I have been stuck in this snow storm in Georgia, since Christmas eve and I was able to drive around 6pm yesterday night back to Texas. During my 22 hour drive and being awake 36 hours, I had a eureka moment or delusional episode, I don't know yet. When people are figuring out math for certain units to do XYZ they are doing it wrong almost 95% of the time and they are way off.
I had flashbacks of my North Korea Ex Special forces Business statistics teacher screaming at us when messing around with Bernoulli's theorem and dice and how to figure out results correctly or probability correctly.
Lets take the classic example of twin- linked assault cannons vs twin linked Lascannons. Everyone will say Assault cannon is just as good as a Lascannon to penetrate armor.
Let's Break down the normal formula we are going to use Space marines as an example with razorbacks shooting Landraiders AV 14
BS= Ballistic skill in percentage format such as BS 4 = .66 bs 3= .50 and so on
BS Twin linked
(4/6)+(1-(4/6)(4/6)= .878 time to hit for one shot.
To pen results
(1/6)(2/6)= .05% for a damage result
.878 x .05 = 0.04 or 4% chance for a pen result for one assault cannon shot
Twin linked lascannon
.878(2/6) = 29% for a damage result
Now this part would be correct if we were only rolling one single die at a time and that was the only thing we were doing. You can't just add 4% 4 times together to get a result of 16% chance. The reason is because we are rolling dice and even if we add enough shots together we can never go pass 100% chance because no matter what there is still a chance of failing even though it would be very slim. You take the 4% for the assault cannon and take it to the 4th power because that is how many shots it has and you have your correct result and add each power to the 4%.
Your results should be
to the first power = .04
second power = .0016
third power = 0.000064
forth power = 0.00000256
Total result should be around = .0416656 or 4.2% chance
So every time you shot that Assault cannon at an Av 14 or really anything above AV 13 your only going to get a 4.2% chance of doing anything to it and you wonder sometimes why the assault cannon is not performing the way its supposed to for you.