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Armor vs HP Math Help

Warning: Theorycraft inside.

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Re: Armor vs HP Math Help

Postby theckhd » Thu Jan 28, 2010 8:35 am

I should actually thank you guys. In retrospect, I think you're right that there's been some tunnel-visioning going on about how we die. We were all convinced that it was due to zero-heal (or low-heal) bursts. Now I'm not so sure, and that means there's some interesting work to be done.

And despite me being stubborn about it, you kept coming back and forcing the point. I have a little more respect for you for sticking to it. I just wish it could have been done without all the insults. Had your first post been roughly equivalent to the quote from Hamlet in my last post, and not just an aggressive insult, I think I would have come around much sooner.

There's still the issue of magic and bleed damage to consider, and I think that my stance is still right on that. But now we can do some interesting theorycrafting even with that scenario - since heals make armor better for the physical component of a combination magical/bleed/physical burst, we can establish armor's value not just as a function of the burst breakdown, but as a function of the amount of healing received during that burst as well.

Which means if we develop a decent model of incoming heals, we can get some useful results for real-world scenarios. Example: If you're getting only HoT's, how much non-AMP damage does it take to make stamina a better choice? What about if you get one direct heal, of approximately Holy Light magnitude? And so on.
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Re: Armor vs HP Math Help

Postby JamesVZ » Thu Jan 28, 2010 8:57 am

theckhd wrote:Had your first post been roughly equivalent to the quote from Hamlet in my last post, and not just an aggressive insult, I think I would have come around much sooner.


Well, hell. What fun would that have been.
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Re: Armor vs HP Math Help

Postby Njall » Thu Jan 28, 2010 8:57 am

JamesVZ wrote:
Well, hell. What fun would that have been.


Indeed.
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Re: Armor vs HP Math Help

Postby lythac » Thu Jan 28, 2010 8:59 am

I had fun.

More fun will be had with Divinity.
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Re: Armor vs HP Math Help

Postby theckhd » Thu Jan 28, 2010 9:05 am

JamesVZ wrote:Well, hell. What fun would that have been.

:P

So I have a question for you then. A lot of your criticism about my trinket purchase seems to stem from the fact that it's a tiny small upgrade over a 258 Satrina's. Does your opinion change, at least partially, with the knowledge that I don't have one, and was upgrading from Heart of Iron?

I mean, the Cat chest is still a bigger EH upgrade over my 258 Monstrosity chest than the key was over the trinket, but it's a much closer call in that case. And again, for a "magic burst" scenario the key would be considerably better, since so much of "the Cat's" value is granted through armor.

Like I said, looking back I should have waited another week and picked up the Cat second rather than the Key. But I got to 155 badges and got impatient, and figured that since it wouldn't matter much either way until hard modes, I could indulge.

Also, thinking back - that Festergut wipe that was quoted earlier was likely before I bought the Key.
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Re: Armor vs HP Math Help

Postby Roots » Thu Jan 28, 2010 9:08 am

Including hots and tics and such in a tank death scenario sounds like it's going to boil down to a probabilities.

I thought the point of EH was to give a flat solid number for the worst case scenario and then reduce damage from there?
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Re: Armor vs HP Math Help

Postby lythac » Thu Jan 28, 2010 9:11 am

Roots wrote:Including hots and tics and such in a tank death scenario sounds like it's going to boil down to a probabilities.

I thought the point of EH was to give a flat solid number for the worst case scenario and then reduce damage from there?


It is. And thats why EH is being partially discredited by some as they disagree that all most our deaths happen with zero heals and in the space of under a second.

When we include healing and look at probabilities it won't really be EH anymore.
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Re: Armor vs HP Math Help

Postby JamesVZ » Thu Jan 28, 2010 9:19 am

theckhd wrote:Does your opinion change, at least partially, with the knowledge that I don't have one, and was upgrading from Heart of Iron?


Depends on the second trinket I think, but if it were me I probably still would have waited to buy the HP trinket. I don't mind going into an encounter slightly undergeared, which I think I am right now, if it saves me a vast amount of resources down the line in gearing. And the Sindragosa trinket is pretty much hands down better in every way to the Corroded Skeleton Key for those fights where stamina matters.

I'm eventually going to pick the key up, I think especially for something like Sindragosa hardmode if we even make it that far, but it's definitely last on my priority list.
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Re: Armor vs HP Math Help

Postby Sabindeus » Thu Jan 28, 2010 9:30 am

so wait, what happened here
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Re: Armor vs HP Math Help

Postby Promdates » Thu Jan 28, 2010 9:34 am

theckhd wrote:258 Satrina's. Does your opinion change, at least partially, with the knowledge that I don't have one, and was upgrading from Heart of Iron?


You couldn't use the one you have with the Glyph trinket? Are you really going to miss that 162 stamina that much?
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Re: Armor vs HP Math Help

Postby Jasari » Thu Jan 28, 2010 9:51 am

Sabindeus wrote:so wait, what happened here

The same phenomenon that the blues allude to on the official wow forums - people are in better moods toward the end of the week. The first thread criticizing the trinket choice was posted on Monday morning.
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Re: Armor vs HP Math Help

Postby Paxen » Thu Jan 28, 2010 10:01 am

Hamlet wrote:You don't have to do much computation to see it. The EH values of Stam and Armor are found by taking the derivatives of H/(1-M), which equals H(1+A/C) for some constant C. Notably, when you work it out, d(EH)/dA will be linear in H, and d(EH)/dH will be linear in A. So when you double H without changing A, you make Armor about twice as valuable (compared to HP) as it was before. From what I've gathered, at current gear values, the equivalence between Stam and Armor for EH purposes is between 1 and 1.5. So even a scenario much milder than the one logged above (in which HP is nearly doubled by all the healing) will catapult Armor up to the top.


I wonder if it's valuable to put this into an equation and solve for dA/dS, and including healing taken between 100% health and 0%. You could only get precise numbers when looking at a death log, but perhaps it would be possible to say that armor gets better when it takes X seconds to go from full to dead while receiving Y amount of healing?

Taking this formula from Theck's extended EH:

Code: Select all
      12.59*(K+A)      1
dA = -------------*---------*dS                 (22)
           H        (1-X-Y)


Could we replace H with the sum of actual health and healing recieved during the time it takes to go from 100% to 0%? Something like


Code: Select all
dA                   1          1
-- = 12.59*(K+A)*---------*----------
dS                (1-X-Y)    (Ha+Hr)


where Ha is actual health and Hr is healing recieved. Hr could maybe then be replaced by an *estimated* incoming HPS times the duration of the burst.

To me, the conclusion from this thread appears to be that there is a continuum from the extreme cases of 100% to 0% in 0 seconds (instant kill) and in 15 seconds (whittled down), and the value of armor compared to stamina will increase as the time increases.

(math shamelessly copied from Theck to make my post look more intelligent)
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Re: Armor vs HP Math Help

Postby theckhd » Thu Jan 28, 2010 10:39 am

Promdates wrote:You couldn't use the one you have with the Glyph trinket? Are you really going to miss that 162 stamina that much?

No, but that's not the relevant comparison. The Glyph trinket is basically identical to the Heart of Iron for EH. Heart of Iron is slightly superior for magic damage and "zero-heal burst" scenarios, while the Glyph pulls ahead if you get any significant healing. There's no question that the Glyph is slightly better overall for Icecrown content at the moment, but I already had it as an option.

The relevant comparison is to compare the upgrade from HoI to Key to the upgrade from Towering Monstrosity to the Cat. I chose the 66 stamina upgrade that I could afford now over the 25-stam, 1.2k armor upgrade I could afford a week later. Note also that you lose a good chunk of avoidance to get that armor, which while not as good for reaching EH thresholds, is a reasonable choice to reduce damage taken when you're above those thresholds. Or if you think you're above those thresholds, which we all did before this thread (and realistically probably are if our healers are on the ball).

I agree that it wasn't the optimal choice for stretching my burst survivability right now, but I had already figured that it didn't matter what order I bought these items in since I'll have them all by the time hard modes are released anyhow. So I made an impulse purchase to get rid of the Ulduar trinket.

Also keep in mind that I've been keeping EoF's banked so I can pick up two tier items as Conq tokens allow. I'd really like the 2-piece damage boost, as one of my guild's perennial problems has been low DPS. If I decided I needed the Cat chest and Cloak (or gloves) more than the tier items, I could have grabbed them immediately. Right now I'd have to choose one or the other, at least until this weekend.

I may end up doing that anyway, and waiting for the tier helm. But our luck with Conq tokens has been so abysmal that I felt I needed to take them when and where I can get them, and I don't like taking one without having the badges to pick up the item immediately.
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Re: Armor vs HP Math Help

Postby Kihra » Thu Jan 28, 2010 10:44 am

It seems like what we're really talking about is HoTs. When my guild loses tanks, it's inevitably the result of a tank not receiving any direct heals during a certain period of time. If that period of time is large, we chalk it up to healer fail (e.g., a paladin let beacon fall off). If that period of time is small, then it's conceivably a burst scenario and the tank's problem.

Tanks do typically receive some healing from HoTs in our death scenarios, so it does seem reasonable to try to account for this healing in the model.

I'm not convinced that HoTs alone make a significant enough difference to really affect how we should gear. Right now according to EH, a trinket like Glyph of Indomitability lags significantly behind Corroded Skeleton Key. It would take quite a a bit of healing from HoTs to make up that difference.

I'd be curious to see the math that works out how much healing it would take though.
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Re: Armor vs HP Math Help

Postby theckhd » Thu Jan 28, 2010 10:46 am

JamesVZ wrote:Depends on the second trinket I think, but if it were me I probably still would have waited to buy the HP trinket. I don't mind going into an encounter slightly undergeared, which I think I am right now, if it saves me a vast amount of resources down the line in gearing. And the Sindragosa trinket is pretty much hands down better in every way to the Corroded Skeleton Key for those fights where stamina matters.

I'm eventually going to pick the key up, I think especially for something like Sindragosa hardmode if we even make it that far, but it's definitely last on my priority list.

I'd agree with that. The Sindragosa trinket is hands-down better, no contest. I'll also want both for hard mode, but that won't be for a while.
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