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Player Statistics

Across the top of the main BOUNCED center, just under the news listing, you will see a table with your player's stats. These statistics (with the exception of commitment) are only updated after "for stats" games are completed. Commitment points are updated for every game played.

From left to right they are:

Ranking

All players begin with a ranking of 100. At the conclusion of a game, the "game's worth" is computed. For each power, its ability score is computed. The ability score of a power is the sum of the rankings of the players who played that power prorated by the number of phases they played the power multiplied by 1/(8*sqrt(#p-1)) where #p is the number of powers in the variant played. The following table shows the values of 1/(8*sqrt(#p-1)) for common values of #p.
# powers 2 3 4 5 6 7 8 9 10 11 12 34
ante 0.125 0.088 0.072 0.063 0.056 0.051 0.047 0.044 0.042 0.040 0.038 0.022
You can think of this table as representing the fraction of your ranking you risk (or ante) to play a game with a given number of powers. If you lose, your ranking falls by this fraction. If you have a solo victory, you gain back your risk plus the amount that all of the other players risked.

The "game's worth" is the sum of every power's ability score. Each power's ability score is subtracted from the ranking of the player who started as that power. The game's worth is divided equally among the winners and added to their rankings. Again, if, for a given winner, that power was played by more than one player, the points are divided up prorated by the number of phases each player played that power.

Here are a few examples:

Seven players sign up for a game and all play until the end. Their rankings just prior to the conclusion of the game are:
player ABCDEFG
rank100.090.0140.090.070.0100.0110.0
The game is worth 5.10+4.59+7.14+4.59+3.57+5.10+5.61 = 35.72.

If player C gains a solo victory (as you might expect from the rankings), just after the conclusion, the rankings would be:
player ABCDEFG
rank94.9085.41168.5885.4166.4294.90104.39
If instead, player E surprised everyone and won, the rankings would be:
player ABCDEFG
rank94.9085.41132.8685.41102.1594.90104.39
If players B and G shared the victory,
player ABCDEFG
rank94.90103.27132.8685.4166.4294.90122.25

If, instead of the above, player B started the game and then dropped after 10 phases and player B' (ranked 120) picked up the power and continued for the remaining 20 phases, then the game would be worth 5.10+(4.59*10+6.12*20)/30+7.14+4.59+3.57+5.10+5.61 = 5.10+5.61+7.14+4.59+3.57+5.10+5.61 = 36.74 (rounding causes this sum to look inexact). All 5.61 points would be subtracted from player B (none from B'). So, if player C again won,
player ABB'CDEFG
rank94.9084.39120.0169.6085.4166.4294.90104.39
Or, if the B/B' power won,
player ABB'CDEFG
rank94.9096.63144.49132.8685.4166.4294.90104.39
Or, if B/B' shared the victory with C,
player ABB'CDEFG
rank94.9090.51132.25151.2385.4166.4294.90104.39

A few remarks on this system: Given two players, A and B, the ratio of A's ranking to the sum of A's and B's rankings is the likelihood that A will beat B (or rather, if enough games are played, we would expect this to work out this way). If you win solo, your ranking will go up. It is possible to decrease your score if you abandon your power but it wins solo. Furthermore, if you are ranked highly enough compared to other players and you win, but in a draw with too many players, your ranking can fall. Note that in a few cases if you abandon, you could have your score become negative by this method, but that is rare and it is reset to 0 in that case. Your score cannot decrease if you fill in as a replacement player. However, boosting your ranking artificially by this method is very slow (people don't abandon good positions!).

Weighted Ranking

This statistic only shows up on the systemwide ranking page and not on the main page. It is computed exactly like the ranking system from above, but retroactively and weighted based on the current power rankings. Specifically, for each power in each variant, that power's win score is computed (these are shown on the power rankings page). Then, a player's weighted ranking is calculated retroactively by returning to the beginning (with the player's rank set to 100) and replaying all of the games and adjusting the ranking. The difference is that the number of rank points a player submits to the "game's worth" (see above) is weighted by the win score of the power played. Thus, playing Italy in a standard game does not cost as much if you lose (and is worth slightly more if you win) than playing Turkey. A few notes on this system: if your goal is to increase your own score, it is always in your best interest to win. If you are playing a variant that hasn't been played much and you lose with a power that has never won, your weighted ranking does not change. However, if later a player wins with that power, you will then retroactively take a weighted ranking loss. In general, your weighted ranking could change without any wins or losses on your part (due to the wins or losses of other players playing powers you have previously played).

Commitment

Your commitment is an average of the percentage of times you get your orders in before the deadline. It is weighted so that the distant past matters less (exponentially). The basic system is: If you want to work this out, you'll see this is equivalent of computing the average of a sequence of 100's and 0's (100 for making a deadline and 0 for missing) where the average is weighted by an exponential (0.95 as the base).


(c)1999-2015. Christian R. Shelton. All rights reserved.