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Armor vs HP Math Help

Warning: Theorycraft inside.

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Re: Armor vs HP Math Help

Postby theckhd » Fri Jan 29, 2010 2:27 pm

Aelfric wrote:Anyone who can adopt a conciliatory tone by (1) making a Star Trek analogy (2) to a prolonged internet argument (3) over the finer aspects of gearing choices (4) in a MMORPG is OK in my book

Yeah, I had a good laugh at that as well. It certainly made me feel a little better about this whole ordeal.

Aelfric wrote:Will this discussion change anyone's thoughts on http://www.wowhead.com/?item=50341? That's certainly more armor than the Glyph and the bonus stacking stamina, though unreliable, only increases the armor's usefulness.

Yes. Trase beat me to it, but I share his opinion (now).

I've already done some modeling of the proc that suggested it wasn't all that good even on a tank-and-spank fight, and there have been a few in-game tests that more or less agreed with them. There's a thread about it in the Gear forum.

But the trinket is strong for its armor already. The normal version might be a weak trade from the Glyph (100 more armor at the cost of a good on-use), but the heroic version is probably strong enough to warrant using over the Glyph most of the time.
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Re: Armor vs HP Math Help

Postby JamesVZ » Fri Jan 29, 2010 2:38 pm

fuzzygeek wrote:I've never said you were actually retarded, and I apologize if my questions come across that way: these questions are not intended to be snarky -- I'd actually like to hear your reasoning.


Whoa there, sweet cheeks. This ain't my first rodeo here, you ain't going to hurt my feelings. Just tryin to liven the place up a little, is all.

I'd use armor gems in red sockets pretty exclusively, and it's not a question of 'how much' armor would have to be on the gems because you and me don't decide these things. The itemization system they have already laid out does. And since I'm too lazy to go look up how much an epic gem's worth of armor would be, you're just going to have to use your imagination on this one. Sorry :(.

That said, it would be an extremely interesting gearing choice. There's definitely a 'safe' level of stamina you want to maintain, and you really can never have enough of it. I just generally value armor as the better stat to stack where I can, and make up for the sta loss in my trinket slots by stacking the everliving shit out of it elsewhere. It's done me good thus far.
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Re: Armor vs HP Math Help

Postby Trase » Fri Jan 29, 2010 2:46 pm

Unbreakable Dreadstone would have 140 armor/15 stamina. Hardened Cardinal Ruby would have 280 armor.

(Made up names for the hell of it.)
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Re: Armor vs HP Math Help

Postby Roots » Fri Jan 29, 2010 2:46 pm

Aelfric wrote:- Will this discussion change anyone's thoughts on http://www.wowhead.com/?item=50341? That's certainly more armor than the Glyph and the bonus stacking stamina, though unreliable, only increases the armor's usefulness.


Since we're already talking about warrior/pally tanks, I'm just going to throw out that in my intended bear set uses both this and the heroic version. As was pointed out in the Organ thread, obviously bears lower avoidance helps with maintaining the stack, but I didn't value the stamina much to begin with.

fuzzygeek wrote: At what point is choosing stam over armor not an actually retarded move, and at what point does it indicate someone is a window licker?


Possibly because the key has a pretty lackluster on use more than the armor:stamina ratio debate. One time 3k absorb every 2 min is less than ideal. I may get it eventually, but my inteded stam trinkets would likely still be heroic juggs and sindragosas (obviously not addressing "what if I don't have it")

Also, wtb mainbearspot.com so we can claw each other to death over the finer points of agility v stam.
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Re: Armor vs HP Math Help

Postby fuzzygeek » Fri Jan 29, 2010 2:53 pm

Trase wrote:Unbreakable Dreadstone would have 140 armor/15 stamina. Hardened Cardinal Ruby would have 280 armor.

(Made up names for the hell of it.)


At these values, the ac:hp ratio would be 9.333... (repeating, of course).
Shifting dreadstone is 1.333...

Key vs Glyph is about 7.86
Engineering gloves vs 18 hp kit is an astounding 49.166... (granted it's a trade-specific buff).

A 9.33 trade-off seems quite delicious. Perhaps we can petition Blizzard to add them for Cataclysm.

I would tend to favour agil over straight AC due to additional benefits from a stat (scaling, crit, dodge), but that high of a ratio would be hard to pass up.

Hopefully they do modify the game to make more interesting gearing choices possible (thus enabling an entirely new generation of endless flame wars). I'm hoping their design philosophy on talent trees will bleed over into gear a bit, in a non-stupid way.
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Re: Armor vs HP Math Help

Postby balloonknot » Fri Jan 29, 2010 3:10 pm

This thread has been a great read, offered some interesting ideas and certainly provided some good laughs.

Perhaps the funniest bit is that despite 21 pages of rabble, both sides are going to end up with almost identical gear sets as virtually all the BiS EH gear, is also the +armor gear.

Perhaps we should just rename this thread armor vs stam trinkets and get it over with?
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Re: Armor vs HP Math Help

Postby Paxen » Fri Jan 29, 2010 3:46 pm

One thing I would like is a further examination of the formula Theck used to find how much healing is needed for an armor trinket to be equal to a stam trinket. If I know this relationship between two trinkets it should be easier for me to choose which to use for which fight.

h = (A+K)/dA*(dH-H*dA/(A+K))

So, here, would you first have to calculate dA and dH to find the proper values?
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Re: Armor vs HP Math Help

Postby halabar » Fri Jan 29, 2010 3:54 pm

fuzzygeek wrote:
Trase wrote:Unbreakable Dreadstone would have 140 armor/15 stamina. Hardened Cardinal Ruby would have 280 armor.

(Made up names for the hell of it.)


At these values, the ac:hp ratio would be 9.333... (repeating, of course).
Shifting dreadstone is 1.333...

Key vs Glyph is about 7.86
Engineering gloves vs 18 hp kit is an astounding 49.166... (granted it's a trade-specific buff).

A 9.33 trade-off seems quite delicious. Perhaps we can petition Blizzard to add them for Cataclysm.


We should suggest their inclusion now. Shouldn't be too hard to add.
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Re: Armor vs HP Math Help

Postby Steve » Fri Jan 29, 2010 4:14 pm

JamesVZ wrote:I'd use armor gems in red sockets pretty exclusively, and it's not a question of 'how much' armor would have to be on the gems because you and me don't decide these things. The itemization system they have already laid out does.


But there exists an amount of stamina that you prefer over an amount of armor. That's his point. You choose 15 stamina over 20 armor because 15 stamina does more to keep you alive than 20 armor does, presumably. So the question becomes, how much armor would it take to be a wash in your mind with 15 stamina?

Obviously that number is going to vary from fight to fight, but you should still be able to articulate the process you use for arriving at your decisions.

The actual itemization values Blizzard chooses is not relevant to the discussion since the itemization cost of a stat does not match its in game practical value. And beyond that, we frequently need to decide between using a higher ilvl item with stamina (for instance) or a lower ilvl item with armor. I get that your general rule is to chose armor when in doubt, and in the case of gems it's pretty easy to pick 15 stamina over 20 armor. But you're ripping into people for choosing incorrectly when the choice is a much, much closer call, and you're doing so without giving us much insight into your decision-making process.

You might be able to arrive at these decisions intuitively for whatever reason (superior experience, intellect, penis size) but it's pretty clear (since some people have failed to) that other people cannot.
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Re: Armor vs HP Math Help

Postby heuvarius » Fri Jan 29, 2010 5:48 pm

Mulack wrote:See this is where I don't agree. Posts like this one or the ones where people say "I just stack stam because it's all overheal anyway and I just soak that up" don't make sense to me based on experience. A couple people get what we're saying, several do not.


This is not what I am saying at all. What I am saying is, for the relative worth of the two trinkets in discussion from the post I quoted, the armor trinket does not perform as well as the stamina trinket for my typical death scenarios. If the armor trinket has twice the armor and allow me to survive longer in crunch situations, I will have no hesitation in using it.
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Re: Armor vs HP Math Help

Postby Hamlet » Fri Jan 29, 2010 6:25 pm

fuzzygeek wrote:Someone mentioned earlier that it doesn't take much for armor to outstrip stamina. My question remains the same: How much is "much"? What criteria or rubric are you using to judge?


I wasn't handwaving, I was saying the result was simple if you understand the underlying mathematical idea in the first place. Theck picked up on it fine (he quoted the post where I spelled it out a bit more above).

Anyway, I think my work here is mostly done. Things seems to be rolling along nicely. I'm not going to really sink into tank theorycraft now; I still have my own classes to work on. Just to clean up the mathematical idea I was talking about before:

Say you have H health and M mitigation, and in the danger window you take D mitigatable damage, U unmitigatable damage, and L healing. You survive if:
H + L > D*(1-M) + U.
Change the > to a = to find the marginal case between non-death and death, and substitute M = A/(A+C), where C is the armor constant:
H = DC/(A+C) + U - L
Take the derivative:
dH/dA = -DC/(A + C)^2
Note that this is a partial derivative (I just can't write it since I don't think this board supports LaTeX). Don't try to take apart the differentials dA and dH and rearrange them into other equations. And remember that D is pre-mitigation damage. To put it in terms of post-mitigation damage Q, substitute Q = DC/(A+C).
dH/dA = -Q/(A+C)
So we see that, in a situation in which you take Q physical damage during the period in question, an additional point of armor is worth this amount of HP:

Q/(A+C)

I did something slightly tricky above, so be careful. Don't think this means that, say, the value of armor decreases as you get more of it, which is false. This applies within a single scenario: if you took a death that involved total mitigatable physical damage Q, what the relative value of armor and HP would have been.

This may be a more helpful way of conceptualizing a death event than EH. L and U drop out and you can more clearly see the value of Armor. And it makes much more clear the relationship between the value of Armor and the total damage it prevents. The result is basically intuitive--if your death involved a lot of total physical damage (like that Festergut log from before), Armor would have done quite a lot to help. But for anyone who wants a simple way of computing it, there you are.

Note that this doesn't directly help you make gearing decisions. But that's fine for now. You all spent so much time bound to the idea that you had to have a simple equation for what gear to wear that you chose to ignore huge components of what was actually going on in-game. Divorce yourself from that and develop a sense of what really matters more in a variety of situations. You'll have to gear more intuitively, but you'll ultimately have a much better understanding of what's going on.
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Re: Armor vs HP Math Help

Postby fuzzygeek » Fri Jan 29, 2010 7:31 pm

Hamlet wrote:Note that this doesn't directly help you make gearing decisions. But that's fine for now. You all spent so much time bound to the idea that you had to have a simple equation for what gear to wear that you chose to ignore huge components of what was actually going on in-game. Divorce yourself from that and develop a sense of what really matters more in a variety of situations. You'll have to gear more intuitively, but you'll ultimately have a much better understanding of what's going on.


Thank you for taking the time to put that together.

I'm not certain how this will directly affect tanks who gear intelligently -- e.g., bring armor to physical fights, stamina to magic fights -- but perhaps it will cut down on the "Trinket A reduces down to N EH using the handy formula, and Trinket B calculates out to N+1, ergo Trinket B is better in all cases" kind of lists, which becomes a kind of dogma, which I would agree does a disservice.

I think the idea that everyone was gearing strictly based on the EH calculation is a gross over-simplification of the tanking community in general and this site's denizens in particular, but I guess a kind of granularity gets lost whenever someone starts talking to "you people."

And yes, it amuses me greatly that the differences in most of our intended outfits heading into ICC hards differ from one way to the other by a matter of percentage points.
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Re: Armor vs HP Math Help

Postby Arjuna » Fri Jan 29, 2010 8:04 pm

Seems to me this is a thread that has a few guys like this in it:

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And fortunately so...

I'm just glad you reconciled in the end, sortof.

And, yes yes I am a sheep that follow the math...gimme teh math! :D
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Re: Armor vs HP Math Help

Postby Fridmarr » Sat Jan 30, 2010 12:34 am

Hamlet wrote:You all spent so much time bound to the idea that you had to have a simple equation for what gear to wear that you chose to ignore huge components of what was actually going on in-game. Divorce yourself from that and develop a sense of what really matters more in a variety of situations. You'll have to gear more intuitively, but you'll ultimately have a much better understanding of what's going on.

This is a two way street though, you should have come to the same conclusions about "armor is always better".
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Re: Armor vs HP Math Help

Postby Awyndel » Sat Jan 30, 2010 11:32 am

I will never gear on intuition.

If the model is incorrect you make a new one. And you try to apply it to the situation and gear choices at hand.

If you're so smart maybe you should make an updated model instead of telling ppl to make guesses.

Don't bother btw, Theck will do that for us, and all he needed was your constructive and civil input.

Pointing out something is wrong, without offering a solution, does not give you the right to feel superior about it. It's not constructive at all, and hardly civil.

Don't expect us to be thankfull that you peeled away from your desk for 5 mins to tell us what's wrong with us, while Theck keeps doing all the real and hard work.
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