Quote (KrQl @ 3 Dec 2016 10:55)
I can't tell if trolling or not (I know, shame on me...) but you do realize that the whole "Bell curve, tendency towards the norm" etc. thing won't work if you just do 10,000 Lightning hits and plot the damage of each, right? You would just get a flat (well, it would be flat it you did it infinitely many times at least) curve showing that the chance of getting a 1 damage hit would be exactly the same as any other damage, including 31,000 or 62,000 damage.
The concept of the normal distribution would work if you did 10,000 Lightning hits 10,000 times and plotted each "run" though.
Ex. You twice cast something with damage 1-2. The chance of the total damage being 2 would be 1/2^2 or 1/4, because you'd have to get exactly 1 damage two times in a row.
The chance of getting a total damage of 4 would also be 1/2^2 because you'd have to get 2 damage twice.
The chance of getting a total damage of 3, though, would be 1/2 because you could start with either a 1 or a 2 and still do 3 damage.
These are the possibilities with each damage of the cast separated by a comma:
1,1 = 2 damage total
2,1 = 3 damage total
1,2 = 3 damage total
2,2 = 4 damage total
Exactly.
This is the Central Limit Theorem.
If you draw enough (large) samples from a distribution, the distribution of the samples will be normal,
regardless of the original distribution.
So if you draw 10000 samples of 10000 shots of lightning from the
uniform distribution of the lightning spell - then yes, you get a normal distribution.
This does
not mean that the damage of lightning is a normal distribution - it just means that the Central Limit Theorem works.