Need Help figuring out a statistics problem

[BruisedOoze]

Wikipedia tells me Bernouilli trials deals with booleans, I have no clue how you want to apply them here.

The simulations are Bernouilli trials by their nature. The bolean property is the hit or miss. We're evaluating run sequences of Bernoilli trials. It's not that it's applied it's that it's the language used to describe trials within statistics that have bolean properties. I apologize for being misleading with the jargon.

I think you misunderstand what he is saying. You can use the bernoulli trials to find the integer values, because that is the actual raw number of actual swings you can take. However, what he's saying (I think) is that the benefit of the non integer value closest to it, even if it is a fraction, is still beneficial to increasing survivability. It's still widening the buffer because even a small heal not equal to current HPS on the tank (or small cooldown, etc.) can push you over into the next swing cycle and give you that many more seconds to live or be healed back to full.

At least that's how I would interpret it, and I think it's a valid argument.

I believe Martie and I are driving at exclusive points, because there are conclusions that are coming up which I have no disagreement with.

I agree that the non-integer values of health do have benefit, and I see why 4.9 is considered to 5 for example. I have no argument with that, and is what I believe and see as well. It's that the nature of the simulation doesn't capture the quantitative value of fractional quantities. 5 is better than 4.9, but in the model we're considering it the same. The simulation works well for telling you what hit sequences to expect and how avoidance changes this. And so far as mentioned, however, appears to be difficult to applying a sensible 'survivability value.'

Such difficulties are that we've established as a testing scenario 5 hits are very bad. Yet according to the model we will see those with almost certainty. But I'm guessing that these encounters aren't causing wipes 98% of the time because of this. There are CDs etc that affect these situations. So what is the quantitative value that can be attached to the results?

By changing the avoidance by 2% the conclusion was that the change in the hit sequences was 'small.' In the scientific world small/large are terms that when used will most certainly be followed with the questions "How small?" and "Small compared to what?". And this simulation can't answer that. 100 Stamina trinket on a EHP based tank (progression content) I can also say is relatively small (not saying unimportant), but it doesn't tell you anything. It's tempting to say it's smaller than 2% dodge (which I would guess 100 Sta>2% because there are a lot of good reasons why that should be the case, which you and Martie have repeatedly pointed out), but we can't show that with this. And comparing the value of 100Sta in your other model (which appears to so far have a sound basis), to 2% in a completely different model (which is shown not to be sound) is extremely dangerous and problematic in a scientific line of thinking,

To be clear, I'm not being critical of the idea or truth of EHP, I'm being critical of just this model. And ultimately so far comes to our best option and your entire conclusion "Tanking is strategy." Building stamina so far has been the winning strategy. Can we say for certain if Blackheart is better than Eitrigg's Oath? No, but EHP so far has shown to be better than avoidance stacking so Blackheart is likely our better bet, and qualitiative reason hasn't shown that it is worse.

[Aggathon]

5 is better than 4.9, but in the model we're considering it the same.

That's because you don't actually take 4.9 hits (well you might take .9 of a hit, that gets into my whole stochastic argument and that's kinda different from this, but I'll show my point in a second). A boss hits an integer number of times. So if you can survive anywhere from 4.0+ to 5.0- hits, this means that the boss will actually swing 5 times and the 5th one would kill you, therefore the model is relevant in terms of the beneficial impact from avoidance.

And ya,the black heart is totally better than Eitrigg's Oath =P.

The whole overarching premise though, is that as time -> infinity, you're gonna take that hit string that RNG can't save you from. Can a marginal increase in stam give you that same safety? Not technically, but it is the only thing that is guaranteed to have some marginal benefit. Those sums added can add up to a lot, more than just the individual parts, and those are the only things that give healers a buffer to insure that they increase HPS > DTPS or for a tank to use a cooldown. That's the whole point. That's why tanks live throughout fights, because even if they take an unlucky hit string like that, the healers have a buffer to heal the tank back up to full.

[BruisedOoze]

That's because you don't actually take 4.9 hits (well you might take .9 of a hit, that gets into my whole stochastic argument and that's kinda different from this, but I'll show my point in a second). A boss hits an integer number of times. So if you can survive anywhere from 4.0+ to 5.0- hits, this means that the boss will actually swing 5 times and the 5th one would kill you, therefore the model is relevant in terms of the beneficial impact from avoidance.

What I mean by 5 and 4.9 is that you have 5/4.9 hits worth of hp. And I already mentioned the model is relevant for avoidance, but it doesn't have any certain quantitative value. Only qualitative.

The whole overarching premise though, is that as time -> infinity, you're gonna take that hit string that RNG can't save you from.

By the same token, you're gonna take an extra hit as time approaches infinity that extra tiny bit of stamina couldn't save you from. But time doesn't approach infinity, otherwise any non-zero probability you could die within a time frame is going to cause your likelihood of death to be 100%. You have to know how the probability behaves for finite times, and as time approaches infinity ask yourself which will cause you to hit 100% first. The tiny extra bit of health versus or extra tiny bit of avoidance? Is 1 stamina better than 5% avoidance in improving your odds of living? Most certainly not. Is 0.01% avoidance better than 100 Stamina? No. So where is the crossover point?

[Aggathon]

Well it is honestly pretty much impossible to determine a cross over point. Also as time approaches infinity is simply a mathematical way of saying "the longer the fight is." I see increase in EHP as adding to the buffer that healers have to heal a tank back up to full. I also feel that those marginal yet reliable increase, however small, are better than the RNG nature of avoidance. I honestly think the point at which avoidance becomes better is both too hard to define because you are comparing apples to oranges and also that given avoidance levels in ICC, it's unattainable to reach an avoidance level where you can reliably say you won't get hit 5 times in a row on the majority of boss fights, so for current content the argument is moot. I'll take my reliable margin of EHP over my RNG margin of avoidance gain any day.