robopirateninja said:
Yakk, experimental error is possible, but wiz's sample size was an entire order of magnitude larger: perhaps there was no tomfoolery from either end and sample size reigns, as usual.
I was testing for experimental error -- those are 95% error bars, given the sample size. (I did use the Normal and not Student's T, so they will be
very slightly off on 100 to 1000 samples).
The 95% confidence interval of the two tests don't overlap on the full resist case -- they aren't even close. This is a sign of something weird going on.
Most likely, there was a swapping of full and partial resists by one party or the other, especially when the total resists line up so prettily.
Let's assume we get 10% full and 20% partial, and that partials are basically a uniform distribution of 0 to 100% damage.
Then when you cast 5 spells, your expected damage is 4 spells.
But, what is the confidence?
Our resist rate random effect is:
R = P(.2) * U[0,1] + P(.7)
E = .8
where U[0,1] is a uniform random variable on [0,1].
Var(R) = E(R^2) - E(R)^2
= E(P(.2) * U[0,1]^2 + P(.7)) - .64
= .2*E(U[0,1]^2) + 0.06
Aside:
1/12 = V(U[0,1]) = E(U[0,1]^2) - E(U[0,1])^2 = E(U[0,1]^2) - .25
7/12 = E(U[0,1]^2)
= .2*7/12 + 0.06
= 7/60 + 3/50 = 53/300
So Var(R) = 53/300.
Var(5 nukes) = 265/300
1.96 * SD(5 nukes) =~ 1.84 (this is the 95% confidence radius).
So on 5 nukes, you are
roughly 95% certain to do between 2.16 times to 5.0 times base nuke damage. So 19 times out of 20, you can rely on getting 43.2% of your max damage on 5 nukes.
Similarly, on 10 nukes you are
roughly[/] 95% certain to do between 5.39 to 10.0 times base nuke damage. So 19 times out of 20, you can rely on getting 53.9% of your max damage on 10 nukes.
Using a 499/500 confidence radius we get 1.18 to 5.0 times base nuke damage: Ie, roughly 23.7% of max damage can be relied upon to land after casting 5 nukes.
499/500 confidence and 10 nukes: 4.02 to 10.0 times base nuke damage, or 40.2% of max damage can be relied upon.
In comparison, heals and melee have lower variance: Melee is a far more often repeated test, which lowers variance, and heals are less likely to be resisted than nukes. 
So a tactic based on healing and melee damage will be more reliable, even if it is less effective on average. And as a player will generally be fighting a creature that they will on average defeat, this higher variance translates into making the tactic less useful.
But that's just the math, not a value judgement.
A 1/20 event is common enough to happen most every day of grinding: So if you fight creatures that you can't defeat if you only do 43% of max damage on your first 5 nukes, you end up dieing.