Conquer Club

Concise description:
Modification of the Dice Stats page

Specifics/Details:
The Dice Stats page currently shows the average roll. This is a poor representation of the distribution of a player's rolls. For example, Player A's last 60 rolls are 30 ones and 30 sixes. Player A's average is 3.5. Player B's last 60 rolls are 10 ones, 10 twos, 10 threes, 10 fours, 10 fives, and 10 sixes. Player B's average is also 3.5. Clearly Player B's rolls are more evenly distributed, even though the average is the same.

In addition to the average, the Dice Stats page should include the mean number of rolls for each number and the standard deviation. For example, the for Player A the mean number of rolls is 10 and the standard deviation is about 14.14 and for Player B the mean number of rolls is 10 and the standard deviation is 0. For player A the ones and sixes are each more than three standard deviations above the mean.

Here are my lifetime (the last month and a half) attacking stats: 457 ones, 458 twos, 428 threes, 473 fours, 450 fives, and 450 sixes. The average shown on my DIce Stats page is 3.5 (3.497...). What I would like to see is "Mean: 452.67" and "Standard Deviation: 13.44." Then I can see that the ones, twos, fives, and sixes are close to the expected values, but the threes and fours are each about 1.5 standard deviations from the mean.

I think this gives a little more insight into the dice and gives a better understanding of what CC is attempting to show and prove.

You can already see exactly what your dice distribution is if you go to medal stats. From what I understand, you want another column that includes the standard deviation. I don't think that's necessary since I doubt people know and care about the standard deviation of their dice. And with the stats provided, it is easy for these people to calculate the standard deviation by going to a player's profile and doing it themselves.

The real problem with the dice stats page is the TERRIBLE way "luck" is calculated.
(I'm going to talk about "Battle outcomes" b/c I couldn't care less about the dice distribution)

From what I can tell, It's currently calculated as:
[kills/(kills+losses)] - (the equilibrium probability) , the equilibrium prob for 3v2 is 54% and 3v1 is 66% the others are some other numbers....doesn't matter

So in this way in the 3v2 column, the max "luck" is +46% and min -54%. and in 3v1 it's +34% and -66%. which doesn't really make much sense imo.

SO for example, in 3v2: Luck[0 wins, 2 losses] = Luck[0 wins, 100 losses] which is ABSURD.

I propose the formula for luck should be something like:
Luck(a,n) = 1 - 2 * Pr[X(n) >= a]
where a = # of kills, n = # of rolls, X(n) = # of kills after n rolls
i.e. "The luck % of getting 'a' kills in 'n' rolls equals 1 minus 2 times the probability of getting mre than or equal to 'a' kills in 'n' rolls."

This formula has a max luck of +100% and min of -100% and will actually tell us something useful!
Especially for large quantities. B/c with the current way, you have to be very lucky or unlucky to not have more than +/- 1% luck with a large sample size.