

Alderian has made some remarks that seem to suggest that the behavior of the current code differs from the specification, so there would certainly be a benefit to the transparency gained by making the GR code open source.

I think we should try to have every Admin have their own Rating system : )

Actually, over at VDip, Oli (the creator of the site) has been working on a new rating system and integrating it into VDip. The prototype is pretty neat. It'll even show you the adjustments that have been made on a game-by-game basis for each player.

The main collaborative discussion (over 500 replies and counting) is in this VDip forum thread:
http://vdiplomacy.com/forum.php?viewthread=38097#38097

The current proposal by Oli is outlined here in his site wiki:
http://www.vdiplomacy.com/wiki/index.php?title=Rating

Very interesting. I suggested something similar to that a while ago when we were talking about different scoring systems. I was actually hung up on the same issues that Decimo is talking about. IMHO, it shouldn't matter who you lose to but collectively who you play against (i.e. really simplify the whole damn thing and play against an average of your opponents) but I see points on both side.

I might be missing some the nuances in the difference to what you're proposing there and what Oli is proposing but they seem very similar.

Or rather, I think I just like Decimo's suggestion (as suggested in the zine previously).

But mostly, survive > eliminated ?! boo.

Oli's original proposal involved making all of the pairwise adjustments the same weight. I just basically added a few tweaks in de-emphasizing "draw:draw" and getting rid of "loss:loss". Ultimately, those suggestions were taken into his proposal. For WTAs survives and defeats should both be considered the same (as losses).

It should only be in PPSC where survive > defeat comes up.

As an aside, I often wonder why VDip and WebDip seem to have such diverging evolution. Wouldnt it be possible to join together? VDip seems to have many features which are neat-o, though I really like the focus on Standard Dip here.

Ah, yeah, that makes sense, yebellz. I guess I only saw the final result after he implemented suggestions.

@yebellz, I'm not going to publicly share the ghost rating code as it isn't mine to share, it is Ghost's. I'll send you a PM to talk about that part a bit more.

The other side of it is that the java program was thrown together to get ghost ratings back running again and I would want to spend some time cleaning it up before I would put it out there with my name on it.

I do concede that you are correct with PPSC you cannot win the game and lose rating. I was focused on the "chance to win" portion possibly being too high, but with it multiplied by 18/34ths that cuts it down significantly, ensuring an 18/34 result will be higher than the expected. There isn't any specific code in there to prevent losing rating when winning, it is just the nature of the algorithms that it works that way, and under further thought it makes sense that it does.

@Minister, the difference between vdip and webdip is that vdip has an owner that is actively working on improving his site, whereas webdip's owner, as much as I'm sure he loves webdip, has other priorities taking precedence in his life. That's my understanding anyway. And don't get me wrong, I really appreciate what Kestas has done and the website he has made for us all.

This might be a little off topic and probably should have been posted in the vdip thread about 2 weeks ago, but I was wondering if there is an algorithm for determine how accurate ratings are, based on game data? If MadMarx was rated very low and some random(often defeated) person is rated first then we can make the conclusion that this rating system wouldn't be very accurate. Is there a simple, obvious or known algorithm to estimate this?

Unless I'm mistaken I would say no because such an algorithm would require knowing who are actually the best players. You would need to do a comparison of several other rankings to determine how accurate another one is, and that requires the other rankings formulas which is inherently as complicated as all of the other rating systems it is basing its "reliability" estimation on.

If it was a two person game, it would be easy to test the rating empirically. A 7 person game, especially with the different skills required per country, would require a lot of samples.

I'm a new player to the site - does somebody mind explaining where I can see all these various ratings (once I've finished one of my games, of course)?
Thanks :)

@JKM

https://sites.google.com/site/phpdiplomacytournaments/theghost-ratingslist

Excellent, thanks!

@JKMatthews, The ghostratings abgemacht gave the link too, win/draw percentage found on your profile page, and your number of points are generally all viewed as the 3 main rating systems. None of them are completely accurate, but taking a look at all 3 can give you a very good view on a players skill level. Welcome to the site!

The easier link to remember for ghost ratings is here:
http://tournaments.webdiplomacy.net/theghost-ratingslist