Introduction

Swordsman3003 (a.k.a. Your Bored Brother) is a very accomplished player on webDiplomacy.net who has recently begun blogging about Diplomacy. He’s most well-known for his incredible article The Biggest Game of All Time, in which he published a journal he was keeping throughout a very highly ranked gunboat game – it’s incredibly in-depth and well worth a read if you want to learn more about how a player at the highest level of gunboat thinks about the game.

It’s not that article I’m here to talk about today, though. Most recently, he received a fan letter asking him to talk about scoring systems; specifically, the difference between the two systems on webDiplomacy, and why games there tend to be overwhelmingly Draw-Sized Scoring. This post is majorly a response to his article on the subject, because while it’s a good read, to me it felt like it was an argument built around a flawed understanding of the Sum of Squares system — one that a great many high level players have simply because of an outright refusal to play it in a high-level setting.

Before I begin, I strongly recommend reading the original article. I will try to make sure this post is understandable on its own, but it will be helpful to have read Your Bored Brother’s views on the subject first. Additionally, this is purely meant as a response and as such will be exclusively focused on the scoring systems available at webDiplomacy.

The Two Scoring Systems

Let’s start off with the basics. WebDiplomacy has 2 current scoring systems — Draw-Sized Scoring and Sum of Squares. Both of these are Winner-Takes-All, meaning that in the event of a solo, all of the available points will go to the player who won and everyone else will leave empty handed, regardless of their supply center count. In the event of a draw, both of these systems give no points to eliminated players, but the way they handle the rest of the draw varies dramatically.

Draw-Sized Scoring splits the available points equally between all surviving players. As Your Bored Brother notes, this is very easy to understand, and it’s always obvious how much you will receive in any situation. It also means that supply center count does not matter; a player with one supply center will earn the same amount of points as a player on seventeen.

Sum of Squares is based around the supply center count of each player, and is significantly more complicated. If you’re interested, Your Bored Brother covers the inner workings in his article, but the basics of this system are:

• You will gain points if you gain a supply center
• You will lose points if you lose a supply center to another player
• You will lose points if a small player loses a supply center to a larger one.

As such, your objective under this system is to gain as many supply centers as possible, while keeping the rest of the board as divided as possible. You’ll earn far more if you have 17 centers and you have 6 opponents on 2 or 3 centers each, than you will if you have 17 to two players on 10 and 7.

Incentives, and What Draw-Size Scoring Does Right

Your Bored Brother’s article begins with the meaning of victory in Diplomacy. I’m fully in agreement with all his points here. Solos aren’t necessarily uncommon in your average game, but at a high level they are incredibly rare. If a player looks to be reaching 18 supply centers, the rest of the board will usually unite to form a stalemate line, a line of units that can enter orders in a certain way to make them completely impenetrable. There are a number of these stalemate lines that hold 17 centers exactly, meaning that even when a player is on the cusp of victory by SC count, the win is far from guaranteed.

His explanation of alternative objectives is on-point too, and I’ve seen all of his examples in high level games before. “Carebears” don’t usually care about the solo win and will deliberately play to draw with their allies, “Desperados” will go all-out to ensure survival by trying to create a position by which a player will solo if the desperado is eliminated or threatened with elimination, and “Revenge-Seekers” will attempt to ruin the score of the player they are annoyed with, sometimes going to the extent of throwing the game.

All of these are legitimate strategies, but some make more sense than others in the context of certain scoring systems. I would argue that the ideal scoring system would punish the Carebear and Revenge-Seeking styles of play, because these run contrary to the objective of Diplomacy in order to fulfill an idealistic objective. Diplomacy is all about playing on people’s’ ideals and emotions, so idealistic objectives are definitely a part of the game, but there needs to be some trade-off for considering your ideals to be more important than going for the win, or attempting to survive to a draw. In the same way, you’d be hard-pressed to find anyone who thinks that the Desparado style of play should not be rewarded — these players do everything they can to hold onto their position in the draw, and are often working harder than the larger players to do so.

It’s due to this that there is one point in Your Bored Brother’s argument that I fully agree with — really, the only thing I agree with in part 3 of his article — Sum of Squares scoring absolutely fails in rewarding Desperado play. Due to the focus on SC count, a player who fights tooth and nail to be included in the draw and survives on one center will be rewarded with almost nothing – oftentimes, even players on 2 or 3 centers will barely receive more points than the zero an elimination would have netted them. This makes smaller powers more likely to go all out for vengeance; if there’s barely a difference between your result if another player solos and if they don’t, why not make another player solo to make sure the player who stabbed you gets nothing also?^[1]A number of ways to fix this have been proposed, usually by adding a base score for surviving to the draw. Unfortunately, that doesn’t work on webDiplomacy, because both D-points and Ghost-Rating require a zero-sum system, so there’s nowhere for those extra points to come from. An alternative … Continue reading

So, deterring revenge-seeking is definitely something Draw-Sized-Scoring does far better than Sum of Squares scoring. In a high-level Sum of Squares game, players will take this into account and attempt to play around it, but that doesn’t change the fact that it’s certainly not ideal.

However, in my view, this is the only one of Your Bored Brother’s points that really makes sense.

Sum of Squares Does NOT Encourage “Dotting”

In fact, the very next point Your Bored Brother makes is that Sum of Squares encourages ‘Dotting’ neighbours – the practice of taking one or two supply centers for no reason other than having a higher SC count – but he’s already gone over one reason why this would be a terrible idea in high level play! There’s nothing that annoys other players more than dotting, and in Sum of Squares annoying players is considerably more risky than in Draw Sized Scoring because of the added incentive for revenge-style play.

One line in the dotting section really stood out to me: “But sum-of-squares scoring adds an additional incentive to just take centers all the time because the number of centers you have will matter when the game ends in a draw.” This reasoning really highlights the two flaws present throughout most of the article – firstly, his discussion on DSS and SOS are from completely different perspectives – most of his strategic reasoning is that of a high-level player where he discusses DSS, whereas in the SoS sections he seems to be thinking at most one turn ahead, something that would be prominent in very low-level play but which is almost entirely irrelevant in mid-to-high level games. Secondly, he separates out playing for a good draw and playing for the win. That separation is very common for players looking at it from a DSS perspective, because in DSS playing for a good draw and playing for the win require entirely different strategies, but which makes no sense in Sum of Squares.

And that brings us to the main problem of DSS – conflicting objectives. For this, we need to quickly answer a question – in high-level play, how do you solo?

Draw-Size Scoring Creates Contradictory Objectives

One thing that’s universally agreed is that in order to have a good shot at winning, you need to try to keep the other side of the board in disarray until you have resolved your side. That way, you probably will not be facing a united front when you need to cross through potential stalemate line positions. It’s for this reason that Italy is such a strong soloing power at high level play: being so close to the home centers of both Germany and France means that Italy can disrupt the west with minimal commitment while growing in the East. Is an EF alliance forming? Send an army to Piedmont to slow France down. England switched sides? One move takes you to Tyrolia and completely flips the pressure against Germany. England starting to dominate? Back off and try to encourage an FG – Italy can do all this with just one unit.

The issue here is that DSS actively discourages doing this. If you play to keep as many players in the game as possible, all at an even power level, you’re outright hurting your score in all outcomes other than the one where you solo. Say, you’ve played this strategy perfectly and, as Italy, you have control of all of Austria, Turkey, the Balkans, Tunis, and all of Russia except for St Petersburg, with Russia, England, France and Germany all surviving in the west and Austria holding on in Berlin and Munich. Although you’re not over the stalemate line, this position is not bad from a soloing perspective; if any one player on the other side fails to coordinate, or is annoyed at another player and decides to take revenge, you’ve won and you take away all of the points. However, if they do manage to coordinate, DSS states that this is an awful position for you; unless you can back off and get them to eliminate players (which is far from guaranteed), you’ll end up taking just one sixth of the points you would get from the solo (no different from if you had drawn immediately after eliminating Turkey).

Now imagine the same position, but with all opposing units under the control of just two powers – England and Germany. This is a far worse position to solo from, since the other side of the board is far more likely to be coordinated and it’s very likely that neither would have any incentive to play for revenge — but in the event of a DSS draw, this gives you double the points you would obtain in the previous scenario.

The problem here is that the objectives of DSS system run contrary to one another. By playing for a better draw, you’re usually actively hurting your chances of achieving a solo, and by playing for a solo, you’re usually hurting your chances of getting a better draw. High level players will usually try to compromise between the two (perhaps by keeping enough players alive to cause disruption, but in positions where they can be easily eliminated), but it’s far easier to just pick one and stick with it. Due to how difficult solos can be to achieve, aiming for a small draw is a very good strategy in this scoring system. As such, I’d argue that the Carebear strategy is actually encouraged under this scoring system due to this; agreeing to a three or four-way draw from the start and sacrificing any chance at a solo carries very little risk and gives a hefty reward, usually the best result you can expect to attain in an average game.

Sum of Squares Has Better Incentives

SoS was built to try to align the draw and win objectives. In SoS, you will win far more on a large SC count with divided opposition than you will against one or two big players, meaning that as you work towards a solo in SoS, you are also increasing your potential draw score, and generally as your solo chances decrease, so does your draw score. In this way, you rarely have to choose between differing objectives; playing for the win in SoS means you will get a good draw result even if you fail to secure the win.

I think at this point, most DSS players have become so used to the conflicting objectives (specifically, used to aiming for the draw and considering the solo a bonus objective), that playing strictly for the solo is not really what Diplomacy is about anymore. That’s a legitimate view, but looking at SoS through that lens is not going to give you a good overview of the scoring system, because SoS plays very differently to that. In SoS the win is the objective – the draw simply measures how close you got to that.

Your Bored Brother does have an answer to this in his article, under the section ‘Wanting a higher frequency of solo wins is fetishistic’. In this section he talks about how solos being rare is important, and making them more achievable lowers their value and defeats the point of obtaining them. I find this to be somewhat missing the point. Sum of Squares makes solos more achievable because it doesn’t punish players for working towards them if they fail to get there, whereas Draw-Survivors Scoring discourages players from going for them in the first place. I would argue that their rarity is only really valuable if they’re hard to obtain while players are playing for the win. If the game encourages people to avoid going for solos, then solos are mostly either going to be inadvertent results of playing for something else, or the result of playing many games in a suboptimal way in order to achieve just one of them. Even if you disagree with that, the fetishistic argument really doesn’t hold much water, since it assumes that the default way of playing is DSS; I could argue that discouraging playing for the win in order to makes your solos more valuable is equally fetishistic.

Diplomacy Shouldn’t Be About Playing For Draws

The next point Your Bored Brother makes is that two strategies which are encouraged in DSS lose their value under SoS. The first one of these is essentially the same as the Desperado, which is a real concern but which we’ve already covered. However, it’s restated to sound like anyone on the defensive suffers here, which isn’t exactly true — players on 3, 4 or 5 centers will definitely receive less than they would under DSS, but it’s still enough to make survival worthwhile unless you don’t care about your score at all. The second is the strategy in which you keep yourself small in order to allow elimination of other players — specifically, playing for the best draw possible by ruling out any chance of you soloing the game. This is again a very DSS-centered argument, because it assumes that deliberately not going for the solo and playing for a draw should be rewarded (and that’s not even mentioning the fact that this assumes player eliminations should be rewarded, even when it’s not you doing the eliminating). Yes, that strategy is not a viable way to earn points, but should deliberately sacrificing any chance at the win be rewarded in the first place? It’s simply the default opinion because Draw-Sized Scoring has been the system webDiplomacy had used for a very long time, not because it has merit in and of itself.

The entire following section details how countries playing for the win destroys the balance of the game, because some countries are not as good for playing for the win as others. But Diplomacy isn’t a balanced game anyway, and Calhamer certainly did not design it around certain countries not playing for the win – in fact, he’s very critical of players who don’t aim for the solo in his 1999 book, “Calhamer on Diplomacy,” and the rule allowing draws at all was actually removed from the rulebook for several editions. Obviously, having no draws at all is not a good solution in a game with stalemate lines, but deliberately playing for the draw from the start is certainly not an intended strategy of the game.

I’m going to jump back a bit now to the one section I’ve skipped, “Treating more Supply Centers as more winning is unstrategic.” This is all under the heading “DSS encourages allies to play strategically, Sum of Squares scoring encourages greed” — which was probably the first thing that rung alarm bells for me when reading this article. This section talks about how SoS simplifies the objective to just be supply center count, and this means that strategic options are limited. Your Bored Brother talks about how in Magic the Gathering, you can afford to lose life points provided at some point you stabilize and bring the opponent to zero, and how in Diplomacy, there are strategies just like this that keep your center count low until you can make a break for the win. The issue here (aside from the fact that there is more to your SoS score than centers) is that your score is what you’ve achieved at the end of the game, not what you’re currently on or what you’ll be on next turn. Strategies that start out slow aren’t suddenly devalued for not starting out with high SC counts, because the game doesn’t end at the start.. There’s still plenty of room to play strategies that don’t immediately make gains, like the Italian Lepanto, because they’re aiming to make gains later on. In fact, this loops back around to the ‘dotting’ reasoning – you don’t dot in SoS because you don’t get those points unless you keep them to the end of the game, and usually dotting will both halt your chances at increasing your score any further later on and will probably force you onto the defensive, generally leaving openings for other players to grow and so reducing your score dramatically.

I’m aware the strategy he’s talking about here is probably the one in which you deliberately never grow and throw out your chance at winning, which is devalued in SoS, but I’ve already written about how devaluing a strategy that doesn’t actually aim to win is not a bad thing. Strategies that aim for the solo are generally rewarded much more highly in SoS than in DSS, regardless of what point the strategy starts showing a current return on points at.

In conclusion, while on the whole Your Bored Brother’s articles are very good, I think this one is ill-thought-out, specifically because he doesn’t play Sum of Squares and so things like dotting seem like a far better idea than they actually are. The scoring system does have problems – namely, the lack of reward for Desperado play – but equally, DSS has massive flaws in the lack of reward for playing for the win. At the end of the day, the scoring system you play with is entirely up to you, but there is a great deal of disapproval towards Sum of Squares ingrained in the webDiplomacy community based on false assumptions like the ones in this article, usually ones that have carried over from the PPSC era (which is a story for another time). In the meantime, I highly recommend trying out SoS, even if you consider DSS to be the way to play – the best way to gain an understanding of the strategy involved is to play.