|WDC Victoria 2007|
|Author||Matt Shields/Jake Mannix||Kind of system||Rank + Center Count|
|Very Short Explanation (No math)|
In order to get the best score possible, try to two things: End the game with as many centers as possible, and try to be ahead of as many players as possible, by as much as possible. Basically, if you can't solo, come as close to soloing as you can. Failing that, don't let anyone beat you by more than you have to. It's better to lose by a little than to lose by a lot.
Short Explanation (Very little math)
There are two separate things going on with the scoring system for this tournament that are good to know about. The first is the scoring system for the individual boards, which is called a “sum of squares” system. The second is the way your scores form the individual boards are aggregated, which is done by use of an “ante” system.
The board scoring system is relatively easy to understand. This part if the system gives you what is called your “Raw Score”. If you solo a game, your raw score will be 100, and everyone else on the board will get zero. The rest of the time, the formulas in the long explanation are used to calculate it.
All you need to know though, is get as many centers as you can, and be bigger than as many players as possible. If you can't top the board, being second or third is still much better than being fourth or fifth. Additionally, no matter what position you are in, if you can secure that position by more centers that's a good thing. If you're trying to decide whether or not to do something, a good thing to ask yourself is “Will this get me more centers than it gives anyone else?” Eliminating a small power is great if you are the guy getting most of the centers. If your ally is getting most of the spoils, then you may hurt your score. (For example, you're probably better off topping the board 10 to 7 than winning 11 to 10.) At the same time it is very important not to let anyone else get too much bigger than you. Ending the game in second or third place with 8 centers is a pretty good score if the leader has 9 or 10. Bit if the leader has 16, he will score 5 times more points than you, making your 8 centers a fairly weak score.
The change to each player's actual score is calculated using the ante system. Everyone begins the tournament with 100 points. Before each game, each player antes 10% of their current point total into the pot. The Raw Score that each play received above, is the percentage of the pot that they take away at the end of the game. If your Raw Score was big, you'll win back more than your anted, and your actual score will go up. If you're eliminated, or your Raw Score is too small, you'll win back less than your ante, and your actual score will go down.
Long Explanation (Lots and lots of math)
Each player begins the tournament with 100 points. Prior to each game, each player antes 10% of their current score into the pot. It is the points in this pot that the players in that game are competing over. Obviously in the first round, all players will ante 10 points (10% of the 100 points they began with) meaning that the pot will contain 70 points. In later round these numbers will differ from board to board.
At the end of the game, a couple of formulas are applied to determine each player's “Raw Score”. Assuming that the game does not end in a solo, initially calculate [2^(SC/4) ] - 1 for each player and call this value “f(sc)”
Then take f(sc) for each player and divide it by the sum of f(sc) for all seven players and multiply by 100, giving you the percentage that their f(sc) is of the total of all f(sc). This is the player's “Raw Score”.
For reference, the chart on the right shows f(sc)for each center count. Although these numbers do not represent points, they are a good relative guide of how good one SC count is compared to another within the same game. So while you can't say how many points 8 SCs is worth till the game ends, it will always be worth 3 times more than having 4 centers, and always 3/7 as much as having 12 centers.
If the game ends in a solo, the winner's Raw Score is 100, and everyone else's Raw Score is zero. While it is mathematically possible for a non soloist to get a raw score above 80, the board topper will normally have a raw score of between the high 30s and high 50s.
f(sc): [2^(SC/4) ] - 1
At the end of the game the pot is divided up between the surviving players based on their Raw Scores. Your Raw Score is simply the percentage of the pot you receive.
So to take an example, in the first round each of the 7 powers antes 10 points, creating a pot of 70 points. Suppose the game ends with the following supply center chart: Austria 15, England 10, France 5, Italy 2, Turkey 2, Germany 0, Russia 0. The sum of all 7 f(sc) in this case is 19.31802. (We get this by adding up the appropriate numbers in the chart above.) The raw scores for all 7 players will then be:
Austria = 64.47 (12.45434/19.31802*100)
England = 24.11 (4.65685/19.31802*100)
France = 7.14 (1.37841/19.31802*100)
Italy = 2.14 (0.41421/19.31802*100)
Turkey = 2.14 (0.41421/19.31802*100)
Germany & Russia = 0
Austria then receives 64.47% of the pot. 64.47% of 70 is 45.129. So, he started with 100 points, put 10 points into the pot, and took 45.129 points out of the pot, meaning that his score after round 1 is 135.129. In the next round, he will ante 10% of this new score, or 13.5129 points.
We do the same thing with each of the other 7 players. England took 16.877 back out of the pot, making his new score 106.877. Still up from the 100 he started with. France, who came in third, takes back on 4.998 putting his new score at 94.998. Notice that in this example, Austria won by such a large margin that even the player in third place lost points.
Turkey 10 SC, Russia 9 SC, Italy 8 SC, Germany 7, France 0, England 0, Austria 0.
The total f(sc) for all 7 powers is 13.77727. So the raw scores for all players are:
Turkey = 33.80 (4.65685/13.77727*100)
Russia = 27.27 (3.75683/13.77727*100)
Italy = 21.77 (3.00/13.77727*100)
Germany = 17.16 (2.36359/13.77727*100)
Austria, England & France = 0
So everyone's new scores after this round will be: Turkey 113.66, Russia 109.089, Italy 105.239, Germany 102.012, and Austria, England, and France are at 90.
A couple things that are different from Example 1 should jump out at you immediately. First off, the power who topped the board in this example got just over half as many points as in Example 1. This is partly because he has 5 centers less, but also because he topped by 1 instead of topping by 5. The second place power in this example actually scored slightly more than the second place power in Example 1, even though he has one less center. This is because he only lost by 1 center, instead of losing by 5. Not also that in this example the third place and even fourth place players gained points in this round, whereas third and fourth lost points in Example 1.
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