@CCR

Agreed, the discussion between Mittag and I is not productive.

The code must store data on at which time people went into CD, as this information is displayed at the bottom of each page of a finished game. I still don't know how practical your idea would be to implement, though.

IMO, CD'd players SHOULD NEVER be rewarded with an improved ranking. They've abandoned the game!#@%!

I'm also against weightings based on country strength for many of the reasons already mentioned.

Second the zero rewards for CD'd players. I realize there's times where unavoidable situations cause people to CD and it's somewhat unfair, but I believe (and if I'm wrong, please correct me) those are the minority. Abandoning a game, and your replacement winning, or doing well, should not net you rewards.

Also second not-weighting based on country strength. If a map is so imbalanced it's unfair (like France in Rinascimento), simply cut it out of the calculations instead of trying to finesse country-weighting on every map (which would end up fairly subjective).

The scoring system was changed a while back, so that people who took over an abandoned position would never lose points, whatever their result. I think this was a good change. I've played in games where players abandoned positions and didn't get replaced, and that really messes with the game dynamics and makes it a lot less fun. This system encourages people to come into games as replacements, and keep things fun for all the other players, without having to worry about a loss of ranking. And I'd say it's working, because now, when I check for replacement positions open, there are a lot fewer of them. So, my opinion is that a possible occasional distortion of the ranking system due to this rule is worth it, because it encourages behavior that benefits the whole site.

Oh yes KoS , Oli did it after my insistence, i repeat this since '17 :o

@KingOfSwords

I am aware of that. When the scoring for people taking over abandoned positions changed, though, the rating did not. One cannot net lose dPoints anymore from taking over an abandoned position, but one can still lose vPoints. Under my proposed changes, the gain or loss of vPoints one could get from taking over an abandoned position would hopefully be fairer, and it would be skewed in favor of the one taking over that position in the same way that buying into an abandoned position used to be skewed in favor of them in the past.

I'm honestly just trying to understand how the system works. I find it a bit surprising that so many are willing to adopt a new system without understanding it. And I have to say, I am indeed allergic to the approach 'I'm a mathematician and you guys are too stupid to understand'.

Soo, if Mercy can't explain it, then I'll try to. You'll have to have mercy, Mercy, with possible misunderstandings.

vPoints, dPoints, GR, and now mPoints (m for Mercy) have one thing in common - they are zero sum. [Funny note, for a while, there was an alternative 1v1 GR rating on webDip which was not zero sum.] It means you can think if it as that each player makes a bet at the beginning of the game, and then the pot will be redistributed according to the outcome of the game.

in dPoints the bet is the same for all players.

in vPoints, GR, and mPoints the bet is different for differnt players.

vPoints has a couple weird quirks. (1) It threats a game between many players as multiple 1v1 games. (2) It does not redistribute points between the participants of a draw. Both of these quirks caus headhunting. The other point systems, including mPoints, don't have these problems. Mercy is perfectly right with regards to that.

mPoints has a different quirk: (3) the bet size depends on the outcome of the game. It means that when the game starts, you don't actually know yet how big your bet is. (Maybe a little weird to think about, but in practice not a problem, since all computaions are made after the game is finished).

Note that (3) is not necessary to stop headhunting. It is included to mimic (2) and make mPoints more similar to vPoints.

Now, let's think a little bit about what (3) does to gameplay. For simplicity, I'll assume it's a WTA game. For the players with a chance to solo or make the draw, (3) doesn't change incentives. Their goal will still be to solo/make the draw, and the smaller draw the better.

However, for players who are eliminated or who are just about to be eliminated, (3) does make a difference. If you're the fifth rank and get eliminated in a game that ends with a solo, then mPoints will say that you were expected to loose. You will not loose that many points. But if you're the fifth rank and you get eliminated in a game that ends in a five-way draw, then mPoints will say that you were expected to be in that draw. You will loose more points.

The consequence is that any player who is about to loose a game, should try to throw the game.

Is that good or bad? I guess we can all have different opinions about that. But, I do think Mercy has a responsibility to explain how his point system works, so that we can evaluate all aspects of it, before we decide whether to implement it or not.

@Mittag

That is actually a good summary of what my rating system (I will adopt the term 'mRating') does in its core.

I have to say, I got annoyed at some of your previous posts. When you e.g. claim that something is 'obviously' true without giving any explanation as to why, then I am left wondering whether you just neglected to explain your thought process and it is worthwhile to figure out what it is, or whether you just didn't have that much of a thought process when you made the claim.

I like this post, though. Like I said, I think it summarizes well what mRating and the other rating systems do. I will now address the concern you raised with mRating supposedly stimulating players to throw the game if they are about to be eliminated. Some if it is true, some of it is not, and some of it needs nuance.

"However, for players who are eliminated or who are just about to be eliminated, (3) does make a difference. If you're the fifth rank and get eliminated in a game that ends with a solo, then mPoints will say that you were expected to loose. You will not loose that many points. But if you're the fifth rank and you get eliminated in a game that ends in a five-way draw, then mPoints will say that you were expected to be in that draw. You will loose more points."

In this scenario, if you are the fifth ranked player in the match, then you will be expected to win with less than 1/5 probability, so if the game ends in a solo, so you will be expected to get in between 0 and 1/5th of the pot. If the game ends in a 5-way draw, then you can at most get 1/5th of the pot, so you will be expected to get in between 0 and 1/5th of the pot, too.

Admittedly, these two expected numbers need not to be the same, though. I think you can find examples where they are the same, but let's for the sake of the example make that not be the case: Assume that the four players who are higher ranked than you, are rated much higher than you, and all the other players in the game are rated much lower than you. Then if the game ends in a solo, the probability you will be the winner will be close to 0 (since there are four players who are rated much higher than you), so your expected gain will be close to 0. If the game ends in a draw, the probability you will be in it will be close to 1 (since there are only four players who can be expected to fare better than you, and the rest is expected to almost certainly fare worse than you). so your expected gain will be close to 1/5th of the pot. So in this instance, yes, you DO gain from throwing.

"The consequence is that any player who is about to loose a game, should try to throw the game."

No, it doesn't extend that way. Suppose for instance that you are the highest rated player in the game. Then if your rating is sufficiently high, you may as well be expected to win with a probability higher than 1/5 if the game ends in a solo, so if the game does end in a solo, you will be expected to gain more than 1/5th of the pot. If the game ends in a 5-way draw however, you cannot be expected to win more than 1/5th of the pot. As a consequence, if you are about to be eliminated, you have an incentive to NOT throw.

This effect undeniably exists. I don't think it is that big, though. These examples were all quite contrived; in a real game, if you are the 5th highest rated player, the 4th and 6th highest rated players are probably rated quite similar to you, and it would not be obvious what the difference between throwing or not throwing the game would mean to your rating.

I don't like this effect, though. I said in my initial post already that in this aspect, I like GhostRating MORE than my own rating system. The reason why I choose to do mRating in this way anyway is twofold: it is both political and practical.

The political reason is that I wanted a rating system that is strictly better than vRating so that there would be no discussion which would be better. I do think it is strictly better than vRating. Any effect the score of other players in your game has on your change in mRating is not depending on their rating (so no headhunting!) and is likely smaller and less obvious than the effect would be under vRating. (Under vRating for instance, if you are losing and you can manage to throw the game to a high rated player, that always greatly reduces the vPoints you will lose from the game). If I were to adopt the logic of GhostRating, which in principe I like more, I would potentially be advocating for a rating system that translates worse across multiple variants than vRating does. High rated players would have an incentive to only play on maps where a large percentage of players tend to get eliminated.

I know of a way to potentially solve that issue, though: We can use machine learning to apply the rating differently across multiple variants in such a way that players are no longer encouraged to play specific variants because of their rating. However, that brings me to the practical reason for making mRating the way it is: That would be more work. Even if I did all the work, I wouldn't know if everyone in the community would prefer my rating system over vRating, as it would still introduce the effect of high rated players losing points in a draw in some instances.

@Mittag I was thinking about what you wrote before: 'solving problem A one ofter introduces problem B'. This is essentially what I try to avoid.

@Mercy - My experience as a replacement player didn't go to way you said. In two games, I took replacement positions, then the rule change was implemented later. In both games, another player ended up soloing, but I didn't lose any points, v-points *or* d-points.

I brought up Arrow's law only to point at that it's essentially a fact of life that every scoring/rating system has a flaw. Not sure I made that point very clear - and getting into a detailed discussion about the theorem itself wouldn't have made it clearer. The point being, if you don't know what flaws your system has, then it's probably because you didn't look for them. That's a bad sign.

The most important part about constructing a new scoring system is to, at the end, take a step back, and think about what incentives it creates in different situations. Holistic and open minded. You can't only describe what the system does in the situation it's designed to handle well - it will obviously handle those situations well - you need to check the situations it's not designed to handle. That's the core of my criticism here. It seems you skipped this part, and essentially assumed that there wern't any bad side effects.

How bad are the side effects in this case? I don't know. How many are there? I don't know. It didn't take me too long to find one, though. I realize it probably looks like I'm an asshole deliberately trying to sink the ship. That's not what I am trying to do. But, in my experience, the creator of the scoring/rating system often refuses to acknowledge even the possibility of flaws until you can find an explicit one. (Since the flaws always exist, it is kinda a fun puzzle to try to find them though, I'll admit to that!)

The guy with the alternative 1v1 GR at webdip knew the system wasn't zero sum. He had, though, assumed that long term it would 'even out'. Actually checking the math, it turned out his system had inflation. Sum of the scores after the game was always greater or equal to the sum of the scores before the game. Pretty bad, huh? The guy was smart enough to write a long and accurate explanation for how ELO worked. Point: these mistakes are easy to make.

"In this scenario, if you are the fifth ranked player in the match, then you will be expected to win with less than 1/5 probability, so if the game ends in a solo, so you will be expected to get in between 0 and 1/5th of the pot. If the game ends in a 5-way draw, then you can at most get 1/5th of the pot, so you will be expected to get in between 0 and 1/5th of the pot, too."

That both numbers are between 0 and 1/5 does not imply that they are independent. I bet you 10 mPoints that, if we do the math, it will turn out that his expected return in the draw case will always be larger than or equal to the expected return in the solo case.

Outline of argument: You showed yourself the benefit from throwing the game in one of the extreme cases. The other extreme is that all players have the same rank, in which case expected return is equal in the two scenarios. Other cases should be interpolations of these two cases.

Ah, but the point about the board leader holds. So, if my intuition is not completely off here, if you are the k'th ranked player and you get eliminated, then you wan't the draw size to be as far away from k as possible. So, low ranked players will always through. Middle ranked players will through if there are three or four players left. Top ranked will not throw.

This side effect, that players throwing the game is predetermine by their rank and the number of players left in the game, is it less sever or more severe than mPoints being different than vPoints? That's a different question. And, my main point is not to say that this is a severe side effect. My main point is to say that I should not have to tell you about this side effect, you should've already known about it. And we shouldn't have to speculate what the math actually says about player k throwing the game, because that computation should've already been done.

'The political reason is that I wanted a rating system that is strictly better than vRating so that there would be no discussion which would be better.'

Better in every aspect is really hard to achieve. Not that vRating is very good, so you probably have a shot at achieving it. But it's gonna be easier to just aim for 'significantly better overall.'

Not sure I have more to contribute here. But I'm still in favor of this - particularly the first problem with the big variants desperately needs a solutions.

@KingOfSwords

Hey I see. That is new information. Interesting. I don't know when that has been implemented. Thanks for pointing it out.


@Mittag

Like I said before, Arrow's theorem does not apply. Mathematical theorems are only applicable in a narrow number of cases. To me this is like as if we were having a discussion that had nothing to do with physics and you said 'Everything is relative! I am sure you have heard of Einstein?'.

I think the main reason we cannot find a 'perfect' rating system is because people have different opinions on what a perfect rating system would require. But like I said in my long post at the start of this thread, I don't even find mRating perfect since there is an aspect where I like GhostRating more.

I amend you for finding a side effect. You wrote 'My main point is to say that I should not have to tell you about this side effect, you should've already known about it.' and I can tell you I indeed already knew about it. vRating has this problem too except it also matters who obtains the result: if you lose, you can decrease your loss in rating by throwing to a high rated player. It was this effect that I aimed to eliminate. You also wrote 'And we shouldn't have to speculate what the math actually says about player k throwing the game, because that computation should've already been done.' and I agree that it would be nice to do such computations. I have only done some basic computations to test mRating and I have never programmed the thing properly. I merely provided the math and explained my reasoning behind it. The next step would be to program the thing, since it looks like people are interested in seeing it implemented or at least tested.

In case you are wondering why I did not write this in my opening post: It simply didn't cross my mind. My goal of the opening post was to outline the main points behind what I suggested to implement in such a way that a wide audience could follow it and read it within a respectabel amount of time, and to provide a link for anyone who wished to dive deeper.

Arrows theorem applies in any situation when you aggregate separate rankings into one ranking.

Yes! You are trying to model the beginning of the universe using classical mechanics, and I am merely pointing out that there is something called general relativity that you probably should know about. Your reply was 'never heard of it, prove it,' to which I responded 'nah'. That is a pretty accurate description.

But, let me give you the benefit of the doubt, and assume you didn't ignore checking that effects were as intended, but you simply didn't bother sharing it with us. Here are a few questions which I think should've been addressed already in the first post.

Iteration is designed to reduce the payoff for solos in big variants. What is the effect in other situations?
a) What about solos in small variants?
b) What about a 7-way draw in Divided States?

Because, iteration in itself only reduces the payoff for a solo/draw. If you implement it accross all variants, then it will not change the relative scores. That is, a divided states solo will still be approximately 49 1v1 wins. The absolute numbers will have changed, their ratios will not have changed significantly.

[An easier way to achieve the same thing is to reduce the amount of points at stake in each game. Go too far in this direction and the 'ranking' becomes a measure of who's been an active member on the site the longest.]

I can hear the answer already: adjust the number of iterations depending on variant size. Sure, sounds good! Does it work? Did you compute a few examples to check? Convince me that iteration has the desired effect for solos and for draws in variants of all possible sizes, also relative eachother. That's what the original post should have done.

[I can think of a simpler method: apply a multiplyer to the amount of points at stake in each game, which depends on the size of the variant. Why is iteration a better method?]

*

Assume we implement mPoints. Two years from now, when the old rating system is forgotten, someone will ask: 'I entered a divided states game and got eliminated immediately. The amount of rating that I loose because of this appearantly depends on how the other 49 players continued the game after I was gone. That's possibly two years of dipomacy, which I was not involved in, that affects _my_ rating! Why is that?' The answer to this question will be 'You know, the old rating system [that noone remembers] had a weird thing with how it handled draws. Everyon though it was bad, but we still decided to have the new system try to mimic that behavior. That's why.' Reasonable?

Because, this is indeed the first ranking system I've seen where the number of points you will loose from an elimination, depends on what the other players in the game do _after_ you were eliminated. That should have been pointed out in the first post.

@Mittag

"Iteration is designed to reduce the payoff for solos in big variants. What is the effect in other situations?
a) What about solos in small variants?
b) What about a 7-way draw in Divided States?

Because, iteration in itself only reduces the payoff for a solo/draw. If you implement it accross all variants, then it will not change the relative scores. That is, a divided states solo will still be approximately 49 1v1 wins. The absolute numbers will have changed, their ratios will not have changed significantly."

No Mittag, iteration only plays a significant role in situations where the rating of one or more players change drastically as a result of one game. If a 1000 vRated player defeats another 1000 vRated player in a 1v1 match, he gains 8 points. If a 1008 vRated player defeats a 1000 vRated player in 1 1v1 match, he also gains 8 points. Hence iteration has no effect whatsoever for 2-player matches. But now imagine someone jumping from 1000 vPoints to 2000 vPoints from a single match. That someone gains a lot more vPoints than a member with e.g. 1200, 1400 or 1600 vPoints would have gotten. Therefore, if in this case iteration was used instead of handing him +1000 vPoints at once, it would have a big relative effect. For situations in between, iteration will have an intermediate effect.

"[An easier way to achieve the same thing is to reduce the amount of points at stake in each game. Go too far in this direction and the 'ranking' becomes a measure of who's been an active member on the site the longest.]"

That is a way to do it, but the beauty of the iteration method is that it dampens large jumps while barely damping small jumps, while your method would dampen everything and indeed risk that ranking becomes too much a measure of activity.

Another issue that iteration solves is that both Agnaar and slypups could have improved their vRating by shortly before winning their Europa Renovatio game, joining lots of 1v1 games and immediately conceding them.

"[I can think of a simpler method: apply a multiplyer to the amount of points at stake in each game, which depends on the size of the variant. Why is iteration a better method?]"

I didn't say iteration is a better method. The multiplier you speak of already exists, both in vRating and in mRating. Did you read the pdf file that I linked? I call the multiplier k(N) there and I leave it as an open question whether we should adopt the same k(N) or whether we should change it. I was actually already thinking about bringing up this question. I think the ceiling of k(N) could be reduced, possible by a factor 2. What do you think?

"Assume we implement mPoints. Two years from now, when the old rating system is forgotten, someone will ask: 'I entered a divided states game and got eliminated immediately. The amount of rating that I loose because of this appearantly depends on how the other 49 players continued the game after I was gone. That's possibly two years of dipomacy, which I was not involved in, that affects _my_ rating! Why is that?' The answer to this question will be 'You know, the old rating system [that noone remembers] had a weird thing with how it handled draws. Everyon though it was bad, but we still decided to have the new system try to mimic that behavior. That's why.' Reasonable?

Because, this is indeed the first ranking system I've seen where the number of points you will loose from an elimination, depends on what the other players in the game do _after_ you were eliminated. That should have been pointed out in the first post."

This is not the first ranking system you have seen with this property. Both vRating and mRating share this property, and since I thought people would be most interested in what I intended to change, I did not bring this up in the first post, no.

Also, no, like I said before, mRating does not have this property _just_ to mimic vRating. I explained before that I think this helps the rating system translate well across multiple variants. I also said that I could think of better solutions, but they would be hard to implement (such as using machine learning to change variables in the rating system depending on statistics of the variants). Now if you think you know a better solution, I am all ears.

I saved the petty part of our discussion for last:

"Yes! You are trying to model the beginning of the universe using classical mechanics, and I am merely pointing out that there is something called general relativity that you probably should know about. Your reply was 'never heard of it, prove it,' to which I responded 'nah'. That is a pretty accurate description."

A more accurate description would be:
You: "X is important."
I: "Never heard of it. You didn't even say what you think the relevance is? I looked it up though and concluded that I don't think X is relevant because blah, blah, blah."
You: "No it is obviously relevant."
I: "Why? Can you elaborate?"
You: "nah"

'No Mittag, iteration only plays a significant role in situations where the rating of one or more players change drastically as a result of one game.'

Yes - you are right. The more points that would have changed owner, the bigger the effect of the iteration.

And there's the side effect: the effect on solo's is bigger than the effect on draws, because the amounts switching owners is bigger for solos. For Europa Renovatio with gV ~ 100, all players with rating 1000, and _no_ iteration, the 2WD is worth roughly 48% of the solo. With 100 iterations the 2WD is worth roughly 73% of the solo. (Assuming I didn't make any mistakes typing in the formulas.) A 6WD in Europa Renovatio will amount to roughly 34% of a solo; it used to be 14%. A 17WD(!) will pay out roughly 10% of a solo.

The effect is smaller on smaller maps, of course. On the classic there is more or less no effect at all. (I'm comparing the sizes of the gains, btw, if that was unclear. Also, these are the kind of numbers I want to see, to get a feeling for what the ranking system does to game play)

So, on large maps, we are deflating solos and small draws relative big draws. It means roughly that, on large maps, you should always play it safe.

'Another issue that iteration solves is that both Agnaar and slypups could have improved their vRating by shortly before winning their Europa Renovatio game, joining lots of 1v1 games and immediately conceding them.'

With only two iterations this issue is still there, but I guess with more iterations it goes away?

'I didn't say iteration is a better method. The multiplier you speak of already exists, both in vRating and in mRating. Did you read the pdf file that I linked?'

It was a rhetorical question, of course. Let me ask another one. If you don't think iteration is a better method, then why are you proposing that we implement it?

'I think the ceiling of k(N) could be reduced, possible by a factor 2. What do you think?'

You know, looking through what vPoints does, I noticed that Europa Renovatio has gV ~ 100. On top of that you get the multiplyer effect of 35 opponents. 1v1 games has gV ~ 15. So it's not that solo'ing ER is like winning 35 1v1, it's like winning 230 1v1. And then on top of that the inflated score that comes from pretending that those 230 games were played at once.

That's maybe something I also don't understand. We have these scaling factors alrady, that depend on the variant. If the big variants pays out too much - why not just rescale them? I have no clue how gV is computed, btw.

'This is not the first ranking system you have seen with this property. Both vRating and mRating share this property.'

Yes, I constantly forget how bad vPoints are.

I don't think you should try to mimic vPoints at all. I don't see the point of it. The transition between ranking systems is a one time thing. Already after a couple of months noone will remember the old system. Just try to make a new system as good as possible.

And, personally, I definitely don't like that the rating, which is suppose to represent your performance, can depend on what happens in a game where you are no longer participating. That just seems fundamentally wrong to me.

I m sorry to cause so much troubles.

Agnaar, I'd say that a lot of people, including many of the most skillful players on the site, have been complaining about the details of the vPoint system for quite a while, so I don't think it's all about your huge win (which was most impressive, even though I was one of the people you stomped).

Mercy and Mittag, you have a lot of common ground in trying to improve on vPoints. Sure, any scoring/ranking system is inherently controversial, and there will never be absolute consensus, and it's also true that a change may introduce some new factor that will prove to be a problem later on. But a change seems like a good idea, all in all. Good luck!

Any updates on this topic?
Would be sad to see this thread leave the frontpage.

I drew a few graphs for myself before, to check what would actually happen in different situations. I'll see if I can find them again and post them somewhere.

If we think of the options as vPoints with or without iteration, and mPoints with or without iteration, then my summary would be more or less as follows.

Regarding big solo payouts, the step from vPoints to mPoints seems to make that worse. I think there is a fairly intuitive explanation for this. In vPoints, the system thinks that you won over each opponent in a 1v1 game. In mPoints, the system thinks that you beat all players at once. Compare Messi beating 35 amateurs 1v1, or Messi winning one game against 35 players. I'll bump your rating up more in the second case.

The iteration solves the problem with big solo payouts, in both systems.

The only problem with iteration that I can see is that it devalues solos and small draw relative larger draws. That is primarily in large variants. It means that once there is only a few players left, it becomes much more important for players to avoid elimination as compared to going for the solo or cutting down the draw.

Is this a problem? Maybe not. My feeling is that in large variants, the player at the end which has a shot at the solo doesn't really risk elimination at all. So this might not affect incentives very much. What do the rest of you think?

One thing, which it is a little surprising to me, is that no-one though about just changing the multipliers for the large variants.

vDip has a pot-modifier calculated as follows:
$gV = $K * pow(((count($Game->Variant->countries) -1) / count($Game->Variant->countries)),2.7)

You can check the code here:
https://github.com/Sleepcap/vDiplomacy/blob/master/lib/rating.php
Calculation starts at line 208

@Oli

"Any updates on this topic?
Would be sad to see this thread leave the frontpage."

This project has been receiving less of my attention lately, but I do plan to finish it. My main problem is that I cannot program in PHP and my suggested changes are mathematically not just a simple adjustment. I have started taking an online programming course in PHP and at least now I know the meaning of all those dollar signs, but I haven't found the time to finish it.


@Mittag

"I drew a few graphs for myself before, to check what would actually happen in different situations. I'll see if I can find them again and post them somewhere."

That is AWESOME. I never managed to do that, as I couldn't program an inverse function. I am delighted you took the time to do some testing.

"Yes - you are right. The more points that would have changed owner, the bigger the effect of the iteration.

And there's the side effect: the effect on solo's is bigger than the effect on draws, because the amounts switching owners is bigger for solos. For Europa Renovatio with gV ~ 100, all players with rating 1000, and _no_ iteration, the 2WD is worth roughly 48% of the solo. With 100 iterations the 2WD is worth roughly 73% of the solo. (Assuming I didn't make any mistakes typing in the formulas.) A 6WD in Europa Renovatio will amount to roughly 34% of a solo; it used to be 14%. A 17WD(!) will pay out roughly 10% of a solo.

The effect is smaller on smaller maps, of course. On the classic there is more or less no effect at all. (I'm comparing the sizes of the gains, btw, if that was unclear. Also, these are the kind of numbers I want to see, to get a feeling for what the ranking system does to game play)

So, on large maps, we are deflating solos and small draws relative big draws. It means roughly that, on large maps, you should always play it safe."

"The only problem with iteration that I can see is that it devalues solos and small draw relative larger draws. That is primarily in large variants. It means that once there is only a few players left, it becomes much more important for players to avoid elimination as compared to going for the solo or cutting down the draw.

Is this a problem? Maybe not. My feeling is that in large variants, the player at the end which has a shot at the solo doesn't really risk elimination at all. So this might not affect incentives very much. What do the rest of you think?"

I don't agree that those are the incentives mRating gives players.

If you play a game on a very large variant and you want to maximize the expected value of your mRating, then yes, you should play it safe. Your calculations support that.

But now consider the following. Suppose we change mRating such that the new mRating is just e to the power of the old mRating. So for instance, if we were to do this with vRating, my new vRating would become e^2068. Would anything have fundamentally changed? I would argue no; all the relative ratings would be the exact same! Would you agree?

Here is the funny part: if players were to maximize the expected value of e to the power of my proposed mRating, I think they no longer have any incentive to play it safe.

And why would we assume players are trying to optimize the expected value of their rating and not some other metric? Why would players value the difference between, say, a rating of 1000 and a rating of 1500 as much as the difference between a rating of 1500 and 2000?

I actually think mRating reflects better how human beings think. Suppose you have a choice: either you take 5th place, or you take 1st place with 10% probability and 10th place with 90% probability. Lots of people would take their 10% chance.

The reason we tend to think that players try to maximize the expected value of their rating is because this is what any metric in which 'a higher rating is always better' always comes down to in first approximation (think of a linear approximation using Taylor series!). I see the fact that large variants lead to problems as a consequence of people trying to use linear approximations where they don't apply. That's how I intuitively came up with the idea of iteration.

"Let me ask another one. If you don't think iteration is a better method, then why are you proposing that we implement it?"

Because they are not mutually exclusive. We can use iteration AND change the multipliers.

"One thing, which it is a little surprising to me, is that no-one though about just changing the multipliers for the large variants."

Well, I thought about it, but because it was a simple change that could be done without my insight, I decided to not bring it up initially and rather focused on the more fundamental changes that I wanted to see. And yes, I think they can be toned down a bit for the larger variants.

"I don't think you should try to mimic vPoints at all. I don't see the point of it. The transition between ranking systems is a one time thing. Already after a couple of months noone will remember the old system. Just try to make a new system as good as possible."

Okay. I am glad you take this position.

"And, personally, I definitely don't like that the rating, which is suppose to represent your performance, can depend on what happens in a game where you are no longer participating. That just seems fundamentally wrong to me."

I don't like that either, but do you see a better solution for a rating system that translates well across variants?

Maybe I'm missing the point here, but I don't understand the problem about rating being affected by things that happen in a game after you have been eliminated from it. It seems natural to me that points/ratings are only determined when the game actually ends, and that's when the changes are made, for a soloist, a survivor, a draw participant, or an eliminated player.

@KingOfSwords Ideally, your change in rating should be determined by your result in the game only. Your score is settled after your elimination, so why not your rating?

Late to the argument, but a couple ideas to throw out. A haven't fully delved into the details, so if they don't make sense, please don't crucify me for it.

- What about having the number of iterations be equal to the number of players who started the game? So ranking jumps for large variants are watered down and we no longer see such massive jumps.
- What about locking in everyone's ranking at the start of the game? So if my ranking is 1500 when the game starts, calculations performed at end-of-game are based off this 1500 number, and not whatever my ranking is at the time. This eliminates some of the stalling/accelerating shenanigans that occur to try and have losses precede wins to manipulate rankings. I suppose that has other perverse incentives: perhaps if I know I'm about to make a huge win, I'm incentivized to join a bunch more games immediately so I get credited with a lower "starting" score before my win is realized. That's a relatively low magnitude disadvantage though.

Short answer @KingOfSwords

What I had in mind was these big variant, say Divided States, which can go on for 2 IRL years. It means that what happens now in a game you were eliminated from two years ago, can affect your current rating.

For dPoints, the score is settled at the moment you are eliminated. That's because you placed your bet at the beginning of the game.

For vPoints, at the moment, you place your bet at the end of the game. It means that once you are eliminated, you know you will loose your full bet, but the size of your bet will depend on your rating at the time the game ends. (And if you play other games in between, that rating will change.)

For mPoints, it's like vPoints but the size of your bet depends both on your rating at the time the game ends and the result of the game.

Here's an extreme example: someone who has never played diplomacy can join the site, join a Divided States game, be eliminated within a week. Then, that player can study the game, play a lot, become the number one player on the site with a rating of 4000. Two years later, that first Divided States game he joined ends in a solo. Then, vPoints will think he was a 4000 player when he played the Divided States game, and it will take away a big chunk of his rating because as a 4000 player he should have done better than being eliminated.

That said, we will not transform vPoints to a version of dPoints. So this 'problem' will remain no matter what. So I'll forget about it from now on.

I suggest the ranking considered powers taken over by the country switch tool as true replacements, that is, not penalizing the replacement player for a negative result.

OK, I think I get it now. Yes, events in a long-winded game, after you are eliminated from it, can affect your score/rating (especially if the game results in a solo), but the bigger issue is changes to your score/rating in all the other games you might play while waiting for the long game to finally finish. Maybe JacobL582's suggestion that everyone's initial score be locked in at the start of each game would be a good idea.