Here are my thoughts on PPSC.

There are two ways that PPSC games can end (normally): with a draw, or with a win.
In the case of a draw in PPSC games, we have to decide on how we want to rate performance. There seem to be (at least) two logical alternatives:
1) Everyone sharing in the draw is considered to have performed equally, regardless of SC count.
2) Relative performance of players sharing in the draw are determined by relative SC count.

I think the first method would be the predominant choice, as that's how the points system splits PPSC pots for draws, how the WTA draws are viewed, and how I think most people think about performance in a drawn PPSC game. However, the second is just an interesting alternative to put out there (but does change the objectives significantly).

Assuming that we go with the first method, I think that drawn PPSC games should result in ratings adjustments using the same calculations as for drawn WTA games.

For Won PPSC games, when doing the pairwise adjustments, I think the relative performance has to be based on the relative SC count, even when comparing between the winner and another player. In a PPSC game (using the classic variant as an example), I think we have to say that a winner with 18 SCs has performed just somewhat better than a strong second survivor with 16 SCs. However, the difference between an 18 SC winner has clearly done much better than a survivor with 1 or 2 SCs. I think a rough way to measure relative performance on a 0 to 1 scale would be to take the difference in SC count and divide by the max SCs (the number needed to win).

However, I think there are some caveats:
1) How do we handle overkill (ending the game with more SCs than needed to win)? We don't want players needlessly delaying a sure win, but setting up a final turn to take more SCs that needed in order to game the system for better ranking.
We could cap the relative performance with minimum of 0 and a maximum of 1, however, it would still be beneficial for a player to delay winning and attempt to abuse the overkill in order to maximize his relative performance to all of his allies. There's a legitimate game on WebDip where a player was able to win with all 34 SCs (by carefully setting everything up while staying at 17 SCs until the very last turn).
2) How do we handle underkill? There's a "concede" feature on this site right? I'm not too sure how that works, but if the game is ended prematurely with a concede, should we project a player out to 18 SCs? Should we deduct SCs from other players? If not, couldn't a grand alliance abuse the concede feature to prematurely end a game where the other player has a sure win in order to preserve their SC count?
3) Perhaps the relative impact of a pairwise adjustment should also be weighted somehow by the total SCs shared between the two players. For example, two players both finishing with 15 SCs can be convincingly be said to have performed at a similar level. However, I find it somewhat less certain to say that two players both finishing with 1 or 0 SCs have necessarily performed at a similar level, since they have both essentially (or actually) been defeated. Making the adjustments for such pairs (with 0 SC to 0 SC) have little or no relative impact is along the same lines as having no pairwise adjustment between two losers in a WTA game. Essentially, it's tough to say that two losers performed at an equal level, since one of them could have performed just bad enough to be defeated while the other could have spectacularly failed at a whole different level but can only do so much as to be defeated in terms of final game results.

Going back to the issue of possibly losing points in a draw. I don't think it's necessarily too bad to have some potential negative effect in some draw scenarios. This is should be relatively rare, being mitigated by reduction of the draw equalization effect, would only occur for relatively large draws involving a significant rating disparity between the players involved. Thus, perhaps its appropriate in some circumstances since the higher ranked player should be expected to do better to reduce the size of the draw, but failed to do so.

Regarding broken games, the Ghost Rating system would ignore games that ended in the first three game years. This would allow games to be drawn early (without interfering with Ghost Rating) in the case of an early CD. Perhaps a similar policy would make sense for Oli Rating.

@PPSC:
There is a problem with very good players winning the game and still loosing many points, because usually the first few players have a similat SC-count. And IF a player needs to score 0.7 against all other players it's very obvious that even winning the game will make you loose points. Esp. is there is a close 2nd one.
Because of this I would rate the winner different. After all he won the game. This would also lessen the problem for all other 1on1-matches, as usually the 1st and the 2nd have a really close SC count. We had the discussion about this many pages down the thread.
I already handle an underkill by giving the game a lower KValue. Basically you can set up games with a very low winning condition. This would screw the stats too.
And I also like not counting games with no more than 6 turns.

Yeah, that's a good point. I completely overlooked that.

Perhaps that suggests that good players shouldn't be wasting their time with PPSC ;P

Would it be possible to classify opponents in groups instead as individuals for purposes of draws? For example, break down all players as being in the top 10%, 2nd 10%, 3rd, etc. Then, if a top 10% draws with another top 10% player, they are equal, and neither gains or loses points. But if a top 10% player draws with a lower group player, they lose points and the lower player gains.

An alternative to that is to say that anyone who is within "x" number of points of the other player, is equal when it comes to distributing points. I would propose that "x" should be at least 5%-10% difference.

As it is right now, If I draw with someone who has only a few points less than me, I will lose points. It seems like the distinction is too precise when you are looking at 1 or 2 out of 1000+ points. For me, 1 point difference is only 8/100ths of 1%.

@Devonian:
Most of the time you don't loose points in a draw. You might loose 1-2 to the other players that did draw, but usually you gain more points from the Defeated to make this matter. The result is still a gain, but not soo much as a player with fewer points that is part of the draw.

Oli,
I have 26 draws, and 14 of them earn me negative points. Some of these games were against good players: I lost 3 for drawing with Bozo in gameID=12237.

It may not be a problem when some of the players are higher ranked, and some are lower ranked. But since most players are lower ranked than me, my only option is to get a win in every case. In fact, in every game, there will be one person who cannot win, unless they solo. This seems too punitive for small differences.

I've only checked my draws quickly, but I know I've lost points in a draw where I was the biggest player by a decent margin. I'm not sure I get how it works with draws.

Might I suggest we consider including (not necessarily in the multiplayer ELO formulas, but maybe along side) some additional metrics? (note I dub these metrics as they aren't complete measures of total skill, but maybe they can provide insight into certain skill components and inform alternative measures of 'skill'.)

For instance in WTA, there is still information to be gathered in how early a player was defeated. Someone who was defeated in the final turn is probably a much better player than someone defeated in turn 2. Should these players score 0.5:0.5 against each other? Probably, since, as an ELO system is based on expectation, the player eliminated in the final turn will probably win other games and so bring his ranking up that way. ELO isn't a tool used for getting things right the first time but for approaching the expected result over time. However, it might be nice to capture this information on when a player was eliminated for possible use in other ranking systems.

Another metric, much easier to record is: Total supply centers held across all games. This is another indicator of some form of skill (not necessarily directly correlated with ability to draw/win games), but a player who consistently controls large number of SC's is probably fairly skilled.

Another metric: share of a draw (while meaningless in terms of game outcome) is still information that speaks to the skill of a player. Often a 1 SC player is kept around as a bargaining chip rather than any real skill on that player's part (though I admit there are from time to time 1SC players who negotiate their way into a draw by diplomacy and maneuver skill). Additionally, the player who was going to solo but got forced into a draw is probably highly skilled, even if they weren't quite skilled enough to pull off the solo that particular game.

I'm sure there are many others we could come up with, and these might be used to make further adjustments or my preference presented alongside the ELO ranking system (or integrated into alternative ranking systems).

As for losing points in a draw, 1v1 games should end in a solo unless one player is able to force the other into a draw. In your case Devonian, your skill level indicates that you are expected to solo against Bozo more often than he solo's against you, and thus a draw would be less desirable for you than a solo as you are expected to solo. This is exactly how an Elo system is supposed to work in a 1v1 setting. 741 solo results on the FvA variant vs 54 draws, means that draws are not the expected result in 1v1. Combine this with an ELO ranking system for 1v1 games and you have essentially the same result as in chess, where the more skilled player having been forced into a draw is a slight failure for the player with better skill.

Now how this should translate to multiplayer games where solos are not the expected outcome, I'm not sure. I see the potential issue of one player only being able to gain points by soloing, and the issue with ELO (inherent even in the chess community) where higher ranked players refuse to play lower ranked players to protect their rating becomes the result much more often, as the chances of soloing against that many lower ranked players are fairly low. It is for this reason that I have been promoting that alternative rating systems be used alongside the multiplayer ELO system.

Leif,

"the issue with ELO (inherent even in the chess community) where higher ranked players refuse to play lower ranked players to protect their rating"

This is exactly where I was going with my concern. If I am in any way concerned with my ranking, this system will cause me to avoid games where I will lose points unless I solo. In fact, being currently ranked #2, I would have to avoid playing everyone, except Ruffhaus. This does not seem to be a good way to keep top players playing on this site.

I thought my solution would somewhat minimize that adverse side effect to this otherwise good system. If, the difference had to be 10%, I could play the top 10% of players without penalty. Someone who is at the 10% mark could play players plus or minus 10% of their skill. So everyone would have plenty of opponents to pick from, without worry that a draw would hurt them.

@Devonian:
With the actual calculations you are No.2 on the list. From there it's nearly impossible _not_ to loose points. You can't get better than No.1 and you will have to beat RUFFHAUS in some games or outperform by a large margin other players.

But that's how an Elo-System works and thats why I always said I will keep the DPoint-system in place and visible behind each name. The alternatives we search here are just additional/optional. So players can check how they compare to all other players on the site in a system that can't be tricked as easy as the GR or the point system.
It will be another HoF independent of the original DPoint HoF and some players won't notice the difference at all. (The HoF is one of the pages usually nobody looks at).

If you are at the top you usually only go down playing on as there is a upper-limit for a rating. But even if you loose some points you will still be one of the best players on this site and you will only move a few places up and down. If your rating drops beneath a certain level you will gain enough points back very quick.
To lessen this effect psychological I might even remove the breakdown per game or the players history or even the points for general access, so players do not get too psyched about their Elo-rating and how it changes as they play games here. At the moment this is mostly for debugging purposes. The DPoints still serve a necessary role here to generate tension and reward for playing. And that's why I won't remove them. But they are not that accurate for measuring a players performance and that's why we need some alternative.

That is an idea I'm not necessarily opposed to, but one that in my mind presents further problems in that the only way to gain against other players is to eliminate them (a possible metagaming issue in non-anon games against higher ranked players?), or to solo against them.

My proposals to address/alleviate this problem are 3-fold.

1. We implement multiple rating systems so that no one ranking system becomes too important:

For instance, I like your idea for a ranking system (I think it was yours from way back earlier in this thread) where each player 'bets' 5% or 10% of their skill rating skill every game, and the winner gets the 'pot' or the 'pot' is divided in a draw. (We'd have to make sure that fractions are apportioned correctly to keep this zero-sum otherwise it grows without bound like D-points do currently).

I'm sure there are others of value as well.

2. We have multiple ranking stats in addition to the current rating (which would be over all games)
-Record each player's all-time-best rating and compare those
-Include rolling monthly or quarterly record like the GhostRating uses.

Players are more willing to risk if they can top the monthly ratings at the expense of possibly losing a #1 position in the current rankings. Also, keeping track of each player's all-time-best and allowing players to compare those is another way to alleviate the pain of losing a 1st place position, as your highest ever rating may still be higher than mine even if I passed on you the current rankings.

On this note, would it be possible to include some timestamps for the resultant rating from each game to be able to plot a player's rating against another player's rating over time for comparison of peak ratings etc?

3. Provide ratings by variant type and game style as well to allow players to compete for more than one top ranking. A player with 20th place in the overall ranking but 1st place in the 1v1 rankings might be willing to risk his 1v1 ranking further to try to better his overall ranking.


One idea (probably worth throwing out instead of my continuing to type this an your continuing to read this) is to include a ratings decay over time to encourage players to continue playing rather than sitting on their laurels. But since this ruins the zero-sum nature of the rating system, I'm going to recommend it's a bad idea for the Elo system (maybe not for an alternative rating system though).

Oli

"To lessen this effect psychological I might even remove the breakdown per game or the players history or even the points for general access, so players do not get too psyched about their Elo-rating and how it changes as they play games here."

NOOOOooooo!! I'm addicted already!!

@Leif:
1. That's No. 3 on my list once we finished the Elo-like-system. (Or use the GhosRating, it's not that different)
2. as we know when each game ended we already have a timestamp of each rating.
3. Thats No.2 on my list and it already works. But as long as the formula is not finished I won't burden the server that much to recalculate everything.
4. A rating-decay over time is a really complex problem. Usually the first few games people play here do cause great rating-changes as the rating is not fixed. Later on the changes are not that big as the real-rating is reached. Now if you remove the first games your actual rating will change quite a lot, as the bigger changes are now back (but in reverse effect). This would only work if we regular rebuild all ratings for all games a given timeframe, but this is very time consuming and the server might not be able to handle this.

Oli,
1. Sounds good!

2. I guess I was wanting to see the timestamp in a column next to the rating since I don't have a script written to go grab the game time stamp from each individual game. I figure it's probably a couple lines of code for you, but if not and it's a big deal, please don't waste time on it.

Also what were your thoughts on a rolling monthly rating and peak rating for each player?

3. Sweet, looking forward to it!

4. I refuted this in my own post, don't waste time on it.

Clarification on # 2:

For a given player you display:
Game Name Variant Status Change Total

I am looking for something to tell me what order a game is finished in, as in a timestamp column or a completion number that gives an ordinal identification for that game to be able to compare historical rankings between players (for instance, what was I ranked compared to other top players when I had my peak rating)..

A rolling monthly rating or peak rating should be possible, but this might take some more time.

PS: I disabled the HoF again, so I can implement the new formulas once they are finished.

@Devonian: Grouping the people together is a very interesting idea.Just wanted to let you know that I did read your suggestion and like it. Just more thoughts on how to use this practically are needed.

Just an idea about how to display the HoF ranking next to the player's name, could be to include a little symbol (like the donator circle).

I'm thinking buildings:

top 1% - a gold skyscraper
top 1-5% - a silver skyscraper
top 5-10% - a bronze skyscraper
10-20% - a mansion
20-40% - a house

etc...

@kaner: cool idea. But someone has to draw the symbols, and I'm really bad at such things.

I'll be happy to do this, but are buildings the best symbol? - perhaps I should open a new thread and ask the community for their suggestions. (swords, tanks, trees, vials of blood... all come to mind as potential symbols.)

Oli,
I wouldn't know how to program something using groupings. I was just making a proposal.

Actually, I think my alternative proposal would be easier to implement.

If player "A" and player "B", are within 10% of each other, they are treated equal for draws. It would apply at all skill levels, but I think the practical part of this is that highly ranked players would then be able to play reasonably similarly skilled players (but slightly lower rated) without the fear of losing ground just because they accept a draw.

I just think a rating of 1 point out of +-1300, is too small of a margin to say that the higher "rated" player should be penalized for a draw. The rating difference of 8/100ths of a percent. (If the penalty was equally as small, then it would be fine, but .0008 would be rounded to zero anyway.)

@Devonian, the draw "penalty" for a higher ranked player would likely not even manifest itself if the players are very closely ranked. For players that are already closely ranked, the expected result would already by very close to 0.5, so a 1v1 draw would not really have too large of an impact on either player.

In larger games, if everyone is relatively closely ranked, and the draw isn't too big, every drawer would most likely gain ranking. This would especially be the case if the Draw Equalization (reduction) Factor was implemented. In the prototypical ratings that you saw, that reduction factor had yet to be introduced.

For a 1v1 game, with two players that draw and have a ratings that only differ by one point, I think the rounding would create no change in rating for both players. For 1v1 games that do end in a draw however, it makes sense that the two players rating move closer together, since the result of a draw would suggest that the players had performed equally well.

However, I do suppose a reasonable argument against that is that 1v1 diplomacy games are not very deep, and that players can generally force a draw despite a rating disparity, given that a variant is well balanced. This would be a good argument toward scaling down the impact of 1v1 games in the overall ratings system. In short, perhaps it's too easy to just force a draw in a well-balanced 1v1 variant? This would create a problem in that very good player playing against a player that is just good enough to force a 1v1 draw would often get a lot of draws that would falsely suggest that they are of equal skill. This problem more apparent when two players with very different ratings player together (assuming that both are still good enough to at least force the draw in 1v1), than when two players of similar ratings play together.

Yebellz, Maybe I don't understand the impact calculation. Are you saying that if player A has a rating of 2 more than player B, and they draw, They will move closer to each other? So, player A will lose no more than 1 and player B will gain no more than 1? If that is the case, then I guess it makes sense on a mathematical basis.

However, there may still be the unintended consequence of causing higher rated players to avoid playing slightly lower rated players in order to maintain their high rating. This would be a very unfortunate unintended consequence. I think someone pointed out that this is already a problem with chess. If we can adjust for this, and still keep the mathematical integrity of the system, maybe we should try to do it.

As far as 1v1's games are concerned, I am not worried about them. They should end up with a win or loss. I am more concerned with the draws with 7 players, and 4 of them draw. In my opinion, a 7 player game should rarely (never) end in a solo if it is a WTA full press game. A 3 way or 4 way draw is the most likely outcome. Won't the higher rated players lose points from a draw in this situation?

Devonian, I don’t understand your concern.

Let me explain:
If you are rated 1300 and play a duel against an opponent rated 1298, your expected result is 0.503 while his expected result is 0.497. A draw gives both a real result of 0.5, so your net score would be -0.003 and his net score +0.003. Now I don’t remember which was the multiplicative coefficient used in front of ratings change calculations for duels (10?). Even if it were 50 you and him would result in a zero change due to numerical rounding.
If you’ve lost 3skill points against bozo… I suppose this has happened due to an old game when you or him were still not properly rated ( that is bozo was still underrated or you were overrated ).

You play vs stronger opponents? Your chance to succeed is lower AND your expected result is lower.

You play vs weaker opponents? Your chance to succeed is higher AND your expected result is higher.

You’re almost on top of the list, so your expected result in a pairwise adjustment will be most of times above 50%.
That’s the price to pay for staying on top.

The spirit of an ELO-based system is not accumulating points: it’s converging to your actual position and keep it. It’s somewhat a different mindset with respect to the D-points system.

Please note that I am a former chess player.

@ Decima Legio : of course, the spirit of Elo points is to gain points ! IT IS NOTHING ELSE !
For example, in order to get the title of "International Grandmaster", "International Master" or even "FIDE Master", one of the conditons is to have an Elo of at least "x".

Also, it is wrong that chess players avoid to play with lower ranked players because :
1° In a tournament, you don't chose your opponent : it is determined by a pairing system.
2° As a matter of fact, many chess players like to play with players that are a litlle less well ranked than they are because they think that the win should be rather easy and that it will reward them some additional points.

Devonian,
if you note, drawing a duel together with an inferior player would result in a net loss, which I think it’s right, even using your initial proposal. The more the opponent is inferior to you, the more will be your net loss.

Retillion,
indeed you are to gain ELO points.

But the more you raise the more the algorithm will oppose resistance to your points growth through an increased Expected Result.
What I meant is: at a certain point, when you are *correctly* rated, the true challenge is keeping your points level.

If sometimes you’ll be overrated, a single mistake can cost you some points and bring you back to a proper level.
If instead you’ll be underrated, you’ll find it easy to gain points, even with a worthless 6 way draw in a classic.

@ Decima Legio, when you wrote :

"Retillion,
indeed you are to gain Elo points."

Who is "you" ? Do you mean me personally or people generally ?