A (Choose: Great/Pointless/Annoying) Scoring System Thread

[NoPunIn10Did]

It also totally throws away the idea that Diplomacy is a fixed-sum game. If the game ends in a draw, the board leader gets 7000 points plus their center count; 2nd place gets 6000 points plus their center count; all the way down to 1000 for 7th place. (Ties split the difference.) If the game ends in a solo, the winner gets 1,000,000 points--solo winners cannot be caught by any number of draws!

Just an FYI: the most recent iteration of Carnage is fixed-sum / zero-sum, in that a solo is awarded 28,034 points rather than 1,000,000 points. 28034 = 7000 + 6000 + 5000 + 4000 + 3000 + 2000 + 1000 + 34.

The "draw pot" isn't necessarily a fixed value, but the grand total of points awarded each game will be the same (barring some weird scenario where an SC remains neutral all game).

[jay65536]

<Shrug> I'm generally a fan of fixed-sum systems, although the creator of the system, Dave Maletsky, used to be adamant that no one who solos in a tournament should ever be able to lose to someone who didn't solo. (I expect he still is.)

The fixed-sum version of Carnage does do this in practice, as over a 4-round tournament, someone who gets 4 board tops but doesn't solo still can't catch someone who soloes and then gets 3 losses.

Your point about Dixie is correct--the games are all fixed-sum when you take into account the fact that some of the points are given to the losers. What's more, not all losses are created equal. I am of the opinion that this feature--counting some losses as more points than others--is a flaw in any scoring system in which it appears, although that does not stop it from appearing in almost every system in use. It's one of the very few things that Dixie (primarily draw-based) and Carnage (primarily lead-based) have in common. I think of the systems currently in use in North America, only Sum of Squares doesn't have this flaw, and it sort of still does in spirit.

[NoPunIn10Did]

No scoring systems currently in use are zero-sum, and only a handful (like sum of squares) are fixed-sum.

This ends up being a somewhat arbitrary distinction, since a fixed-sum scoring system can be trivially converted into a zero-sum system. This is how webDiplomacy and vDiplomacy both handle scoring.

The Elo rating layer in use on PlayDiplomacy yields a nearly zero-sum result, albeit with some extra tweaks that make it more zero-sum in aggregate rather than zero-sum for any individual game.

[NoPunIn10Did]

I think of the systems currently in use in North America, only Sum of Squares doesn't have this flaw, and it sort of still does in spirit.

Say more about this. How would it still have the flaw "in spirit," as you say?

[jay65536]

In SoS, if someone votes a game end while they have a 1- or 2-center hopeless position, they have technically made it into the draw and they will earn a scant amount of points. In a different system, though, the player might have voted himself out of a draw, or the others would have played on to eliminate that player. In that way, I feel like a lot of positions that are lost "in spirit" can earn >0 points in SoS, just because SoS doesn't incentivize playing on solely to turn someone's position from a "spirit" loss to an actual loss. SoS, like C-Diplo, though, is a system where that sort of thing matters extremely little.

[NoPunIn10Did]

In SoS, if someone votes a game end while they have a 1- or 2-center hopeless position, they have technically made it into the draw and they will earn a scant amount of points. In a different system, though, the player might have voted himself out of a draw, or the others would have played on to eliminate that player. In that way, I feel like a lot of positions that are lost "in spirit" can earn >0 points in SoS, just because SoS doesn't incentivize playing on solely to turn someone's position from a "spirit" loss to an actual loss. SoS, like C-Diplo, though, is a system where that sort of thing matters extremely little.

Gotcha. While I've certainly benefited from other people voting themselves out of a draw, I'm not particularly fond of that mechanic on the whole. Draw-sized scoring almost necessitates it, lest games get dragged out to what was already an inevitable conclusion.

I do find it frustrating how many people (clearly not you) treat the all-share-equally-in-a-draw rule as sacrosanct while clearly being okay with breaking the other original draw stipulation (that a draw must include all survivors).

For my part, I'd much rather flip the two, breaking the equal-draw rule and keeping all draws DIAS for simplicity's sake.

[NoPunIn10Did]

One thought on SoS:

Has there been a system that mathematically "squishes" SOS scores towards a midpoint such that they're still fixed-sum, but limits the maximum points a draw can award?

[jay65536]

One thought on SoS:

Has there been a system that mathematically "squishes" SOS scores towards a midpoint such that they're still fixed-sum, but limits the maximum points a draw can award?

There hasn't been yet. It's actually very hard to do something like this without accidentally introducing some other issues. For example, my first thought was applying a "dampening formula" where you multiplicatively shift the scores closer to a fixed fraction (like 1/7). You'd have to do this by subtracting the fraction, multiplying the adjusted score by some other fraction (that would be based on how much worse than a solo you want the maximum draw score to be), then adding the first fraction back in. Unfortunately, that will either do one of two things: if you apply this formula to solos, you actually shrink the distance between a solo and a draw, not increase it; but if you apply it to draws only, you've now created a situation where not all losses score the same.

If you apply a varied formula based on draw size, so that you can keep all losses worth 0 and keep a solo worth 100, you've now introduced an element of draw-based scoring into the SoS system, which seems to me like it goes against what the system was designed to do. So when you try to fiddle with the math, it gets hairy pretty fast.

EDIT: I guess my point here is, if you wanted to change the SoS system to reward solos more than good non-solo results, probably the easiest and best way to do it, as much as I hate to say it, is to scrap the zero-sum element and just make a solo worth more than 100 points, but draws still add up to 100.

[jay65536]

I do find it frustrating how many people (clearly not you) treat the all-share-equally-in-a-draw rule as sacrosanct while clearly being okay with breaking the other original draw stipulation (that a draw must include all survivors).

For my part, I'd much rather flip the two, breaking the equal-draw rule and keeping all draws DIAS for simplicity's sake.

A few things about this:

1) My view is that those 2 rules go hand-in-hand. I think having no-DIAS but draws splitting points equally is anti-competitive. It encourages creating situations where solos are a lot less likely. And as I said earlier in the thread, equal points for draws is theoretically supposed to create situations where small powers fight on, but in practice (in my experience anyway) it's actually the exact opposite.

I know you're the one who posted about your board at Dixie where a 4-power endgame ended in a 3-way draw where someone who had no business voting himself out did. Your case is an extreme example, but I wasn't exactly surprised it happened; to me that's the logical conclusion of what happens when you play a small number of tournament games in a draw-based system without DIAS. You don't tend to get people fighting on; you tend to get people NOT fighting on.

2) There are other questions where the rules are ambiguous but players act like the rules are clear, for the sake of them being purists. For example, the rules state that draws must occur "by consensus". Why, then, does no one interpret that as mandating open voting? Why is secret voting sacrosanct? The rules as written also do not imply that Diplomacy is a fixed-sum game; but I bet if you showed a proponent of draw-based scoring this system:

Solo 40
2way 10
3way 9
4way 9
5way 7
6way 7
7way 5
Loss 0

they would not like it, even though it adheres to all of the written rules.

To me I think the biggest thing is that when we talk about what we prefer in a scoring system, there's no excuse for saying "I'm in favor of this because it's in the rules". You like what you like, and you should have your own reasons why.

3) What I've been wondering for awhile is, is there a way to make a scoring system that bends the "equality in a draw" rule partially but not completely? Like, maybe there's a way to make a good scoring system where most draws split points equally, and/or most players share equally in a draw, but with some kind of mechanism that rewards exceptional performances so a tournament field can have separation at the top? Perhaps this is just a pipe dream, though, because as I said upthread I'd probably need to run my own tournament to ever have a chance to try it out.

[NoPunIn10Did]

A few things about this:

1) My view is that those 2 rules go hand-in-hand. I think having no-DIAS but draws splitting points equally is anti-competitive. It encourages creating situations where solos are a lot less likely. And as I said earlier in the thread, equal points for draws is theoretically supposed to create situations where small powers fight on, but in practice (in my experience anyway) it's actually the exact opposite.

I know you're the one who posted about your board at Dixie where a 4-power endgame ended in a 3-way draw where someone who had no business voting himself out did. Your case is an extreme example, but I wasn't exactly surprised it happened; to me that's the logical conclusion of what happens when you play a small number of tournament games in a draw-based system without DIAS. You don't tend to get people fighting on; you tend to get people NOT fighting on.

A fair assessment. In Dixie's scoring it's more likely in part because those who vote themselves out of a draw can get points. I generally do see this as beneficial from a pure exhaustion standpoint though, at least in a face-to-face context. Those 6 PM rounds can be brutal in a format where a game has no foreseeable end. Even an online game, which doesn't necessarily have immediate attrition problems, can be mentally draining as it drags on toward an inevitable consequence (or until somebody just "breaks").

2) There are other questions where the rules are ambiguous but players act like the rules are clear, for the sake of them being purists. For example, the rules state that draws must occur "by consensus". Why, then, does no one interpret that as mandating open voting? Why is secret voting sacrosanct? The rules as written also do not imply that Diplomacy is a fixed-sum game; but I bet if you showed a proponent of draw-based scoring this system:

Solo 40
2way 10
3way 9
4way 9
5way 7
6way 7
7way 5
Loss 0

they would not like it, even though it adheres to all of the written rules.

Definitely agreed. It's a big component of the "any scoring system is a variant" axiom. Nothing in the rules attaches a numeric value to a draw or solo, and nothing yields an objective comparison between a draw or solo.

To me I think the biggest thing is that when we talk about what we prefer in a scoring system, there's no excuse for saying "I'm in favor of this because it's in the rules". You like what you like, and you should have your own reasons why.

Agreed, though I would say that "it's in the rules" is a flawed way of saying, "I like this scoring system because it feels the closest to an unscored game." It's definitely an opinion rather than a fact (which some players refuse to accept), but there is at least a foundation there. I even consider this to be the case for draw-sized scoring; it seems to me to be the system that yields the most similar gameplay to an unscored game. Over time, however, I've found that's not necessarily a good thing.

3) What I've been wondering for awhile is, is there a way to make a scoring system that bends the "equality in a draw" rule partially but not completely? Like, maybe there's a way to make a good scoring system where most draws split points equally, and/or most players share equally in a draw, but with some kind of mechanism that rewards exceptional performances so a tournament field can have separation at the top? Perhaps this is just a pipe dream, though, because as I said upthread I'd probably need to run my own tournament to ever have a chance to try it out.

What you're describing is, at least in part, the Dixiecon tournament scoring system. It's probably not what you want, and it has its own downsides, but its hybrid of draw size, center count, and rank seem to be geared to fulfill that exact purpose: keep draws mostly equal, and provide incentives for secondary goals beyond win/draw/lose.

Unless one moves away from a fixed-sum system (or a near-fixed-sum system, like PlayDip's), I just don't see a way to do this without bringing draw whittling back into the mix. Small tournaments can definitely operate with a non-fixed-sum system; I'm actually doing that very thing this year with the Tournament Through Time. But for a perpetual online platform, I just don't see that being scalable in the long term.