That should be "The sum of the ratings of all players in this game, divided by 17.5". Not all players on the site.

It doesn't make the rich get richer, though. Because the lower player contributes less to the pot, a low end player in a high end game has a better chance of making out than the high end players he is playing. The only way the high end players get richer is off other high end players. They don't get richer off the low end guys because there is very little contribution by them.

Player 1 = 150
Player 2 = 260
Player 3 = 265
Player 4 = 265
Player 5 = 265
Player 6 = 270
Player 7 = 275

Total is 1750 so 100 GR in the pot.

Player 1 contributes (150/1750) * 100 = 8.57
Player 7 contributes (275/1750) * 100 = 15.71

The rich have contributed way more to the pot and the richest player's potential ROI (just over 6 to 1) is significantly lower than the poorest player's (nearly 12 to 1).

To follow up a little bit with Draug's post, if a lower-ranked player were to beat a higher-ranked player, their rating would jump substantially, but for the higher-ranked player, they've got to beat other high-ranking players in order to gain. It puts the best players on at a higher standard.

And in PPSC or in the case of a draw, it is possible for a high ranking player to win (or be part of the draw) and actually lose SC against lesser opponents where as the lower ranking players against high ranking opponents may well make a profit even with a simple survive of just a few SCs as the distribution of GR after the game ends is the same as points.

A Tin Can, there are significant differences between the Elo and GR systems so I'd be weary to make conclusions from the wiki page on Elo.

If you're defeated/survive, you lose the same number of points regardless of who your opponents are. In that sense, the game does not affect your rating any more (or less) if you play against tougher competition. IMHO, this is a flaw with the system. I may be wrong, but I believe vdip has incorporated a system without this characteristic.

GR could use an overhaul, there is no doubt. I often wonder why the complex calculations Ghost put up when it boils down to "Everyone contributes 2/35ths of their GR to the pot and it is divided just as points would be."

Yeah, GR with the PPSC games is strange. If I weren't ranked in the top 15 I wouldn't pay any attention to it.

Just because a formula boils down to something simple doesn't mean you can completely disregard how you got there. Using the more general form of the equation is good because it allows you to modify it in a sensible way. If the GR page just said 2/35, we'd all be wandering around like idiots trying to figure out where that ridiculous looking number came from.

Also, there is already a disincentive for highly ranked players to play with lower ranked players because even if they do well, they gain very little. If they also stood to lose even more (they're already putting more into the pot, so that would be like a double tax), then there would be no reason to play with people lower than you. This is not behaviour we want to encourage, so I would advise against Yonni's suggestion.

Yeah, I guess it boils down to if you want it to act as an incentive/deterrent for certain behaviour of if you want it to be the best measure of your success. I tend to think that people don't spend too much time trying to game the system so I'd rather it act as the latter but perhaps I'm being a little naive if with that. Adding GR-free option for games would also alleviate some of the issues of high-GR players being weary of playing with low-GR players. But I feel like I'm sort of beating a dead horse here.
I'm plenty happy with the way things are - it functions just fine for what it is.

It functions just fine for what it is, so let's create a site policy that encourages creation of GR challenge games. Then people can complain about it.

GR challenge games discourage high GR players from playing with low GR players. Ban 'em.
Otherwise, people miss out on the (ugh) 'pleasure' of playing with THM. ; )

A possible way it could work is for each game to be scored as 6 for each player, one against each of your rivals and a fairly low k-factor. I haven't worked through any calculations to see how this would affect things here.

Yup, that's a method that's been discussed before. The issue is that would lead to some meta gaming as you'd rather lose to someone with a high rating than a low rating.

GR is "inspired by" the Elo system, but there are very significant differences between the two. As TinCan pointed out, the computation of the "K factor" is very different. However, an even bigger difference is how the expected result is calculated. These two differences cause GR to behave very differently than Elo.

In the Elo system, as the rating gap between two players increases, the stronger player is considered exponentially more likely to win (this is equivalently computed via the ratio of an exponential function of each player's rating). The philosophy behind Elo is to predict the result of a game between two players from their rating difference, and then make corrections to their ratings based on the actual result. A small correction happens when the more likely outcome occurs, but a slightly larger correction happens when the less likely outcome occurs. If the player's ratings are "accurate" (in the sense that they reflect their performance, on average, as predicted by the model), then the ratings won't change much except for some minor noisy fluctuations. However, when the ratings are "inaccurate" these corrections will push the ratings closer toward better predicting their performance. For Elo-based systems, the K factor is often made larger for provisional players with little game history (and presumably an inaccurate rating). This is to amplify corrections when player's rating is assumed to be inaccurate. As a player accumulates more games, the K factor is often gradually reduced (down to some minimum), which will help stabilize his rating as it gradually converges toward reflecting his true skill. Should his actual skill change over time (which presumably happens gradually), the reduced-amplitude corrections should still allow for his rating to track these changes provided that he continues playing games. Another thing that is often done with Elo-based system is to decrease the K factor for the opponent of the provisional player. This limits how much a provisional player with an inaccurate rating can disrupt better established ratings, while still allowing the provisional player's rating to be adjusted by large increments. This also leads to a non-zero-sum system, but that does not necessarily mean rating inflation/deflation. In fact, with a zero-sum system, rating inflation/deflation (in absolute terms) must happen if players stronger or weaker than the average join or leave.

The GR formula appears to be of a similar formula, but it's behavior is actually quite different due to how the expected results are calculated and how the K (or V) factor is chosen. For the WTA games, it basically simplifies down to everyone putting a fixed fraction of their rating points into a pot that is later divided WTA-style.

They were experimenting with a system like that suggested by mendax on VDip. I think it's been fully deployed now after some tweaks.

Abge said: "Just because a formula boils down to something simple doesn't mean you can completely disregard how you got there. "

I agree. My question is: Is there information on how Ghostrating got there? I can't find the rationale to disregard in the first place :)

Imagine 7 similarly-ranked players with a high rank play a game, and 7 similarly-ranked players with low rank also play a game (this isn't unreasonable, it happens all the time in the GR series games). Say both games end in three way draws. The drawing players in the higher ranked game get a higher boost to their score than the drawing players in the lower ranked game. That doesn't seem right to me.

As I understand it (and as yebellz described), the objective of Ghostrating (and similarly Elo) is to adjust the ratings based on new information, to ultimately converge on a "true rating". In the case of similarly ranked players producing a three way draw, it makes sense to say "we thought these guys were all about equal, but maybe these three were a little better than the others".

However: the current system instead says (for high ranked players) "we thought these guys were all about equal (and awesome), but maybe these three were a *lot* better than the others". I'm not sure I understand why the rating change increases with a sum of the ratings of the players - typically systems that have a scaled change instead *decrease* it with higher ranked players. Does anyone know what the rationale was?

@Tin

You can read Ghost's original article starting on page 33 here http://www.diplomacyworld.net/pdf/dw105.pdf

Thanks. It looks like it's mostly the same text as the web page, though. I guess the only rationale available is the line "clearly it has to be some function of the ratings of the players involved"..

Here is the only rationale I can come up with:

In chess, you know that the winner played the game better than the loser.

If you draw a game of Diplomacy, though, are you really better? That is much harder to answer, I think. Did you actively convince Italy to suicide into France, or was he just pissed off and your reaped the benefits? Experience players are less likely to do stupid things, and so if you make it to the draw, it's probably due to your own success. In this way, in makes sense that games with higher ranked players pay out more than lower ranked games, even if the players in each game are closely ranked.

@tincan

"Imagine 7 similarly-ranked players with a high rank play a game, and 7 similarly-ranked players with low rank also play a game (this isn't unreasonable, it happens all the time in the GR series games). Say both games end in three way draws. The drawing players in the higher ranked game get a higher boost to their score than the drawing players in the lower ranked game. That doesn't seem right to me."

This is true, over a single iteration, but as iterations -> infinity it's a null gain whether you're high or low rank. Each player is equally likely to win/draw against 6 other players of equal skill, regardless of what that skill is. Add to this that with successive wins, a players GR increases, so he risks more to back up his claim of superiority. It's a very nice system imo, that does a good job of preventing artificially high or low ratings. The only flaw is that it's inaccurate for new players (appreciate yebellz explanation of the elo system, btw!). As the number of games played increases, it is a great estimate of expected outcome regardless of who a person is currently playing against.

YJ, wouldn't the same be true for a more traditional V, though? Can you explain why this V function is inverted?

I agree that GR is a reasonable way to rate players, but I'm just trying to understand the reasons for the choices made when it was constructed. I'm now tempted to just email Ghost and ask him :)

Hey Tincan, what do you mean inverted? I haven't looked over the actual formula in a long time.

If you are just suggesting that V should be lower as a player's rating increases, so as to avoid the scenario you describe above, that may seem at a first glance a reasonable idea.

However, doing so is actually even worse for low ranked players, because then higher ranked players risk less than their skill rating dictates they should when they play low ranked players.

Yes - by inverted I mean that the ranking change possible increases as your rating increases, rather than decreases with your rating (as is more typical).

Abge's suggested rationale is not unreasonable, although I'm not sure I'm sold on "better players deserve better rewards".
----
To answer your followup post, it's worth noting another change from Elo that GR has is that the V function is dependant on all the players in the game, not just on the individual player being calculated. This means that currently, higher ranked players risk less when playing lower ranked players than when playing against their peers. I don't think I agree that a more traditional V would be measurably worse for games with mixed players. Anyway, at this point it's academic.

I want to be clear that I'm not saying "I think GR isn't right", I'm saying "I'd like to understand why it is the way it is". I might *then* conclude that GR is not right yet, but I don't want to start a religious war, so if I make that conclusion I'll probably keep it to myself :)

....besides, if we dream up alternative GR implementations we'll have to consider how to rate a rating system. And that's a religious war all on its own...

So compute the average GR of the group. Anyone above the average is expected to do better than anyone below. Those above get less for a solo or draw inclusion than those below. The farther above, the less you win or more you lose. The farther belwo, the more you win or less you lose.

I see, yes I understand you are just trying to get clarification.

"This means that currently, higher ranked players risk less when playing lower ranked players than when playing against their peers."

I don't think you quite have the gist of it. IIRC the risk (an individual player's contribution to V, we'll call it Vi) is unchanged, regardless of the rating of your opponents. It is the reward (all of V) or, more importantly the reward/risk ratio (V / Vi) that changes, and the reward/risk ratio decreases against poorer players, and increases against better players, as it should be.

Now, if all of the players ratings accurately reflect their skill, we can normalize the reward to risk ratio by the perceived odds of winning (call it V*o / Vi Take the case where all 7 players have the same rating of 100 (for simplicity we'll pretend they wager all their points instead of just a fraction):

potential points gained = 600
V / Vi = (7*100( / 100 = 7, but the normalized ratio V*o / Vi = (7 * 100) / 100 * (1/7) = 1

Zero sum game, as it should be.

Instead take the case where all 7 players have the same rating of 800:

potential points gained = 4800
V / Vi = (7*800) / 800 = 7, but the normalized ratio V*o / Vi = 7 * (800 / 800) * (1/7) = 1

Still a zero sum game. Sure, the absolute point value gain increases for higher ranks, but it normalizes itself over multiple iterations, and it becomes very difficult for a highly ranked player to expect to gain points when playing against inferior opponents. Consider the following:

A player with a GR of 800 plays against 6 opponents rated 100, and he manages to attain a 2 way draw. The high rated player actually drops in ghost rating. (800 + 6*100) / 2 = 700.

@Draug, that's the method I would take. An average of the quality of competition and calculate each persons expected outcome from it. It has it's drawbacks too but is the best method I've heard of yet.

I think the concern was that 7 equal players have a game with a higher value if the players are high skill than with a group of noobs. So making the reward potential and contribution very based on distance from the mean or median (would have to play with the numbers) while making all games have an equal value would male the games equitable without altering the way the GR is doled out.

Another simple way would be to just set a fixed game value then computer how much each player contributes based on their GR to the sum of all players GR.

I see. The only issue I can see with that is that you'd have more wild fluctuations in ratings among the lower rated players, and therefore relatively more stable ratings among the higher ranks. I'm not sure whether that's a good idea or not.

I'm inclined against it, since 90% of players have ratings below 150.

@YJ: You're right- I was wrong about the risk. Nice explanation.

I think the system works for mixed ranks, but if you're keeping the ratings similar in a game, it still feels wrong. For example, in your simplification, a player of rating 100
who solos against 6 identical player gets a new rating of 700. But if 7 players of rating 700 sit down to a game that ends in a solo, then the new rating is 4900. That still doesn't feel right.

I'm still not sure I'm convinced that a variable outcome is the right way to go. But, as you say, it might not matter in practice.

Sure, and I do take your meaning re: the potential for a strongly rated player to artificially boost his instantaneous GR with, say, 3 consecutive wins against high-caliber opponents. Just keep in mind that things like that aren't sustainable. Our resident champion, MadMarx, for example, had a GR of over 1000 at one point after going on a tear, but he usually hangs around the 600-800 range. Clearly a ~30% ranking fluctuation at the high end isn't desirable.

Maybe it's more important to control for fluctuations at the top than the bottom, and a system like you and Draugnar describes would be preferable - I think that that argument could be made that we want more stable ratings at the top echelons, because honestly who cares about the bottom?

A fixed game value with present rating determining contribution would level out the curve into a line and bottom fluctuations would only really occur as new and potentially skilled players entered the system or players got better for a time (went on a tear).

YJ, I think we simply play too few games over too long of a period to expect a well stabalized system for diplomacy.

@yonni perhaps, but to me it's a more interesting question as to whether a system can be designed that is both stable at the top and the bottom.

@draug not really. My point is that under an "every game is worth the same" system, players with fewer points to wager must necessarily risk a large portion of their points, even if its a player who plays a lot but just isn't very good, this will mean that each win/loss will have a relatively larger impact on their instantaneous GR.

Take the extreme hypothetical example for clarity: what do you do when all players are so poorly rated they can't afford to pay up their share of the total? If all 7 players have a GR of 30, and the "fixed" value for starting a game is 200 , the players risk virtually all of their GR to play. If the fixed value is 250, they can't afford to play at all. This could never happen under the current system.

Then we are back to being stuck with the present system...

Well, I have always rather liked the current system... but I thank you and tincanman for clearly identifying what I see as the only real issue with it.

I like the present system too. It's just an interesting thought experiment to try and find ways to improve upon any system. Creatign and/or improving systems is what I do for a living, so I always find it interesting to look for flaws or areas of improvement.

The bottom part could be fixed with equitable games simply by refilling those who drop below a certain value like we do with points. It would result in some inflation, but that isn't necessarily bad. However, I actually think having high ranked games worth more total by being a fixed percentage of the total GR of the players in the game is a good way to allow someone who is skilled but not yet reached their appropriate GR due to being new a means of getting there quicker, like a challenger for a title fight who KOs his opponents getting noticed and being offered a shot at the title before his peers are.

YJ - your betting analogy works well for understanding how the system works, but since we're just looking to rate players, there's no reason that players couldn't have a negative rating if they lose enough games.

One problem with the percentage system is that it makes ratings hard to compare. The difference between players with score 100 and 150 is not the same as the difference between players with score 150 and 200. Currently, many players just use the ranking instead, which is one way around that. However, it won't be as effective when we have enough population to put many players on a similar score.

With a percentage system, there's quite a bit of bias towards the result of high rated games: Say two players both join the site (initial rating=100). They both join games with 6 experienced players (say 6 players of rating=250). One has a positive result (3 way draw), and goes to a rating of 124.7. The other player is defeated, and gets a new rating of 94.2.

Say the defeated player goes on to play four more games with players of rating 100. If they achieve four 3-way draws in each of those games, they'll have a rating of 124.2 (close to the rating of the first player). So we have:

Player A: one three way with 6 experienced players = rating of 124.7
Player B: one defeat with 6 experienced players, 4 games each ending in 3-way draws with 6 new players = rating of 124.2

If we had a constant K-factor (say 40), it would instead be:

Player A: Rating 110.8
Player B: Rating 126.2

I'm actually not sure which is more desirable. We certainly have more information about player B, but that's what provisional ratings are for. I guess the question really is "should some games be worth more than others?". My intuition is no - rewards for performing well against higher rated players are already modelled in the expected outcome part of the formula, so if it is also modelled in the K-factor we'll be double counting.

I don't really know what's best. It would be interesting to try a few different GR implementations, and see which ones are best for predicting the outcome of games. But, really, who has the time for that? :)

As was mentioned in reply to my earlier comment, vdip run a different implementation. It will be interesting to see what sort of results that gives.

If you wanted to take into account the provisional nature of some of the ratings, perhaps some variation of Glicko rather than Elo would be better.