Armor vs HP Math Help

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Re: Armor vs HP Math Help

Postby Awyndel » Sat Jan 30, 2010 11:57 am

Ow and btw, nobody ever said armor wasn't godly. What NEH is supposed to do is find a value to compare it to stamina, based on the specific bursts in specific fights. Some guy even wrote an addon wich records these bursts for us and calculates the values.

And all you had to say in that topic was that we needed to include the healing received in the burst window. And we could have updated the model.

You can't hold us responsible for the interpretation of the masses wich frustrates you so much. Especially if you yourself haven't read the topic carefully enough to see it is trying to apply itself to the situation at hand. The fact that it does so incompletely does not change the intend, nor the importance of that intend.

Not that it really makes a big difference in gearing. Only trinkets leave us a real choice. But that is what the discussion should be about by now.
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Re: Armor vs HP Math Help

Postby Awyndel » Sat Jan 30, 2010 12:25 pm

theckhd wrote:
Kihra wrote:I'd be curious to see the math that works out how much healing it would take though.

That should be pretty easy.

EH = H(1+A/K)
d(EH) = 0 = dH(1+A/K) + H*dA/K


Setting those two terms equal (to indicate that they give exactly the same EH boost), and solving for dH gives

dH = H/(A+K)*dA

Just as we found in the past. Using 50k health and 30k armor as approximate values, that works out to 1.07 armor being equivalent to one health.

To convert that to stamina, you turn dH into 12.59*dS (for paladins, the value is different for warriors), for

dS = H/(12.59*(A+K))*dA

which using the same values gives us 11.7 armor to match 1 stamina for EH. It gets lower for higher H, and higher for higher A, as expected.

To factor healing in, we take the same approach as Hamlet. Pretend each point of non-overheal healing h received was actually a point of health. You'd have:
dH = (H+h)/(A+K)*dA

Now let's compare Glyph to Satrina's (non-heroic). 192 Stam is 2417 health. Glyph gives 1792 armor, which when multiplied by H/(A+K) is only 1921 health. The amount of healing needed is then:
h = (A+K)/dA*(dH-H*dA/(A+K)) = (A+K)*496/1792 = 12.9k

So if you received 12.9k in heals during the burst, they're equivalent. Any more and you're better off with the armor trinket, any less and the stamina trinket has an edge.

<edit> If you compare the Key to the Glyph, h works out to be 24.7k healing.


Theck, if that healing tops you off, the whole thing resets and the extra value of the armor is reset to 0 right?

I think this is a fairly interesting theory. We already knew increasing your effective health beyond a certain amount of melee hits + incidental damage is always usefull because of the incidental healing received before being topped off again. We just never looked into how that would affect armor differently then stamina. I do hope you realise we have already been over this topic, it just needs an update :D .

I can't help but wonder though, if the value of armor is increased by healing because it can be applied to the amount of health just received once again, isn't the value of stamina increased by it as well? Not sure in what ways that would be, but there is ofc AD range, and there is the fact that it's a buffer that can be re-used every time you're healed. Although when we're not being topped off max health might not matter in that way. Not sure if I am making much sense here but I needed to check my doubts.

And let's not forget one very important thing here. This health received due to healing, only actually increases the value of armor for the physical damage taken untill death.
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Re: Armor vs HP Math Help

Postby Kihra » Sat Jan 30, 2010 1:34 pm

Hamlet wrote: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)


It does seem like you need to include damage reduction from talents (and optionally the 10% DR from priest/shaman if it was in effect) as well when looking at the relationship this way. Otherwise you risk overvaluing armor I think?
Last edited by Kihra on Sat Jan 30, 2010 2:09 pm, edited 1 time in total.
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Re: Armor vs HP Math Help

Postby rocket » Sat Jan 30, 2010 2:05 pm

Similar to a few others, i missed most of the explosion of this enjoyable thread.

Thank you for the 2 hours of entertainment value.

What i think i have learned:
James, Hamlet, et. al. are warrior nerds as many of us here are paladin nerds (myself included)
We all use empirical data from our own raids to maximize our guilds ability to progress. We apply corrective action to root causes of deaths/wipes.
We all like to play the game whoever yells the loudest wins, then realizing that a truce is also possible.
i will still carry too many pieces of gear in all 22-slot bags sans backpack to have gear which can accomodate the different encounters - of which i have made specific gearsets for (e.g. anub add tanking)

PS I am surprised no one started an argument for "Gearscore" gearing. it sure seems relevant in the LFM spam! (lol)
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Re: Armor vs HP Math Help

Postby Hamlet » Sat Jan 30, 2010 2:39 pm

Kihra wrote:
Hamlet wrote: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)


It does seem like you need to include damage reduction from talents (and optionally the 10% DR from priest/shaman if it was in effect) as well when looking at the relationship this way. Otherwise you risk overvaluing armor I think?


It won't change in the presence of any other %-based mitigation buffs that multiply with Armor mitigation (which is pretty much all of them). Just go through my above post, but instead using DCR/(A+C) for mitigable damage taken (just threw in an R to represent whatever other buffs are present). It will cancel out when you substitute Q back in.

The only other important thing, which some people have mentioned, is blocks. Blocks can basically be thought of as heals--they're worth a constant amount of HP regardless of Armor.


rocket wrote:James, Hamlet, et. al. are warrior nerds as many of us here are paladin nerds (myself included)


I actually play a Druid: http://www.wowarmory.com/character-shee ... &cn=Hamlet . I just came across this discussion because people linked it and it was kind of interesting, and not something I'd thought about in detail before. I do a ton of theorycraft work for Resto and Balance Druids.
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Re: Armor vs HP Math Help

Postby rocket » Sat Jan 30, 2010 3:49 pm

even better bud.

i think that we all enjoy hardcore analysis.
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Re: Armor vs HP Math Help

Postby Kihra » Sat Jan 30, 2010 4:06 pm

Hamlet wrote:
Kihra wrote:
Hamlet wrote: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)


It does seem like you need to include damage reduction from talents (and optionally the 10% DR from priest/shaman if it was in effect) as well when looking at the relationship this way. Otherwise you risk overvaluing armor I think?


It won't change in the presence of any other %-based mitigation buffs that multiply with Armor mitigation (which is pretty much all of them). Just go through my above post, but instead using DCR/(A+C) for mitigable damage taken (just threw in an R to represent whatever other buffs are present). It will cancel out when you substitute Q back in.


Right, the relationship won't change.

Sorry, I was not very clear in my previous post. I was just cautioning against people trying to reverse engineer D in your equations from Q while forgetting about damage reduction talents. When people do that they tend to overvalue armor. It's something I see occasionally on this forum when people are trying to compute how much they would reduce their damage by when they add in more armor, typically when trying to compare with avoidance.

The health <-> armor equivalence and stamina <-> armor equivalence both remain unchanged by additional DR (including AD).
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Re: Armor vs HP Math Help

Postby knaughty » Sat Jan 30, 2010 4:19 pm

What the hell...

I read first page and last 3, someone want to recap the 18 pages in the middle?

Or does "Wrong on the Internet" cover it?
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Re: Armor vs HP Math Help

Postby Gowron » Sat Jan 30, 2010 5:18 pm

TL;Dr version till now:

Remark: Armor is better than Stamina, and for that matter Effective Health

-this only apllies to trinkets, because most higher armor-gear also has a better EH-ratio.


So the discussion is really which is better, some armor trinket or some stam-trinket (latter giving more EH)

A lot of discussion considering including healing in the EH-maths, which probably would give armor a little more edge.

Conclusion (IMHO): currently it doesn't really matter, maybe ICC-hard modes will. We need to wait till ICC-hard to see which of the trinkets is better, and then, I suppose, it will be a very small difference, and probably not a reason for a possible wipe.

And just as always: every fight is different, so is gearing for different bosses.
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Re: Armor vs HP Math Help

Postby Destruktive » Sat Jan 30, 2010 11:23 pm

I haven't had time to read the entire thread, but the pages I did read had no mention of Ardent Defender.
What I mean is that the stam trinkets also increase the pool of health a paladin has when he is below 35% and taking 20% less damage.

Taking myself as an example, self buffed (sanc & dev aura) with the Corroded Skeleton key and heroic Juggernauts Vitality my stats are: 52699 hp, 31332 armor (67.29% damage reduction)
Ardent Defender is active at 18445 hp.

When I equip Unidentifiable Organ and Glyph of Indomitability my stats are: 47119 hp, 35014 armor (69.68 damage reduction)
Ardent defender is active at 16492 hp.

So that's almost a 2000hp difference from when AD is active. Not only that but extra hp also results in a bigger heal from the AD proc when you 'die'. I think the 20% reduced damage should be included in the calculations because if you never dip below 35% hp or AD never procs, then it's all irrelevant really. In that case ap trinkets would be more beneficial to the raid in extra dps.
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Re: Armor vs HP Math Help

Postby Kihra » Sat Jan 30, 2010 11:54 pm

Destruktive wrote:I haven't had time to read the entire thread, but the pages I did read had no mention of Ardent Defender.
What I mean is that the stam trinkets also increase the pool of health a paladin has when he is below 35% and taking 20% less damage.


As I said earlier in the thread, AD isn't relevant when comparing armor and stamina. It's just damage reduction, which does not affect the relationship between armor and health/stamina. Either you have a bigger health pool but take bigger hits, or you stack armor and have a smaller health pool but take smaller hits.
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Re: Armor vs HP Math Help

Postby Fridmarr » Sun Jan 31, 2010 12:40 am

Kihra wrote:
Destruktive wrote:I haven't had time to read the entire thread, but the pages I did read had no mention of Ardent Defender.
What I mean is that the stam trinkets also increase the pool of health a paladin has when he is below 35% and taking 20% less damage.


As I said earlier in the thread, AD isn't relevant when comparing armor and stamina. It's just damage reduction, which does not affect the relationship between armor and health/stamina. Either you have a bigger health pool but take bigger hits, or you stack armor and have a smaller health pool but take smaller hits.

It does with their model though, which is what I was getting at earlier. Their model is that armor makes healing better, they aren't taking a 100-0 straight burn down of health because they are considering heals. You can cross the AD threshold multiple times with their model. So when AD is triggered can have an effect. I think theck did some quick math on it a few posts up though.
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Re: Armor vs HP Math Help

Postby Kihra » Sun Jan 31, 2010 1:27 am

Fridmarr wrote:
Kihra wrote:
Destruktive wrote:I haven't had time to read the entire thread, but the pages I did read had no mention of Ardent Defender.
What I mean is that the stam trinkets also increase the pool of health a paladin has when he is below 35% and taking 20% less damage.


As I said earlier in the thread, AD isn't relevant when comparing armor and stamina. It's just damage reduction, which does not affect the relationship between armor and health/stamina. Either you have a bigger health pool but take bigger hits, or you stack armor and have a smaller health pool but take smaller hits.

It does with their model though, which is what I was getting at earlier. Their model is that armor makes healing better, they aren't taking a 100-0 straight burn down of health because they are considering heals. You can cross the AD threshold multiple times with their model. So when AD is triggered can have an effect. I think theck did some quick math on it a few posts up though.


Even in the "healing makes armor better" model I don't understand why Ardent Defender would be relevant. It's just damage reduction, is it not? Does the threshold trigger really matter in this model?
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Re: Armor vs HP Math Help

Postby Aedh » Sun Jan 31, 2010 1:57 am

I think the logic is the larger your health pool is the more health you have when you drop in AD damage reduction, and therefore the longer you can stay in it. The longer you can stay in the AD thresh hold, the more damage AD will prevent vs less stamina and more armor.

That's what I got out it. I am probably wrong.
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Re: Armor vs HP Math Help

Postby Darkside » Sun Jan 31, 2010 8:54 am

Aedh wrote:I think the logic is the larger your health pool is the more health you have when you drop in AD damage reduction, and therefore the longer you can stay in it. The longer you can stay in the AD thresh hold, the more damage AD will prevent vs less stamina and more armor.

That's what I got out it. I am probably wrong.

theckhd wrote:This is an interesting point, and something that hadn't crossed my mind. Though I'm not sure the numbers work out right.

Let's say you have H=40k hit points with an empty trinket slot, 60% mitigation from armor (roughly 25k armor), and take an D=80k hit after Armor mitigation (pre-mitigation 200k).

Boosting armor mitigation by 2% reduces damage to 76k, a reduction of 4k. It would take about 3k armor to accomplish that.

Extending the range of your health by 2850 (in the ballpark of a stam trinket) extends the range of AD by 1k, which means that you reduce the damage taken by only 300. In a "whittle-down" situation with healing, you may cross this region a few times, but not enough to catch up with the armor trinket.

Admittedly, I'm not comparing apples to apples here, since there isn't a 3k armor trinket available, but scale it down to 2k armor (~1.5% mitigation) and you're still reducing damage by 3k with the armor trinket.
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