In my last post in this series I suggested what a good scoring system should look like. In this post, I’m going to suggest my own scoring system for your delectation.
What the DC(C) system aims to achieve
First, let’s make it clear why the system is called DC(C).
The initials stand for Roman numerals:
- D = 500
- C = 100
- DCC = 700
In this scoring system, then, each game scores a total of 700 points. It could just have easily have been called LX(X) or even VI(I) but dealing with hundreds is easier than dealing with tens or units. I’m a simple man.
The points break down in the following ways.
- 600 points are shared by the players involved in a draw at the end of the game, and
- 100 points are shared between the survivors at the end of a game based on some form of Supply Centre Scoring (SCS) system.
So, yes, this is a combined scoring system that I’ve said I don’t particularly like: Which system do people play towards?
However, this system focuses very much on Draw Based Scoring (DBS) system, with 600 or the 700 points awarded based on the result of the game. Well, hopefully. The final 100 points are designed to provide a way of differentiating between players who draw games.
Incidentally, I do apply a secondary system for those – hopefully rare – occasions where DC(C) doesn’t differentiate effectively.
How it works
Solo Victory
A solo results in the winner scoring 700 points and all other players scoring 0.
Draw
If the game ends in a draw, 600 points are shared equally between the players involved in the draw:
- 2-way draw = 300 points each; all other players receive 0
- 3-way draw = 200 points each; all other players receive 0
- 4-way draw = 150 points each; all other players receive 0
- 5-way draw = 120 points each; all other players receive 0
- 6-way draw = 100 points each; the other player receives 0
- 7-way draw = 0 points each
The idea behind the 7-way draw scoring 0 points is that this should never happen in a tournament game.
The final 100 points are awarded to any players who survived at the end of the game owning supply centres on the board, using the Sum of Squares (SoS) system.
If the game ends in a 7-way draw, then, the game is worth only 100 points, using the SoS system to allocate those points.
Example 1: Game ends in a 5-way draw; Draws Include All Survivors (DIAS)
- Player 1: 12 SCs = 120 + 50.35 = 170.35 pts
- Player 2: 8 SCs 120 + 22.38 = 142.38 pts
- Player 3: 7 SCs 120 + 17.13 = 137.13 pts
- Player 4: 5 SCs 120 + 8.74 = 128.74 pts
- Player 5: 2 SCs 120 + 1.4 = 121.4 pts
- Player 6: 0 SCs = 0 pts
- Player 7: 0 SCs = 0 pts
Notes on DIAS scoring: DIAS games, where all survivors share the draw, follow exactly the published rules of Diplomacy. This is the most common system used in online tournaments. It is also the most likely way games are scored if they end because they reach a Game End Date (GED), rather than when the game finishes in an agreed draw.
Example 2: Game ends in a 3-way draw; Draws Include Nominated Survivors (DINS)
- Player 1: 13 SCs = 200 + 49.42 = 249.42 pts
- Player 2: 10 SCs = 200 + 29.24 = 229.24 pts
- Player 3: 3 SCs = 200 + 2.63 = 202.63 pts
- Player 4: 8 SCs = 0 + 18.71 = 18.71 pts
- Player 5: 0 SCs = 0 pts
- Player 6: 0 SCs = 0 pts
- Player 7: 0 SCs = 0 pts
Note on DINS scoring: It is quite common in FTF tournaments for games to end in an agreed draw but not all survivors are part of the draw. In this situation, a player will nominate surviving players to share the draw, and some survivors may not be involved in the draw. You may ask why players would accept a draw proposal – the proposal still needs to be unanimously accepted – when they aren’t part of the draw, and that would be a good question. However, it can happen, and the DC(C) system recognises the difference between a player who survived to the end of the game while not been part of a draw. I don’t think there’s anything wrong with this modification to DINS scoring, especially as DINS scoring is a modification of the rules itself.
Final Results – Final Game format
Players play in R number of rounds, and the tournament (T) score is the total of points scored over each round divided by the number of rounds played. So, if a tournament features 4 rounds, and a player enters each round, their score will be the total of the points they scored divided by 4.
If a player enters 3 rounds, the game scores are modified by scoring at 95%. The total points scored are divided by 3.
If a player enters 2 rounds, the game scores are modified by scoring at 87.5%. The total points are divided by 2.
If a player enters 1 round, the game scores are modified by scoring at 80%. The total points are divided by 2.
If a tournament features 3 rounds maximum, and a player enters all rounds, their T score is calculated as: T = (R1 + R2 + R3) ÷ R
Again, games scores modified by: enter 2 rounds: 85% so T = ([85%R1] + [85%R2]) ÷ R, and enters 1 round: 75% so T = (75%R1) ÷ 2R
If a tournament features more than 4 rounds, then find the total of all games played and divide by the number of rounds played. If players don’t enter every round, then the total of game scores is divided by the number of rounds they enter to a minimum divisor of half the number of rounds in the tournament.
Once T has been calculated for each player, the top seven players play in the Final Game.
- The player who wins the Final Game wins the tournament.
- If the Final Game ends in a draw, it is scored as a single round game (ie at 100%) and the scores for this game are added to the qualifying scores.
Final Results – League format
The tournament is scored as above, except that no Final Game is played. When all rounds are complete, the standings at this point are final.
Final Results – Top Board format
Played as the League format but, when playing the final round, the top 7 players in the league after the penultimate round, will face each other in a Top Board. These players will finish in the top seven positions in the tournament.
Players below the top seven after the penultimate round can either be grouped randomly or in groups of seven, so that players in position 8-14 would play each other, players in position 15-21 would play each other. If these players are grouped randomly, they can move anywhere in the final league table from 8th. If they are grouped in positional boards, then – like the Top Board – they can only be ranked within their group.
The final round is scored as a one-off round (ie at 100%) as in the Final Game format. All preliminary rounds are scored as if they were a tournament of one round less than the number of rounds in the tournament.
Modifications
The simplest modification to the DC(C) system is to change the system used to score the final 100 points (C). I chose SoS because it is an interesting way of scoring SC count.
You could use a simple SC% score. So, the final 100 points would be based on the percentage of SCs a player owns at the end of the game.
I also find the Tribute system an interesting system. I didn’t use it as it features an aspect of DBS in it, and given that the DC of the DC(C) system is pure DBS, I wanted to use a variation of SCS only for the (C) aspect.
Another modification would be to not use the game score modifications I’ve used to calculate tournament points. I included them for tournaments where a player may not be available in each round or when replacement players join the tournament (fairly common in online tournaments).
Doing away with weightings for each round could be replaced, for instance, by simply dividing the number of points scored by the number of rounds (or preliminary rounds) in the tournament. At best, then, if a player enters just one round, wins a solo, they can only score a fraction of the 700 points awarded.
It could also be that players can only qualify for the Final Game or to feature on the Top Board if they play a minimum number of games.
Some of these things are incidental. The idea of the DC(C) system is that it is primarily a DBS system, with an element of SCS to overcome the problem of differentiating between players who would otherwise be tied on DBS only.
Secondary Scoring
It would be unusual for players to be tied on this format. This is simply because SoS scoring produces different outcomes for players who end games on the same number of SCs. Take a look:
Example 1
- Player 1: 15 SCs = 50.45
- Player 2: 14 SCs = 43.95
- Player 3: 5 SCs = 5.61
Example 2
- Player 1: 15 SCs = 67.37
- Player 2: 8 SCs = 19.16
- Player 3: 5 SCs = 7.49
- Player 4: 4 SCs = 4.79
- Player 5: 2 SC = 1.2
However, for these unusual situations, I suggest the Mean Score Difference (MSD) system.
To calculate MSD, all games are scored at 100%, ie no weighting.
First, find the average number of points scored by each power across all games.
Second, find the difference between the points each player scored for the powers they played and the mean score for those powers. If a player scored more than the mean score for a power, that will result in a positive score; if less than the mean score, that will result in a negative score.
Third, find the total MSD for each player and divide by the number of rounds played in the tournament.
Posts in this series:
- The Introduction of Scoring Systems to Diplomacy.
- Discussing Various Scoring Systems.
- What Should a Scoring System Achieve?
- A Suggested Scoring System for Tournaments.
THE DIPLOMATICON 