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Thinking of AD as an EH bonus (math)

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Thinking of AD as an EH bonus (math)

Postby Eanin » Thu Sep 04, 2008 7:58 am

I've been fiddling around with the math on AD, and here's what I came up with.

For any mob that can kill us in two hits, it is useless.

For any mob that can kill us in three hits, the third hit would be affected by AD. So, in order to kill us:

x+x+0.7x=100%
2.7x=100%
x=37%

That means that, in order to kill us in three hits, a mob would need to do 37% damage to us on each hit. This translates into:

37%*3=111%

So, for a mob that can kill us in three hits, AD is like a 11% hp bonus.

For a mob that can kill us in four hits, the fourth hit would be affected by AD.

x+x+x+0.7x=100%
3.7x=100%
x=27%

27%*4=108%

For a mob that can kill us in five hits:

x+x+x+x+0.7x=100%
4.7x=100%
x=21.3%

21.3*5=106.5%

Note that 21.3%*3 is very close to 65% (it's 63.9%), so if one of the first hits is a little larger, the last two hits will both be affected by AD:

x+x+x+0.7x+0.7x=100%
4.4x=100%
x=22.7%

22.7%*5=113.5%

For a mob that can kill us in six hits, though, the last two hits will definitely be affected by AD:

x+x+x+x+0.7x+0.7x=100%
5.4x=100%
x=18.5%

18.5%*6=111%

So, assuming we get hit by a mob for about the same amount (not exactly a fair assumption, but true in many situations), the bonus EH from AD is:

2 hits: 0%
3 hits: 11%
4 hits: 8%
5 hits: 6.5%/13.5%
6 hits: 11%

There's the math :). Any suggestions would be appreciated, but it's a useful way of thinking about how much AD contributes to our EH, depending on how hard they hit.
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Re: Thinking of AD as an EH bonus (math)

Postby æ » Wed Apr 22, 2009 6:41 pm

Im not sure how this works....

As far as I know AD = .35*.3*Health. Which is %10.5 absolute best case.

If I get hit three times, as you say AD is effecting the 3rd hit.
Thus .33*.3*health. or %9.9 EH

Can anyone shed further light on how that is wrong? It seems pretty clear from the tooltip. At 35-x% health, 35-x% of your health is 30% bigger.


I realize this is a necro, but AD still works the same way, and I would only make a new thread and link to this one anyway.
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Re: Thinking of AD as an EH bonus (math)

Postby Candiru » Thu Apr 23, 2009 4:14 am

You need to be dividing by 0.7, not multiplying by 0.3!

a 30% reduction of X, is 0.7*X.

This puts it as a 15% maximum effect.

0.35*0.7=0.5, 0.5-0.35=0.15 = 15%
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Re: Thinking of AD as an EH bonus (math)

Postby æ » Thu Apr 23, 2009 6:29 am

Alright, but my question is why are we dividing by .7? Is it due to the nature of being incoming damage being reduced. There is some subtle difference I'm not getting ;(
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Re: Thinking of AD as an EH bonus (math)

Postby Isetnefret » Thu Apr 23, 2009 6:42 am

Hmmm....

When Health is less than 35%, damage is reduced by 30%.


so...

.70 X = .35 H

Where X = damage required to kill you and H = Health

X = .35H/.70

X = .5 H ????
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Re: Thinking of AD as an EH bonus (math)

Postby Isetnefret » Thu Apr 23, 2009 6:44 am

If you have 25,000 health, 35% of that is 8750 health.

However, with Ardent Defense active, it would require 12,500 damage (before AD) to kill you.

12,500 is 50% of 25,000.

So ummm....I have no clue if that answers your question, I may be just stating the obvious...
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Re: Thinking of AD as an EH bonus (math)

Postby Rasmfrackn » Thu Apr 23, 2009 7:13 am

I'm a little fuzzy on what the question is. Are you asking what the simplest way of thinking about AD as EH is? Your numbers seem ok but it depends on how you're describing it.

If you're going to assume hits of size 1, then Candi's number seems right. You take 65% of the damage as 1:1, and you take 35% of the damage as 0.7:1.

0.65 + 0.35 / 0.7 = 1.15

More realistic, though, is your italicized sentence:
"At 35-x% health, 35-x% of your health is 30% bigger"

That's how it comes into play with larger hits. The larger the hit, the smaller the potential EH bonus, up to the point where hitting for exactly 1/2 your hps at all times makes it useless. (.35/.7 = .5, so if you're *just* inside AD range and the hit is 1/2 your health, it'll just bring you to 0) Are you looking for how to find X?

I haven't worked through the original post thoroughly, but it looks like it's assuming hits without heals? That's the tricky part of this sort of analysis (and for Divinity, imo). You're never really living without any heals and you're not always topped up to full, so the easiest theorycrafting situations aren't necessarily the most accurate. In reality you end up with a chance of ending up in the range where AD/Divinity helps or not, depending on the difference between the last few heals and the last few hits.

Assuming an average of every possible hitpoint (1 damage hits) is also unreasonable, but coming up with something that simulates reality is pretty hard because of so many things that depend on the specifics of what's happening. E.g. how much haste does your healer have, is it a healadin or a disc priest or something else, do you have fast hots or slow hots or both, how variable is the mob's damage range, etc.

Whoops. /ramble off.
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Re: Thinking of AD as an EH bonus (math)

Postby majiben » Thu Apr 23, 2009 7:16 am

Rasmfrackn wrote:"At 35-x% health, 35-x% of your health is 30% bigger.

That is inaccurate. At sub 35% health you have 42.86% more EH not 30%.

For a similar situation, if you took 100% less damage you would have more than 100% more EH. In fact you would have infinitely more EH.
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Re: Thinking of AD as an EH bonus (math)

Postby Isetnefret » Thu Apr 23, 2009 7:25 am

You icon gives me horrible flash backs of Guk.
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Re: Thinking of AD as an EH bonus (math)

Postby Rasmfrackn » Thu Apr 23, 2009 8:04 am

Majiben wrote:
Rasmfrackn wrote:"At 35-x% health, 35-x% of your health is 30% bigger.

That is inaccurate. At sub 35% health you have 42.86% more EH not 30%.

For a similar situation, if you took 100% less damage you would have more than 100% more EH. In fact you would have infinitely more EH.


True, but it's closer to reality than summing up 1 damage hits, which is what I was pointing out. I guess I put the wrong emphAsis on the wrong syllAble.
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Re: Thinking of AD as an EH bonus (math)

Postby Elsie » Thu Apr 23, 2009 10:40 am

The safest method of calculating the benefit of AD is simply looking at the worst case scenario in a given situation. Since AD is pointless in the 2-shot scenario, we can simply assume it takes 3 hits for a boss to kill the paladin, else AD_EH=0.

Thus, the only cases you have to deal with is:
1) 3 normal hits
2) 1 special hit -> 1 normal hit such that HP/0.7 > 1 normal hit

Then pick the lower of the two as the effective EH, since you can't rely on the other.
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Re: Thinking of AD as an EH bonus (math)

Postby PsiVen » Thu Apr 23, 2009 12:30 pm

Keep in mind that the values you attribute to EH here are basically minimum contributions -- there are indeed situations where AD will save you from a boss which hits you for 50%+ of your health, thanks to absorption, damage reduction, resistances, etc.

With regard to the minimum values, there should be a closed form mathematical expression for X-sized hits on a health pool of Y, that you could also use to represent N hits required to kill. This is the EH, and more factors in the analysis will reveal other savior scenarios.
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Re: Thinking of AD as an EH bonus (math)

Postby Rasmfrackn » Thu Apr 23, 2009 12:56 pm

PsiVen wrote:Keep in mind that the values you attribute to EH here are basically minimum contributions -- there are indeed situations where AD will save you from a boss which hits you for 50%+ of your health, thanks to absorption, damage reduction, resistances, etc.


Good point. Does PW:S benefit from AD? I could see a shield from a disc priest gaining significant effect in that case.
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Re: Thinking of AD as an EH bonus (math)

Postby æ » Thu Apr 23, 2009 1:05 pm

I know this seems simple, but it almost seems like looking at some illusion where one person sees it and the other cant.

Im seeing where all the numbers are coming from, and 0.7 inverce is 1.43. But im also seeing that at 35% you have 30% more, thus being 10.5% EH? How is that wrong, and if its not, how can 15% also be correct?

For now im thinking that 10.5% is incorrect value for the EH as damage incomeing is put through a .7 modifier so it just works out differantly (and i suppose at a higher real EH). (??)
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Re: Thinking of AD as an EH bonus (math)

Postby Rasmfrackn » Thu Apr 23, 2009 1:48 pm

æ wrote:I know this seems simple, but it almost seems like looking at some illusion where one person sees it and the other cant.

Im seeing where all the numbers are coming from, and 0.7 inverce is 1.43. But im also seeing that at 35% you have 30% more, thus being 10.5% EH? How is that wrong, and if its not, how can 15% also be correct?

For now im thinking that 10.5% is incorrect value for the EH as damage incomeing is put through a .7 modifier so it just works out differantly (and i suppose at a higher real EH). (??)


Hrm, ok.

I guess your confusion is that at 35% you don't have 30% more, you take 30% less. Hence the 43% that Majiben corrected.

How about this:

taken = incoming * reduction

reduction = 0.7, so taken = incoming * 0.7

Another way to write the equation is taken / 0.7 = incoming. So the amount you're able to "take" from a fixed "incoming" gets increased by dividing by 0.7, which is the same as multiplying by 1.43.

65% + 35% * 1.43 = 115% in the best-case, 1-damage-at-a-time case. Larger hits reduce the 35% to a smaller number as the hit that brings you into AD range skips more and more of that portion of your health. So, your EH with AD is 65% of your health, plus x% of your health, plus (35%-x%) * 1.43 of your health that actually gets increased. That x depends on the granularity of the hits.

Is that what you're asking?

-- There're also the complications that Psiven mentioned. Fixed reductions like block value and absorptions get tweaked as their power goes up relative to the damage per hit (and we get to consider block value for our EH thanks to holy shield uptime). I'm sure we've all experienced the fun when soloing old content elites with a lot of hitpoints where post-block hits are small until you hit AD range, and then they become full-blocks, making you effectively immortal under 35%.
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