I was not going mathematically, I was going by real world use. My ISD's with Vader rarely roll less than 8 damage after the reroll.6 actuallyI am pretty sure that 4 red and 4 blue is average 7 damage. . . Hmmmm that is usually me though. . .
.75x8=6
but it has a very good chance of having an acuracy
I'm surprised that Lyraeus would suggest 7. I come to it by a different calculation than clontroper5 , but I agree on 6 average damage.
I'm surprised by Lyraeus' calculation, because I know he adheres to the 80-20 rule. Going by that rule, however, you should not count on more than 5 damage from 4 red + 4 blue at <long range. The plurality of results is 6 damage (which you should expect only 24.6% of the time), and you can count on at least 6 damage only 66% of the time (ie. less than 80%).
Okay, but I didn't think we were factoring Vader into the equation.
Anyway, I did run the probabilities on the Imperial arcs, and I have to dispute at least one of clontroper5 's assessments.
Between Vic I and Vic II. While the criticals and accuracies will obviously differ, there is such a marginal difference between the expected raw damage output of R³Bl³ (3 red and 3 blue) and R³Bk³ (3 red and 3 black) that I would not categorize the danger zone of the Vic I's close range and the Vic II's close/medium front arc any differently from one another. Both are what I would call 4(5) - meaning 4 reliable damage, 5 expected - 5 being the average, and 4 being what you can count on with a 80% confidence level*. Therefore, using his schema, I would say that both the VicI close range and the VicII close/medium range would be orange, rather than the former red and the latter orange.
To give you the numbers:
R³Bl³ R³Bk³
0 0.001 1.000 0 0.001 1.000
1 0.011 0.999 1 0.008 0.999
2 0.050 0.988 2 0.037 0.991
3 0.140 0.939 3 0.101 0.954
4 0.252 0.799 4 0.183 0.852
5 0.279 0.547 5 0.232 0.669
6 0.184 0.268 6 0.210 0.437
7 0.069 0.084 7 0.137 0.227
8 0.014 0.015 8 0.064 0.090
9 0.001 0.001 9 0.021 0.026
10 0.004 0.005
11 0.001 0.001
12 0.000 0.000
The first column on both sets gives you the possible raw damage output. The second column the probability of each of those outcomes, and the third column the declining cumulative probability of 'at least' that much damage.
R³Bl³ is not going to give you the same upper range as R³Bk³ is going to, and it's going to be a smidge better on average, but you can see that the plurality is still 5 expected damage and you're 80% certain to get at least 4 damage on R³Bl³, and 85% on R³Bk³.
That smidge is not enough to matter in my book.
Also, because R1H4 makes a great point , I think, that you shouldn't base your decisions on expected damage, but on reliable damage - ie. that third column, where you can count on 4 damage at a 80%/85% confidence level.
* I realize that ' confidence level ' refers to the probability that a sample reflects the true distribution of a given population. Also, I think that when R1H4 is talking about the 'Pareto principle' of 80-20, that he is skewing what Pareto meant by it. But, I'm quite fine with bastardizing the terms to suit our purposes.
Edited by Mikael Hasselstein