Fibonacci Scoring System

The Fibonacci Scoring System is a mathematical extension to the Carnage Scoring System that is designed for play of either classic or variant Diplomacy games.
Unlike Carnage, it is built to scale proportionally for variants of differing player counts (a minimum of 4, with no maximum).
== Points in a Solo ==
Similar to Carnage, Fibonacci is a winner-takes-all system. In the event of a solo victory, the winning player receives all of the possible points for a game, while the other players receive zero points.
Because Fibonacci scoring is intended to be adapted to specific variant play, the actual number of total points awarded may vary between contexts. The important component is that 100% of the points go to the winning player in a solo, regardless of what that total is.
== Points Per Rank ==
In the event that a game ends without a solo victory, Fibonacci awards a large amount of points according to the player's rank as compared to other players, and a small amount of points based on the player's total SC count.
Ranks are calculated according to each player's final SC counts and years of elimination. Higher ranks receive more points, just as with Carnage.
However, while Carnage points per rank scale in a linear sequence (1000, 2000, 3000, etc.), Fibonacci points scale according to the Fibonacci sequence (1, 1, 2, 3, 5, 8, 13, etc.).
 Fibonacci Points by Rank, Seven Player Example
Rank 	Points	Approx. % of Total
1st (board topper)	13000 	39.39 %
2nd 	8000 	24.24 %
3rd 	5000 	15.15 %
4th 	3000 	9.09 %
5th 	2000 	6.06 %
6th 	1000 	3.03 %
7th 	1000 	3.03 %
If players tie for ranks, they split those points, rounded down. For example, three players tying for the 2nd, 3rd, and 4th positions would receive 5333 points each ((8000+5000+3000)/3, rounded down).
In the seven-player example shown above, there are 33000 total rank points at stake. For a ten-player game (below), there are 143000 total rank points.
 Fibonacci Points by Rank, Ten Player Example
Rank 	Points	Approx. % of Total
1st (board topper)	55000 	38.46 %
2nd 	34000 	23.78 %
3rd 	21000 	14.69 %
4th 	13000 	9.09 %
5th 	8000 	5.59 %
6th 	5000 	3.50 %
7th 	3000 	2.10 %
8th 	2000 	1.40 %
9th 	1000 	0.70 %
10th 	1000 	0.70 %
The exact point numbers in Fibonacci matter less than whether the rank points scale by the Fibonacci sequence. The end result is such that the top-ranked player ends with a score in the range of 38-43 percent of all points granted for the game. This overall percentage breakdown holds for any number of players, though it breaks down past a minimum of 4 players.
 Fibonacci Points by Rank, Four Player Example
Rank 	Points	Approx. % of Total
1st (board topper)	3000 	42.86 %
2nd 	2000 	28.57 %
3rd 	1000 	14.29 %
4th 	1000 	14.29 %
== Points Per Supply Center ==
Fibonacci scoring may additionally include some amount of points per Supply Center. Similar to Carnage, these points are a de facto tiebreaker.
As variant maps may have a wide range of possible SC counts, it is recommended that players receive points according to the percentage of the overall map that they occupy, with a total of 100 points granted in this manner.
For instance, if a player holds 12 centers out of the 34 SCs available in classic Diplomacy, that player would be awarded 35 points (100*12/34 = 35.294, rounded down to 35).
== Bonus Points for a Solo ==
Depending on the specific context, those implementing a Fibonacci scoring system may even wish to grant some amount of bonus points above-and-beyond 100% in the event of a solo. 
For instance, if a ten-player match follows the methodology described above, there are approximately 143100 points at stake (143000 for the ranks, ~100 points for the SC percentage tiebreaker points). However, a solo might award 144000 points instead, assuming that makes sense for the context. Discretion is left to the implementer and/or tournament director.
Category:Scoring System