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Armor vs HP Math Help

Warning: Theorycraft inside.

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Re: Armor vs HP Math Help

Postby Mex » Thu Jan 28, 2010 12:08 am

Lemme have a crack at this.

Here's the thing. We're trying to eliminate / prevent tank deaths. The first step we take is to examine what causes them. There are 25 (or in some cases, 10) possible answers to this question, of which we only have control over one. So let's focus on that one. Let's not muddy things by introducing logs with dead healers, or flame patches dragged through the raid, or whatever other external factors may have contributed to a wipe. If you're regularly going 2.4 seconds without a heal, you're going to die eventually. This isn't news to anyone.

How do deaths happen? I don't think it's a stretch to claim that most tank deaths are the result of anamalously large bursts of damage in relatively small time periods. Whether these periods are 2, 3, or 4 seconds isn't really relevant. We're talking about spikes here. I won't go as far as to dismiss the whittle effect, because there are times where it does occur, it just does very quickly, with lots of small hits instead of big ones. The important thing here though is the time period.

Let's start with instantaneous damage. Sparked Malygos breath. Empowered Sartharion breath. High-HP-immortal hits coinciding within ~0.1 seconds. These are the sorts of situations I'm referring to when I meant instantaneous damage. The previous examples are some (not all) of the few capable of killing tanks that we've seen this expansion. In the context of a normal boss, 'instantaneous damage' is going to be a single melee swing, or a melee swing + special ability. This is where EH matters, and where stamina stacking is critical. You get enough to survive the max instant damage.

However, as time increases, EH begins to matter less. Or, actually no that's not true. EH matters the same, it's just that we start looking at it differently. Or rather, calculating it differently. It's no longer a static number. Allow me to elaborate slightly. As time increases, so do heals. Now I know, I know, you can't model heals, you can't rely on heals, you can't generate exact numbers for heals. That's fine, bear with me. What you can do is acknowledge that heals will land. For <1 second bursts, this isn't always the case. However, there aren't many bosses that can kill you in 1 second but not 0.1 seconds. Double parry haste is probably the biggest cause of these events. Once you start going past 1 second intervals though, the frequency of heals starts to climb. This is especially true in situations where tank death is a very real possibility.

For these encounters, I don't think that it's unreasonable to assume that tanks will have 2 tank healers spamming heals on them. I can't speak for disc priests, but for Holy Paladins, you're looking at about ~10-15k healing done every 0.75 seconds on average, with a 'worst case' synchronisation leaving a gap of ~1.3 seconds between heals. The logs Theck linked are not 'worst case', they are 'blame* the healer case'.

Okay, so how does this effect armour, stam, and the time window of the burst? Well (and again, we're acknowledging here, not quantifying), as time increases, so do heals. Heals that take place within this burst window, or spike period, are functionally identical to tank health. And armour scales with health, stamina doesn't. That's where this armour fetishism comes from, because when you're taking burst damage (apart from the instantaneous outliers), you're generally dealing with an effective health pool of 70-80k (more for the druids). This just keeps climbing as the window widens. In situations where healers can just stand and spam, then you're going to be able to factor in a significant amount more of effective health (and I don't mean this in the conventional sense). In a 2.4 second window, you fairly realiably count on 30-45k more health from paladin heals alone.

Now, this is (and this has been noted before), really quite impossible to accurately (or rather, reliably) model or quantify, so let's not bother. Instead let's simply acknowledge that as the burst window widens, assuming your healers are not dead (a note on 'moving out of fire' -- holy paladins should be holy shocking every time they do this, with their fingers hovering over LoH. In especially bursty situations, they should be bubbling and ignoring the fire), that armour value will increase.

So yes, H Northrend Beasts, H Anub, Sarth 3D, etc (at the appropriate gear levels) were fights where stamina really mattered. However, as we start moving into slightly wider burst timeframes, armour's value begins to increase. While we can't generate exact numbers to represent this, we can make sure that we're aware of it, and when and where to apply it.

fake edit -- above log is a pretty good example of this.
Last edited by Mex on Thu Jan 28, 2010 12:11 am, edited 1 time in total.
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Re: Armor vs HP Math Help

Postby Aergis » Thu Jan 28, 2010 12:10 am

and short of programming an entire simulation with varying boss damage


That's a great idea. How do you want it to work?

Throw me some numbers. What is the raw damage? Do you want to incorporate healers? How many? What type? What should they heal for? Let's get enough basic hps going while tanking enough damage and we can parse 1000's of logs quickly. I can program that.
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Re: Armor vs HP Math Help

Postby Rhiannon » Thu Jan 28, 2010 12:32 am

Hamlet wrote:
Eminai wrote:[20:10:39.356] Ellienet Nourish Theck +1030 (O: 5188)
[20:10:39.777] Festergut hits Theck 39430 (A: 825)
[20:10:39.777] Ellienet Regrowth Theck +0 (O: 1426)
[20:10:40.011] Celwe Wild Growth Theck +972
[20:10:40.216] Healing Stream Totem IX Healing Stream Totem Theck +251
[20:10:40.246] Murse Flash Heal Theck +6110
[20:10:40.573] Festergut hits Theck 23487 (O: 9350, B: 2003)
[20:10:40.651] Rawberry Holy Light Theck +13328
[20:10:40.747] Ellienet Rejuvenation Theck +2748
[20:10:40.747] Ellienet Lifebloom Theck +575
[20:10:41.717] Celwe Wild Growth Theck +934
[20:10:41.833] Murse Renew Theck +2311
[20:10:42.523] Festergut hits Theck 14584 (O: 23510, B: 2003)
[20:10:42.539] Guilliman Divine Storm Theck +854
[20:10:42.558] Ellienet Glyph of Rejuvenation Theck +1374
[20:10:42.915] Theck dies


Cropped that so it's a bit less painful to read. I don't want to get into a huge log-reading operation myself, but this is as good as example as any. Looks like around 30,000 healing taken over the course of this typical "3-second death." (And are you sure you got everything? One Lifebloom tick in 3s is odd, at least). And it would have been upwards of 50,000 to actually survive it. Anyway, it's simply one nice example of a situation where the value of armor is around twice that of the plain EH computation.


Lag's definitely screwing with that section of the log a bit, as even with 90% increased attack speed from a 3 stack of inhaled blight Festergut swings at 1.26s interval with an attack speed debuff up (which it is), and the interval between swings is reported as 0.8s, 1.95s, and the parser is reporting two overkills. Ardent Defender is on cooldown from earlier, so the cheat death effect can't be interfering in some way, which means the log order must be a bit jumbled, as in its current order it doesn't make a whole lot of sense. But indeed, this looks a nice crossover example between the "whittle down" scenario and the EH/healing vacuum model. I'll have a crack at it if someone else doesn't beat me to it tomorrow, but I'd be curious if someone would be able to work out what the damage profile would have looked like if Theck had 2.05k less hp, but 1.8k more armor (heart of iron vs glyph). Ballparking I'd guess at this point in time (from a month ago) Theck was around 56k raid buffed hp, 32k raid buffed armor (no indestructible up on this parse). Specifically - the moment before "[20:10:42.523] Festergut hits Theck 14584 (O: 23510, B: 2003)" occurs, how much hp would he have in each setup, and how big would the next hit need to be to kill him in each setup?
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Re: Armor vs HP Math Help

Postby Fridmarr » Thu Jan 28, 2010 1:18 am

Yeah he took 72k damage and received 7k healing for his first death, which was 100% to 0 in .8 seconds. I had assumed that was AD, but I don't see the absorb. Can you link this parse?
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Re: Armor vs HP Math Help

Postby Hamlet » Thu Jan 28, 2010 2:06 am

Rhiannon wrote:Lag's definitely screwing with that section of the log a bit, as even with 90% increased attack speed from a 3 stack of inhaled blight Festergut swings at 1.26s interval with an attack speed debuff up (which it is), and the interval between swings is reported as 0.8s, 1.95s, and the parser is reporting two overkills. Ardent Defender is on cooldown from earlier, so the cheat death effect can't be interfering in some way, which means the log order must be a bit jumbled, as in its current order it doesn't make a whole lot of sense. But indeed, this looks a nice crossover example between the "whittle down" scenario and the EH/healing vacuum model. I'll have a crack at it if someone else doesn't beat me to it tomorrow, but I'd be curious if someone would be able to work out what the damage profile would have looked like if Theck had 2.05k less hp, but 1.8k more armor (heart of iron vs glyph). Ballparking I'd guess at this point in time (from a month ago) Theck was around 56k raid buffed hp, 32k raid buffed armor (no indestructible up on this parse). Specifically - the moment before "[20:10:42.523] Festergut hits Theck 14584 (O: 23510, B: 2003)" occurs, how much hp would he have in each setup, and how big would the next hit need to be to kill him in each setup?


Someone can try to do that, but it's probably not worth putting quite so much effort into one random example. Besides, EH (or my mental modification of EH concepts, rather) already gives you the answer without having to work it out line-by-line. Like I said above, you're really working with around HP + 50k in a scenario where he survives that. At those values, the derivatives will work out such that Armor is far more marginally effective than Stam in stopping that death.

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.

You guys always talk about how you're so focused on the "worst case," as if some single strictly worst case in fact existed. There's no such thing. There's of course the 0-second spike with no shields or cooldowns--that scenario might seem intuitively "worst" in a certain sense. But what about a scenario like the one logged above--3 seconds, far more damage, significant healing present? It's possible to have a setup where you survive the first but not the second, and it's possible to have a setup where you survive the second but not the first. The former favors HP, the latter favors Armor. Neither case is strictly "worse" than the other, and there's no logical reason to simply accept as an axiom that that first scenario is worthy of your undivided attention. Especially when experience dictates that the more complex latter scenario may be far more common in practice.
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Re: Armor vs HP Math Help

Postby Fridmarr » Thu Jan 28, 2010 2:49 am

Worst case is generally the amount of damage the boss can do in X seconds. X of course is sometimes subjective depending on the boss, but a line needs to be drawn at some point. You aren't surviving 3+ hits unhealed against many bosses for instance. Special attacks are included when they make sense. The worst case that is geared for is meant to be a pragmatic representation of what the specific boss you are working on can possibly do, there is no single worst case, it's boss specific.

If a boss hits for 20k in a simple example and you have 62k health, then it's likely of little value to keep increasing stamina. You can take 3 hits unhealed, you won't be able to reach 4 hits (with any gearing strategy), and that should give the healers reasonable time to recover. Anything less than that should be heal-able given the HPS capabilities of the game, and gearing wise you want to look at reducing damage. That's why some of this reaction took a few of us aback, because not everyone is all about all EH all of the time, and certainly not just Stamina. The stamina trinket merely provides more EH, and works on any damage source adding flexibility.

I presume you are correct, and in this you vastly differ from James and the others, that neither model is strictly worse. My experience seems different from what you've expressed though, I generally die when healers are otherwise occupied and my HPS received drops dramatically. However, that is just my anecdotal observation, and I plan to examine some logs when I get a chance.
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Re: Armor vs HP Math Help

Postby lythac » Thu Jan 28, 2010 2:57 am

Fridmarr wrote:Yeah he took 72k damage and received 7k healing for his first death, which was 100% to 0 in .8 seconds. I had assumed that was AD, but I don't see the absorb. Can you link this parse?


http://www.worldoflogs.com/reports/ghw5 ... 493&e=8642

2 DPS dead
1 Healer dead
AD goes off
Theck gets to nine stacks
Offtank takes over
Offtank dies
Theck bubble removes stacks
Healing drops right off
Theck dies

Raid DPS needed - 135,000 DPS
Their DPS - 95,000 - 115,000

2nd ever attempt on boss



It looks to me they were so far behind on enrage, with 3 dead including the offtank that healers were told to stop healing and wipe it. The only ones that would know were present in the raid.
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Re: Armor vs HP Math Help

Postby Koatanga » Thu Jan 28, 2010 3:27 am

Lythac wrote:2 DPS dead
1 Healer dead
AD goes off
Theck gets to nine stacks
Offtank takes over
Offtank dies
Theck bubble removes stacks
Healing drops right off
Theck dies


So in other words it's not quite so clearly a situation where the armour trinket instead of the stam trinket would have saved the day.
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Re: Armor vs HP Math Help

Postby Eredor » Thu Jan 28, 2010 5:04 am

The thread is interesting if not always civilized as it reminds us that:

- a tank is not alone, s/he is in an environment which will affect his gearing choices (are healers having a hard time keeping him alive? Are dps good enough to keep the fight timely?) Conversely, it may be possible that the tank affects the way healers gear / specialize, etc.

- armor vs stamina may be a valid debate. At the very least I can image that one strategy is superior to the other given a raid team, e.g. that an armor oriented tank may be better for a certain kind of guild and that a stamina oriented tank may be a better fit for some other kind of guild. In today's gear, what kind of trade-offs are realistic? Can these trade-offs make a difference in a realistic fight? Can these trade-offs be made alone, or will there always be a significant additional side-effect(s), such as significantly more/less avoidance or these more/less dps (assuming that threat is a non-issue nowadays).

- Also do we have statistical evidence that stamina-oriented in fact do require more healing than armor-oriented tanks, or does it simply lower the percentage of overhealing done?
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Re: Armor vs HP Math Help

Postby bashef » Thu Jan 28, 2010 6:11 am

Firstly, somewhat off-topic, it genuinely does seem that there's a discussion to be had here, and that there's great value in pursuing it; and conversely none in perpetuating the tone with which the discussion was started, in which case I'd implore posters here to refrain from snide, flippant remarks since they contribute nothing to the discussion. While we can't enforce this upon new registrants (or indeed anyone), established members of the community should take this opportunity to prove why it's such a special one by refusing to stoop to that level. If you don't have anything relevant to the discussion to post, don't post at all. I'd also like to add that my personal preference would be to not see these new registrants banned from posting (provided it's not causing undue stress to Theck, against whom most of the vitriol seems to be directed for no real discernable reason) since I don't want to give them any justification to think they're martyrs to their cause, or that we attempt to censor contrary viewpoints on the site. Which in no way means I support or condone the tone or presentation of the arguments, or the descent into name-calling and mud-slinging. But I think everyone reading those posts recognises the tone is childish, inappropriate and offensive, and thus there's no real harm in allowing them to continue to make spectacles of themselves.

Onto the substance of the post. Reading over the last couple of pages has confirmed that others have come to similar conclusions or viewpoints that I did, although I don't think they've made them explicit. I'll try to present my understanding as coherently as possible.

The point is that in a window of any size, one can consider effective healing done (i.e. not overheal) as well as the magnitude of absorbs to be part of your health. The discussion of whittling down is something of a red herring because you can receive healing in a window of any size, although the probability of receiving any healing of note diminishes as the window size does. For example, if your burst window is one second, you have 60k health and take 20k healing, you can consider that you have 80k health for the purposes of determining something like EH (that is, how much raw damage you can absorb in that burst window). Absorbs complicate this further, but not impossibly, by further reducing that damage by a fixed amount once armour reductions have been applied to the raw damage. I for one had never thought of this, and I am grateful to the more measured posters in this thread for this insight. The reason armour is more valuable in this case is obvious; armour is more effective the more health you have. If you take enough healing to fill your health bar two or three times over in that burst window, one way of looking at this is that you should rate armour's effectiveness as though you had three or four times the amount of health you do.

This is why the argument of the whittle-down is not relevant, nor is a discussion of reducing the overall damage received during the course of the fight. It's also not about healers going OOM because a stamina stacking tank requires more healing - as has been noted many times over, healing patterns will not change because of a swing in 2k armour and 3k health. They'd have to be an order of magnitude bigger. In fact the point (although I wish someone had spelled it out earlier, instead of just insulting people) is that through healing received, armour is having an effect as though you had (HP + effective healing + absorbs) health in your burst window.

Unfortunately, the point of these models is to make gearing decisions. Incorporating healing into a model is considerably more involved than ignoring it, and absorbs add a further layer of complexity. In order to answer the question "how much stam is one point of armour worth?" you need to be able to model the amount of healing you're likely to receive in that critical window. The first thing that springs to my mind is to use combat logs to determine a probability distribution for this, and then integrate out the actual amount of healing you receive to make gearing decisions. In reality, since this is highly unlikely to be modelled by a conventional distribution you'd probably be way better just deriving a histogram over suitably coarse/fine healing ranges and using empirical frequencies as probabilities. As usual, you sacrifice ease of computation and simplicity (standard EH) for fight-specific and more complex models, and you have a lot of work deriving these distributions for healing received in tank-killing burst events... but at least it might be (more) accurate. Once you've done this, you can also adjust for the proportions of damage types encountered in this window, as Theck did in extending standard EH to burst events with multiple damage types.

On a side note, does anyone know if it's possible to download combat logs for specific fighs en masse from one of the parsing services? You'd really need to do this to be able to do the automatic processing necessary to get remotely accurate estimates of probabilities.
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Re: Armor vs HP Math Help

Postby mazater » Thu Jan 28, 2010 6:54 am

JamesVZ wrote:There is a reason that every veteran warrior I know is stacking armor, and it's not because they failed to take into account your 5 year old kiddie equation.

Maybe that was a little harsh. But you need to realize that your number is just a number.

It doesn't really matter what the warriors are stacking, since we're paladins and paladins have a bit different things than warriors do. Though in general the difference isn't that huge.
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Re: Armor vs HP Math Help

Postby bashef » Thu Jan 28, 2010 7:34 am

The class he plays is pretty much irrelevant, barring the slightly different stamina scaling. We're talking universal tank mechanics; sure, the equivalency between stamina and armour will be slightly different across classes due to scaling, but the fundamental issue is how to assess this.
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Re: Armor vs HP Math Help

Postby Ziggi » Thu Jan 28, 2010 7:46 am

I think the raid comp point brings a very important subject to the table.

I'm currently tanking with a DK who was previously stacking stam but has switch to armor. I'm not saying it's a the right call for paladins but supposedly it's incredibly good for DK's since they can approach armor cap. Me, on the other hand, I've been a firm believer in the balance methodology, which is probably vastly apparent by my gemming choices.

Anyway, to my point, you'll notice i said a DK i tank with. Not "he's my OT" or "i OT for" because we swap, quite frequently. It depends on which of us the fight is more suited for. Jarraxus fire balls, i tank them because i can clean them off sometimes before they even tick. Obviously i OT anub adds because well, lolihasshield. The only big ballin' tank damage fight in the zone thus far is Festergut but if you're not popping CD's on the 3 stack, you're doing it wrong. I haven't seen anything as of yet in ICC that's going to come close to time stamping either of us, hopefully heroics will show otherwise.

disclosure: i realize there is some hand waving and lack of numbers to back it up but the entire point of the post was..... why not have both. 25 people in the raid, 5-6 healers, a bunch of pewpew, and 2-3 tanks, a diverse well balanced raid will deliver the best perfromance.

ps. i have a warrior and tanking on it fucking sucks.... give me that fury action!
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Re: Armor vs HP Math Help

Postby kanst » Thu Jan 28, 2010 8:05 am

Me and our other main tank have been discussing this topic for a while now. As a way of testing it we both tanked Blood queen, him last week, me this week. My warrior, Ewrakilr, sits at 32940 armor and 43,906 HP unbuffed. I sit at 28700 armor, and 46,200 HP unbuffed, we have similar avoidance. My kill lasted 4 seconds longer because it was sloppy. Here are the logs:

Gatgat as MT:
http://worldoflogs.com/reports/e6thulnu ... 924&e=6243

Ewrakilr as MT:
http://worldoflogs.com/reports/6lgtfax4 ... 744&e=4059

I took 1.11 Million melee dmg, 4635 DTPS overall, he took 1 million melee dmg 4596 dtps overall. The healing done by our main tank healer (Nikoro) was very similar in both cases, the primary difference is he overhealed less healing me. What this says to me is that an armor tank takes less damage, however healers aren't going to really change their healing style since the difference is minor. So why my damage may have been a little spikier both people were able to be healed without any issue. Now I know this isnt perfect since hes a warrior and I am a pally and the raid comps werent the same, but I figured it was a good example of two different gearsets getting the job done.
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Re: Armor vs HP Math Help

Postby theckhd » Thu Jan 28, 2010 8:14 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.

This is exactly correct. I have no argument with that. It's a bit of a stretch from normal EH theory (in that it's treating healing as "effective hit points"), but it certainly seems to apply well enough to the situation where you're receiving regular healing and die to accumulated "whittle-down" damage.

Eminai wrote:I feel dirty.

Don't. You've found a valid example that supports your argument. That's what this discussion needs to make it useful.

Lythac is right that it's not a great example. There were a number of other circumstances involved (no armor pot, off-tank suddenly died, 2nd attempt ever, and so forth). I don't remember whether I called a wipe before I died on that attempt, it was a few weeks ago. And realistically, swapping a stamina trinket for an armor trinket there wouldn't have saved me.

But regardless, it's an example where armor overshadows stamina for EH. Note that this is still a case of burst in 3 seconds where the tank did not have enough EH. It just happens to be one in which I received enough healing that the armor trinket would have been a better choice for survival, based on the type of analysis I quoted from Hamlet.

Though again, it's still a window of 3-5 seconds that we care about. Your original example of 15 seconds is just too long - by that point reactive healing will kick in and even the slower players will be popping cooldowns and focusing effort on topping the tank off.

So you and I both have valid arguments that hinge on different models of tank death, and we have evidence that both types exist. The question it comes down to is "what's the more common scenario?"

The answer to that is going to be hard to come up with though, for a number of reasons:

  1. It will likely vary from guild to guild, depending on the healer profile, make-up, and quite frankly the quality of healers.
  2. Even more tricky is the fact that it will vary based on tank-gearing. A stamina-heavy tank will be less likely to die to "zero-heal" burst, so you'll find a greater proportion of events where they die to "whittle-down" scenarios than "zero-heal" scenarios. The opposite would be true of an armor-stacking tank.
  3. It will vary with instance as well. A three-hit string from the boss is much more likely in Icecrown than it is in ToC due to CotT, for example.
  4. It's very hard to filter out irrelevant examples if you're working in bulk. Things like Lythac pointed out: Are there healers dead? Off-tanks? Did the healer disconnect? Did the tank disconnect? Were there enough people dead that a wipe was called? Some of this can be answered by logs (though in some cases with a lot of difficulty), and some of it can't

At the very least, I will give you this though. I haven't given you and James enough credit so far in this thread. I think I put too much stock in your "15-second" scenario, and maybe I knee-jerked the other direction when I shouldn't have. You've successfully reinforced your point that healing strengthens armor's value relative to stamina as a survival stat. And now you've presented evidence that it may be more common than many of us thought.

If it makes you feel vindicated at all, this discussion has made me reconsider armor more carefully. Enough that if I were able to turn back the clock, I might've gone back and picked up the chest instead of the trinket. Actually no, not might've. Would've. There's just not enough magical burst in ICC at the moment to make the portability of the trinket relevant.

But again, I'd like to emphasize that none of this makes either of us bad tanks. James and I are going to end up in identical heroic-mode progression gear load-outs, barring one trinket slot. I've had my focus on gearing for a wider variety of situations, since stamina covers zero-heal bursts as well as magical burst. He's had his focus on gearing for the "whittle-down" scenario that's mostly melee damage, because he feels that's the more common scenario in Icecrown right now.

We're both gearing intelligently for the situations we're preparing for, we're just preparing for different situations. Without data to tell us which is more common, or which will prevent more wipes in aggregate, neither of us can be right or wrong about which is going to be "optimal." In reality, there's probably never going to be a single answer to that, just because every guild's healing profile is going to be different.
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