SCORING DIPLOMACY 2: Discussing Various Scoring Systems

In the first post in this series, I discussed how scoring Diplomacy was introduced. In this post, I’m going to look at various scoring systems by looking at their strengths and weaknesses.

Draw Based Scoring Systems

DBS scoring systems usually have a game which ends in a victory – a player that achieves ownership of 18 SCs – gaining all the points available in a game. If the game ends in a draw, however, the points are distributed equally between the players participating in a draw.

The Calhamer Point system

In this system, designed by Allan B Calhamer himself (the game’s creator, just in case you’re not sure), is as simple a system as you could wish for: The winner gains 1 point; if the game ends in a draw, the participants gain 1/n points, where n = the number of players in the draw.

Most DBS systems utilise this simple idea. Some of them may involve more points per game (a good number of points, for instance, is 420, because 420 is a multiple of 2, 3, 4, 5, 6 & 7 – the number of players who could be involved in a draw). Some DBS systems have variations for some reason.

Declining Centre systems

One such is the Armada/Regetta system. Here the number of points available in a draw is reduced based on the number of players who share the draw. So a 2-player draw gives each player 80 points, a 3-player draw gives each player 56 points. The problem with this system is that a solo in one game (which scores 104 points) is of less worth than two 3-way draws (a total of 112 points). This system then added to include some form of Supply Centre count for some reason, presumably to further differentiate between players on the same DBS score.

Dragonfly Draw system

Here, a solo is worth 61 points. In a draw, the participants gain an equal share of 60 points. In this system, then, two 2-way draws do not equal a solo victory (2 x 30 points). To differentiate between ties, there was a system used whereby a not well explained modification was used based on power- and player-weighting.

Supply Centre Scoring systems

SCS scoring is based on the number of SCs players hold at the end of the game. Again, a solo typically takes all the possible points on offer. When the game ends in a draw, players are awarded points on their SC count (as the name suggests).

A very pure system, for instance, would be a solo resulting in the winner gaining 34 points, everyone else 0. In a draw featuring 3 players on 16, 11 and 7 SCs, they would score 16, 11 and 7 points respectively.

Sum of Squares

This is a very popular system. Let’s take the results as above – players ending the game on 16, 11 and 7 SCs.

The number of SCs a player finishes on is squared, make a score of 256, 121 and 49. This results in a game score of 426. The players then score the percentage of the game score they have achieved: 16 SCs = 60.1 pts, 11 SCs = 28.4 pts, and 7 SCs = 11.5 pts.

The quirk in this system is that achieving the same number of SCs at the end of the game over two different games doesn’t necessarily result in the same number of points. It will depend on the game score – the points earned will vary depending on the game score.

Tribute Scoring system

This is a new system which is intriguing. It is based in some degree on SC count but it involves players gaining or losing points based on their relative positions in the game.

A solo earns 100 points and everyone else gets zero. In a draw the system is that every participant scores 1 point per SC held. This leaves 66 points to be distributed.

These 66 points are shared equally between the remaining players. In the game I’ve used above, three players would receive 22 points. But it doesn’t end there – this is where the tribute payment comes in!

The player who finishes on the highest number of SCs is known as the ‘Top of the Board’. This is a common concept in Diplomacy (and one which, according to the rules of the game is meaningless – but then SC scoring is meaningless in this area anyway). Each player pays the Top of the Board 1 point for every SC the player controls above 6.

In our game, the Top of the Board held 16 SCs which results in 16 + 22 + 20 = 58 pts; 11 SCs results in 11 + 22 – 10 = 23 pts; 7 SCs results in 7 + 22 – 10 = 19 pts.

If two or more people finish equally on top of the board, they share the tribute points equally.

This system has some intriguing aspects, the most obvious of which is that it pays to keep the little guys alive, especially if you’re the Top of the Board. Look what happens under two variations based on a fourth participant in the draw hanging on with one SC:

1. 16 SCs = 16 + 16.5 + 30 = 62.5 pts (+4.5)
2. 11 SCs = 11 + 16.5 – 10 = 17.5 pts (-5.5)
3. 6 SCs = 6 + 16.5 – 10 = 12.5 pts (-6.5)
4. 1 SC = 1 + 16.5 – 10 = 7.5 pts (+7.5)

1. 15 SCs = 15 + 16.5 + 27 = 58.5 pts (+0.5)
2. 11 SCs = 11 + 16.5 – 9 = 18.5 pts (-4.5)
3. 7 SCs = 7 + 16.5 – 9 = 14.5 pts (-4.5)
4. 1 SC = 1 + 16.5 – 9 = 8.5 pts (+8.5)

Compare this with what happens under Sum of Squares scoring:

1. 16 SCs = (256/414) x 100 = 61.84 pts (+1.74)
2. 11 SCs = (121)/414) x 100 = 29.23 pts (+0.83)
3. 6 SCs = (36/414) x 100 = 8.7 pts (-2.8)
4. 1 SC = (1/414) x 100 = 0.24pts (+0.24)

1. 15 SCs = (225/396) x 100 = 56.82 pts (-3.38)
2. 11 SCs = (121/396) x 100 = 30.56 pts (+2.16)
3. 7 SCs = (49/396) x 100 = 12.37 pts (+0.87)
4. 1 SC = (1/396) x 100 = 0.25pts (+0.25)

C-Diplo

This isn’t pure SCS either but it is more closely based in SCs held in a draw. A solo scores 100 pts and everyone else scores zero. In a draw:

• Everyone gets a point for playing the game (yeah, I know) = 7 pts total.
• Everyone scores 1 point per SC held at the end of the game = 34 pts total.
• The player with most SCs scores 38 pts.
• The second highest SC score gets 14 pts.
• The third highest SC score gets 7 pts.

For our game, with 16 SCs, 11 SCs and 7 SCs players score 55 pts, 26 pts and 15 pts, with four players scoring 1 point each – a total of 100 pts for the game.

This is an example of a bonus points system and I’m not sure I like it very much, as simple as it is.

Detour 98F

Another bonus points system, and one which is markedly inferior to C-Diplo.

A solo = 110 pts and no other player scores.

In a draw, points are distributed by:

• Everyone scores 1 per SC held at the end of the game.
• If a player reaches a certain date (officially Fall 1905 but I’ve seen it for reaching 1905) they score 1.
• Every player with an SC at the end of the game receives a score of 1.
• A Top of the Board (on their own) scores the number of SCs they hold minus the number of SCs held by the player who finishes second (if two or more players tie at the top of the board, nothing is awarded).
• Highest number of SCs scores 4.
• Second highest number of SCs scores 3.
• Third highest number of SCs scores 2.
• Fourth highest number of SCs scores 1.
• If players tie in the above categories, the points awarded are the lowest level (so if players finish on 16SCs, 9 SCs, and 9 SCs, 16 SCs will score 4, the two players on 9 SCs will score 2).
• Games must be standardised so that each game totals 100 points.

In our game, then, if two players who were later eliminated survived to Fall 1905:

1. 16 SCs = 16 + 1 + 1 + 5 + 4 = 27 which is standardised to 48.21 points.
2. 11 SCs = 11 + 1 + 1 + 3 = 16 which is standardised to 28.57 points.
3. 7 SCs = 7 + 1 + 1 + 2 = 11 which is standardised to 19.64 points.
4. 0 SCs = 0 + 1 = 1 which is standardised to 1.79 points.
5. 0 SCs = 0 + 1 = 1 which is standardised to 1.79 points.

Why do I say this is inferior to C-Diplo? Because it includes more that isn’t relevant to Diplomacy play. What does it matter when you survive to if you’re eliminated, for instance?

Alternative Systems

There are any number of alternative systems. I want to look at two.

Super Pastis

This system relies on games finishing at a certain point, officially 1909. At the end of that year, the game is drawn. If a solo is achieved, then the soloist scores 102 points and other players score 1 point per year they survived – anyone surviving to 1908 (if that’s the year a solo was achieved) would score 8 points, for instance.

If a game ends in a draw and there is a single Top of the Board:

• All survivors score 10 points.
• All survivors score 2 points per SC held.
• All eliminated players score 1 point for each year they survived to play in.
• All players within 3 SCs of the Top of the Board receive 3 points each.
• All players within 2 SCs of the Top of the Board receive 6 points each.
• All players within 1 SC of the Top of the Board receive 12 points each.
• The Top of the Board receives 51 – the second highest points total.

For our game, assuming eliminated players were eliminated in 1907, 1906, 1905 and 1903:

1. 16 SCs = 10 + 32 + (51 – 0) = 93
2. 11 SCs = 10 + 22 = 32
3. 7 SCs = 10 + 14 = 24
4. Eliminated 1907 = 7
5. Eliminated 1906 = 6
6. Eliminated 1905 = 5
7. Eliminated 1903 = 3

If the game ends with two or more players tied on the highest number of SCs:

• All survivors score 10 points.
• All survivors score 2 points per SC held.
• All eliminated players score 1 point for each year they survived to play in.
• All players within 3 SCs of the highest SC count receive 3/n points each.
• All players within 2 SCs of the highest SC count receive 6/n points each.
• All players within 1 SC of the highest SC count receive 12/n points each.
• The players tied for the highest SC count receive 48/n points each.
• n = the number of players tied with most SCs.

Tier System

This system was based on the idea that a soloist is raised to a higher tier than non-solists. So, if a game ends in a solo, the soloist will move to another tier. Positions are based on which tier players end on.

I like this idea, as it rewards playing for a solo highly. I’m not sure how effective it would be when games feature a GED, however.

For drawn games, points are awarded based on positions. Positions are based on a hierarchy:

• Survive and score higher number of SCs.
• Eliminated: year of elimination, later eliminations ranked higher.
• If positions are tied, they score the average number of points for the rankings.
• Survivors also score 1 point per SC held.

In our game, then:

1. 16 SCs = 7000 + 16 = 7016 points
2. 11 SCs = 6000 + 11 = 6011 points
3. 7 SCs = 5000 + 7 = 5007 points

Ranking points go from 7000 to 1000 for finishing 7th in the game.

The problem with this system is that a player could have one great game, and three mediocre games, and still win.

Different Systems?

As you can see, even from this small selection of scoring systems, there are differences that affect how people play the game. Well, unless you approach it in the same way no matter what, of course. As we’re talking about scoring tournament games, and assuming that people who enter a tournament are serious about doing well, you’d expect them to know the importance of playing to the scoring system.

It’s time to ask what a scoring system should achieve.

Posts in this series

1. The Introduction of Scoring Systems to Diplomacy.
2. Discussing Various Scoring Systems.
3. What Should a Scoring System Achieve?
4. A Suggested Scoring System for Tournaments.