Sum of Squares scoring

The Sum of Squares scoring system is one of the more sophisticated Supply Centre Scoring systems for Diplomacy tournaments.

Before I get into examining the SoS system itself, there are a couple of strange ideas to get rid of. The first is that SoS isn’t a Supply Centre Scoring system. I once came across someone on the Playdip forum who told me it wasn’t. As you’ll see below, it counts SCs. How isn’t this an SCS system ?

Second, it’s a tournament scoring system. It is designed to be used over a small number of games. It can be used for a larger series of games, I suppose, though there are distinct weaknesses in doing this. It certainly shouldn’t be used as a ratings system, to score an on-going series of games, as webDiplomacy uses it.

In fairness, I’m not sure why webDip went down this route, and I’m sure there were some good reasons. SoS was introduced to replace a basic SC count ratings system and could be argued to be an improvement on that. But, as SC counting is against the design of Diplomacy, and the objectives of Diplomacy, then as a ratings system it is a complete failure.

What is the SoS system?

You can see SoS explained here, but I’ll explain it myself. It isn’t, in concept, complicated, although it is complex enough to make playing to the system risky.

A Solo = 100 pts. Everyone else scores 0.

In a drawn game, the system works in the following way:

  • For each power, count the number of SCs held at the end of the game.
  • For each power, calculate the square of the number of SCs held. I’m sure you don’t need an example but, if a power holds 12 SCs when a draw is declared, this result is 12×12 = 144.
  • Find the sum of all the squares calculated above. This is the Game Score.
  • For each power, calculate the percentage of the SCs2 they hold. To do this you use the following formula: P = (SC2x100)/G, where P=points and G=the sum of SCs2 held by all powers in the draw (the Game Score).

Here’s an example of a game that ends in a 4-way draw:

PLAYERSCsSC2SCOREPOINTS
A14196(196×100)/34856.32
B10100(100×100)/34828.74
C636(36×100)/34810.34
D416(16×100)/3484.6
E000
F000
G000
GS = 348
SoS example 1

Here’s a second example, still a 4-way draw, but with the number of SCs changed:

PLAYERSCsSC2SCOREPOINTS
A12144(144×100)/33043.64
B11121(121×100)/33036.67
C749(49×100)/33014.85
D416(16×100)/3304.85
E000
F000
G000
GS = 330
SoS example 2

1. What is the SoS system designed to do?

The system is designed as a tournament scoring system. It provides a system that has a significant amount of differentiation between game results. It compares the number of SCs in a game held by each power and, as you can see in the examples above, it magnifies the difference between the SCs held in games. As such, despite both the games described above being 4-way draws, Player A in eg1 scores significantly more points than Player A in eg2. However, in eg2, other than Player A, every other player that scores points does better than those in eg1. This is because the Game Score on eg2 is smaller than that of eg1.

2. Is the system effective in differentiating between players/results?

This is a good system because it is unlikely to require a secondary scoring system. The primary scoring system should provide enough differentiation between player scores that ties should be unlikely.

If a secondary system is needed, a simple SC count across all games would be enough. This is because the SoS system doesn’t just count SCs, and players on tied points may well have different totals of SCs held at the end of games. You could end each game on 10 SCs and have the same points total as a player who finished on 17 SCs in one game.

3. What are the objectives when playing to the system?

The first objective is to win the game. A game that ends in a solo scores 100 points and nobody else in the game scores anything. A score of 100, accompanied by middling scores in other games, will result in a good points total at the end of the tournament.

Players also play to accumulate SCs in the game. Because this is an SC count system, and given that a draw is likely in a tournament game, the more SCs you have at the end of the game is important.

However, because a draw can give the player that ended the game with most SCs a score that is better than 50 points, it isn’t just the number of SCs held at the end of the game. Also important is the difference between the SCs held between the players. In eg1 above, the 4-SC difference between Players A and B meant that A scored almost twice as many points as B. Also, when the difference between SCs is reduced, as in eg2 above, the difference in points won by Players A and B is dramatically reduced.

It’s important, then, when a game is moving towards a draw, not only to play towards increasing the number of SCs you hold, but to increase the SC gap between players. This means taking risks to grab SCs from targeted players, rather than just increasing or decreasing an SC count.

4. Are the objectives consistent with the design of Diplomacy?

This is more complicated than it seems, due to the inclusion of the “Short Game” rule to the rules of Diplomacy in 1961, a rule that was in place until 2000:

Since gaining control of Europe takes a long time, it is generally advisable to set a time limit for the game. The player with the most pieces on the board at that time is the winner.

“Rules for Diplomacy” 1961.

Now, a tournament game can be played until the game ends. I’m reliably informed that in North America this is often the case in the early rounds of a tournament, with generally only the final round being ended at a set point. Everywhere else this is not usual. In Europe, games tend to have a Game End Date that makes the games quite short. In Australia, it seems, a Game End Date is generally used but is later in the game.

Why use GEDs? Well, games can go on for a long time. Face-to-face tournaments are often held over a weekend (or an extended weekend). This means there is a finite time in which to complete the tournament.

Online tournaments tend to use GEDs, somewhat counter-intuitively. You’d think that, because they’re remote tournaments, there isn’t the pressure to get games – and the tournament – ended in a timely fashion. However, in reality, nobody wants games to role on interminably. The tournament needs to end and it needs players to stay around long enough to end the tournament!

The use of GEDs, then, seems to allow for the Short Game rule. If your game is ended in an enforced draw in, say, 1910, then the game may not be resolved by that date. It even makes sense for some players to deliberately delay the ending of the game until that point.

The problem is that this rule doesn’t seem to have been part of Calhamer’s thinking at all. There is no indication that Calhamer ever endorsed the rule’s addition. In fact, in 1974, Calhamer wrote an article called “Objectives other than Winning” in which he ignores the Short Game rule completely. In fact, he states that the number of SCs held at the end of a drawn game is irrelevant.

The Short Game rule is notable by it’s absence in the first rules published for Diplomacy, and it has been absent since the 2000 edition of the rules. Given that the objectives for Diplomacy have always been to win the game or to accept a draw in which all players share in the draw equally, this suggests that this rule is an aberration. Was it introduced by the game publishers without reference to Calhamer? Who knows?

However, on the basis of this rule, a tournament could certainly be scored by using some form of SC count. As I say, complicated.

Personally, I don’t think any SCS system fits in with Calhamer’s design. I can understand SCS systems being applied to tournament games but still.

5. Overall, is the system a ‘good’ system?

Based on the fact that SoS doesn’t fit in with Calhamer’s design, this raises doubts. The question becomes whether you want a tournament game to come as close as possible to Calhamer’s design or not.

Tournaments are already a variant of Diplomacy, on the basis that the games are part of a series of games (not a stand-alone game) and that they are scored. However, do we want tournaments to find the best players of Diplomacy, in a tournament setting, or do we want them to find the players who can collect SCs, with whatever modification of that goal the scoring produces? For me, it’s the former. A tournament champion should be someone who plays Diplomacy, rather than someone who can gather SCs in a game of Diplomacy.

If you enter a tournament, though, you are agreeing to play with the scoring system used. SoS certainly provides a good way to produce differences between players, something a Draw-Based Scoring system and other, less sophisticated systems, do. As such, if you want to focus on the primary scoring system as a way to find a winner, SoS certainly does that!

As a ratings system, it is a failure. Yes, it will do exactly the same thing as it does in a tournament but, in an on-going series of games, games should certainly be played as close to Calhamer’s design as possible. The SoS system pulls people away from this design. It is NOT a ratings system.

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Published by Mal Arky

I'm a Diplomacy nut... if you haven't guessed. I write about the game Diplomacy, mainly as played online on websites, such as Playdiplomacy, webDiplomacy and Backstabbr. I write books on Diplomacy, too. First one to be published soon!

5 thoughts on “Sum of Squares scoring

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