Tournament Scoring - Part 4: Supply Centre Scoring

The thing with tournaments is that a lot of games end in a draw.  This means that DSS systems aren't necessarily going to produce a great result because a lot of players could well finish on the same score.  An alternative to DSS is a Supply Centre Scoring (SCS) system.

I'm going to use the game above as an example to explain SCS systems.  (The game is from Playdiplomacy and so the colours are different from those I use for my maps.)  The game ended with the following outcome:

1. England - 12 SCs
2. Russia - 9 SCs
3. Turkey - 8 SCs
4. Italy - 5 SCs

France, Germany and Austria-Hungary were eliminated, with 0 SCs each.

Supply Centre Scoring systems are based on the number of SCs the players owned at the end of the game.  The basic pattern is:

• A solo results in all the points available.  No other player scores points.
• A draw will be scored using the number of SCs the players hold at the end of the game.  In the above game, on a pure SCS system, England would have 12 pts; Russia 9; Turkey 8; Italy 5; France, Germany & Austria 0.
• Points are usually converted to percentages so that England would have 35.29 pts, Russia 26.47 pts, Turkey 23.52 pts, and Italy 14.71 pts.

Sum of Squares

Often, SCS is changed so that it isn't just the basic number of SCs held that generates the number of points awarded.  Perhaps the most popular system is the Sum of Squares system.

This system squares the number of SCs owned at the end of the game and then standardises them as a percentage.  This means that if a player solos she scores 100 pts.  Using our example game:

1. England - 12 SCs; 144 raw pts; Score = 45.86
2. Russia - 9 SCs; 81 raw pts; Score = 25.8
3. Turkey - 8 SCs; 64 raw pts; Score = 20.38
4. Italy - 5 SCs; 25 raw pts; Score = 7.96

The game score is 314 points, so each power's score is the power's raw score as a percnetage of 314.

The difference in points between England and Russia is 20.  What would have happened if England had taken one more SC from Russia?

1. England - 13 SCs; 169 raw pts; Score = 52.48
2. Russia - 8 SCs; 64 raw pts; Score = 19.88
3. Turkey - 8 SCs; 64 raw pts; Score = 19.88
4. Italy - 5 SCs; 25 raw pts; Score = 7.76

That single SC meant that the difference between England and Russia (& Turkey) is now 32.6 points, more than 50% greater.  It also meant that England scored more than 50 pts, so two such results would be better than if England had soloed a game.

If Russia had taken one SC from Turkey..?

1. England - 12 SCs; 144 raw pts; Score = 45.28
2. Russia - 10 SCs; 100 raw pts; Score = 31.45
3. Turkey - 7 SCs; 49 raw pts; Score = 15.41
4. Italy - 5 SCs; 25 raw pts; Score = 7.86

Russia's score is now double Turkey's score.

Evaluation based on objectives

In a previous post I identified what objectives a scoring system should meet.  Let's have a look at how SCS meets these objectives.  Green objectives are achieved, orange objectives are partially achieved, and red objectives are not achieved.

• Players should be aiming to win the game.  Winning the game is still the objective, and 100 points is going to give a player a significant advantage.  However, the scoring system means that the most important aspect is the number of SCs players can get at the end of the game.
• If unable to win, players should be playing to (be included in the) draw.  Again, this isn't the case.  It isn't just about playing to survive, it's about the number of SCs you have for surviving.  Surviving on 1 SC is going to make very little difference as compared to being eliminated.
• As far as possible, being able to play each game as you would a stand alone game.  The aim in a stand alone game is very different from in a game with an SCS system.  SCS means the game is more about collecting as many SCs as possible, and about increasing the gap between you and the player behind you in the scores.
• Within the practicalities of the tournament, games should be played to a natural finish.  Because of the SCS system, it may be better to give a player a victory than to end the game in a draw.  By doing this, you prevent other players scoring and may not lose too many points yourself while other players lose a lot of points.
• Games should be fun and interesting, not predictable.  Risky strategies are more likely in this kind of game.  When it becomes about grabbing SCs then anything else, then this can make for exciting games.
• Players being able to play a game which allows them to play to the scoring system.  Basically, while the system is about who gets most SCs, it is also about judging the gap between players, increasing that gap or reducing it.

Practical Considerations

Generally, unlike DSS, you're more likely to get results using SCS.  There is a smaller probability that players will finish tied on points and therefore less of a need to differentiate.  Personally, I find the definitive nature of the Sum of Squares system satisfying, even though I think it exaggerates small gaps between powers.

And, if nothing else, games are less likely to be dull affairs.

TOURNAMENT SCORING series:

1. Tournament Games are Variants
2. What should a good scoring system do?
3. Draw Size Scoring (DSS)
4. Supply Centre Scoring (SCS)
5. Other Scoring Systems
6. Summarising the Problem with Scoring Systems
7. The Mystery Scoring System Explained
8. Does Mystery Scoring meet the objectives?