Simulation: Stamina vs Mastery

Warning: Theorycraft inside.

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Re: Simulation: Stamina vs Mastery

Postby Onewinged » Tue Jan 18, 2011 4:54 am

Finaly got a chance to reply. Too busy with work and exams ><

The initial target of this sim (the first ones are definately rng generators, while last post was based on real stats and Maloriak 25n melee swings) was too predict how Stamina fares vs Mastery under specified conditions - a boss pounding you for predictable damage for a certain ammount of time while being specifically healed for certain ammount.

Simulating a whole encounter with cooldown usage, realistic healing and realistic mechanics is QUITE exhausting work.

However, I do agree that healing model should be improved somehow. But I disagree about cooldown usage. Cooldowns should not affect DTPS while doing simulations, just because simulations should provide data on how a stat does while being beaten.

In the end tanks shouldnt die at all. They die as stated because healers go oom, not using cds to mitigate incoming PREDICTABLE damage, going out of range and various reasons.
Thus in my opinion just like simulating DPS you're not accounting moving, in the same manner incoming damage should be simulated as well - being pounded.

Its just too many factors affect tank death, that imo it is just better to ignore most of them while simulating. It's just basically to see - how will you survive longer IN GENERAL - with more mastery than stamina or more stamina than mastery?

I will improve the sim, I just need some suggestions... atm thinking of:
Adding more damage sources, like
>>> Swing / Damage / Type
1: 2s / 50000 / Melee
2: 30s / 100000 / Magical
dunno how that will work, because it would probably require a cooldown to survive, in the end making it JUST ANOTHER hit, which can't be blocked. :/

Healing:
>>> cast time / healing
1: 2s / 4000
2: 3s / 8000
3: 0.5s / 500
etc etc

But still in the end it will only show for how long can mastery tank survive vs how long can stamina tank survive.

So if anyone can provide me with suggestions - Ill sim it. However I can't really dedicate enough time to sim whole encounter mechanics.

In the end it might as well be a result that some encounters would fare better with mastery gear, and others with stamina gear... or it would help to find breaking point of health where you just have it and then stack mastery to reduce DTPS.

Another alternative: someone provides me their stats and a few logs of wipes, and I could probably resim that encounter with changed stats for more mastery and see if anything breaking would change in it?
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Re: Simulation: Stamina vs Mastery

Postby Maelsstrom » Tue Jan 18, 2011 1:22 pm

I'm not convinced this is something you can simulate and reach actionable conclusions. Frankly I'm not sure there's enough variation possible due to gem/trinket choices alone to make a difference.

The purpose of stamina is to provide the cushion or float such that healing can adjust their healing delivery in response to damage taken. When the window is 170k vs 190k (a 20K difference, max possible before we get to epic gems), I'm having trouble believing that one is demonstrably better than the other. And frankly, if you balance it which happens if you take the "best itemization" enchants and catch your gemming bonuses, the breadth to either end of the window is just not big enough to be concerned about.

If you're dying repeatedly, it's not because you made the wrong gem or enchanting choices. They don't swing the results appreciably in the current raiding environment. In WOTLK, the difference between 50k and 60k hp was a world of difference and the fact you had more dodge or more parry was totally immaterial when all it took was 3 hits to kill you. In Cataclysm, the difference between 170k and 190k is simply nowhere near that dramatic. It doesn't swing the "time-to-live" calc by 33% like a small fraction did on WOTLK.

I believe that if the tank has the right gear level and is doing his job properly (including using CD's appropriately and are making adjustments and learning from each wipe), then trading stamina for mitigation or avoidance is not the root problem (or solution!) to wiping.
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Re: Simulation: Stamina vs Mastery

Postby theckhd » Tue Jan 18, 2011 4:49 pm

Onewinged wrote:Simulating a whole encounter with cooldown usage, realistic healing and realistic mechanics is QUITE exhausting work.

That's true. In fact, I'd argue that a truly realistic simulation has never been made. And probably never will be, simply because the number of factors one has to include is enormous.


Onewinged wrote:However, I do agree that healing model should be improved somehow. But I disagree about cooldown usage. Cooldowns should not affect DTPS while doing simulations, just because simulations should provide data on how a stat does while being beaten.


What justification do you have for that assertion, other than your own opinion? What a simulation "should" provide isn't something you arbitrarily decide, it should be consistent with the goal.

If the goal is to provide a useful comparison of two stats in a combat scenario and determine which is better, then you can't ignore cooldowns and expect to get an answer that has global significance. Because cooldowns are present in a combat scenario, and they get used in ways that actually do make a difference in the outcome.

If your goal is to compare mastery and stamina in a very specific situation (robot healers, robot tanks, very limited combat environment), then ignoring cooldowns might be reasonable. But most people don't actually care about that; it might be an interesting footnote, or something to discuss on a forum. In the end they care about real combat scenarios which include a lot of factors that you're simply dismissing.

Onewinged wrote:In the end tanks shouldnt die at all. They die as stated because healers go oom, not using cds to mitigate incoming PREDICTABLE damage, going out of range and various reasons.
Thus in my opinion just like simulating DPS you're not accounting moving, in the same manner incoming damage should be simulated as well - being pounded.

Its just too many factors affect tank death, that imo it is just better to ignore most of them while simulating. It's just basically to see - how will you survive longer IN GENERAL - with more mastery than stamina or more stamina than mastery?


And that's my point. It's not better. Easier? Yes. Better? No.

In fact, I'd say it's objectively worse to ignore most of the factors that affect tank death, especially when those factors play critical roles in the outcome. By doing so, you guarantee that you will not get any results that can be considered "general," because you've limited your simulation to one small sandbox that doesn't adequately reflect a real encounter. In fact, some of the better DPS simulators (simcraft, for example), do include a variety of "movement" parameters to help include time-off-target estimates in their simulations.

In other words, this type of simulation will never give you information about "how you will survive longer IN GENERAL," because it can't. You threw "in general" out with the bath water, so to speak, as soon as you decided to ignore all of those factors that are difficult to model.

I realize I'm sounding pretty harsh here, and I don't want you to think I'm being unkind. Your sim seems to do a great job of modeling the limited combat environment it set out to do, and it does give us some useful information. But you have to be really careful when drawing conclusions from such a model. "Mastery increases expected TTL more than Stamina under conditions X" would be a reasonable conclusion, "Mastery is better than Stamina" or "Mastery wins" would not.

Always try to know and understand the limitations of your model, so that you don't fool yourself into extending its results into regions of parameter space where it doesn't apply.


Onewinged wrote:I will improve the sim, I just need some suggestions... atm thinking of:
Adding more damage sources, like
>>> Swing / Damage / Type
1: 2s / 50000 / Melee
2: 30s / 100000 / Magical
dunno how that will work, because it would probably require a cooldown to survive, in the end making it JUST ANOTHER hit, which can't be blocked. :/

Healing:
>>> cast time / healing
1: 2s / 4000
2: 3s / 8000
3: 0.5s / 500
etc etc


What I've always wanted to see, and never had the time to do myself, is a simulation like this that tries to model real healers and real tanks. One of the major limitations of every simulator I've seen before is that it treats every tank and every healer like an automaton rather than a human being. It wouldn't have to be a very complex model to start out with; anything would be better than "I cast Generic Heal (Rank 4) over and over." Refining the model could be a longer-term project.

A slightly more sophisticated healer model would be something like this:
Code: Select all
if tank.health>70%
   cast Mana-Efficient-Heal
elseif tank.health>50%
   cast Big-Slow-Heal
elseif tank.health>20%   
   cast Mana-Inefficient-Heal
else
   cast Panic-Heal
end


That sort of model (with some tweaking) would allow for a little bit of healer reaction; when the tank gets low, he starts ramping up to higher HPS in an effort to counter the incoming damage. Similarly, you could write a simple tank model such that he starts popping available cooldowns when he drops below a certain threshold (40%?).

Again, this is still very limited. For example, it doesn't account for a second healer helping to cover the tank during spikes, which almost certainly happens in real raid situations. But it's an order of magnitude better than another generic heal-bot and tank-bot simulation.
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Re: Simulation: Stamina vs Mastery

Postby Koatanga » Tue Jan 18, 2011 7:43 pm

theckhd wrote:This assertion keeps getting repeated despite being wrong. Healers are not robots. They have mana efficient heals (generally slow) and mana-inefficient heals (generally fast). More stamina extends the time your healer has to react to a spike, which can impact his choice of heals.

I'm not sure why so many people seem to miss this point, because it's a pretty obvious one. Your healer's mana-efficient heal is designed such that they can cast it almost indefinitely without going OOM. As long as the HPS generated by that heal is greater than the average incoming DTPS, that healer could keep you alive indefinitely. The only thing that prevents this is your finite health pool, which a period of increased DTPS can exhaust. Increasing that health pool makes it harder to exhaust, increasing the range during which your healer can use his mana-efficient heal, and extending time-to-OOM.

I imagine the reason why so many people miss this point is that while healers can heal endlessly in sims using the most efficient heals, real healers do go OOM.

Perhaps they make bad choices. Perhaps they heal themselves or a DPS or someone other than the tank for a moment. Perhaps they have to move for something or get interrupted and they can't heal for a moment, so need to cast more expensive heals to catch up.

But in reality, they do go OOM.

An increased health pool increases the amount of time you can live between full health and death with no heals, assuming equal avoidance/mitigation. But we're talking about trading some stam for more avoidance/mitigation. It seems to me that if you can get more avoidance/mitigation that you give up in stamina, you increase your survivability in non-burst scenarios by talking less overall damage, which logically requires less overall mana to replace.

In burst scenarios, there are cooldowns, self-heals, and other tricks we can use to reduce the strain. And while I have not done a lot of the fights in Cata raids, what I have experienced thus far is a lot more sustained damage and a lot less burst damage than Wrath had.
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Re: Simulation: Stamina vs Mastery

Postby Onewinged » Wed Jan 19, 2011 12:37 am

theckhd wrote:
Onewinged wrote:However, I do agree that healing model should be improved somehow. But I disagree about cooldown usage. Cooldowns should not affect DTPS while doing simulations, just because simulations should provide data on how a stat does while being beaten.
What justification do you have for that assertion, other than your own opinion? What a simulation "should" provide isn't something you arbitrarily decide, it should be consistent with the goal.

If the goal is to provide a useful comparison of two stats in a combat scenario and determine which is better, then you can't ignore cooldowns and expect to get an answer that has global significance. Because cooldowns are present in a combat scenario, and they get used in ways that actually do make a difference in the outcome.
Yes, in my opinion cooldowns should be ignored while simulating. Because they do not change much in the STA vs MAS miniwar. You're taking damage anyways, be it reduced or not, and at any rate I don't think (yet again, imo) that there's a tank that uses cooldowns when they go off cd. Since anyways you will be using them somehow - they do impact DTPS, however they do not impact how STA scales vs MAS, because they don't increase your health pool percentagely nor they increase your block chance/value. They *just* reduce the damage taken. Basically just doing the same as adding more healing, which doesnt cost mana.

theckhd wrote:In fact, I'd say it's objectively worse to ignore most of the factors that affect tank death, especially when those factors play critical roles in the outcome. By doing so, you guarantee that you will not get any results that can be considered "general," because you've limited your simulation to one small sandbox that doesn't adequately reflect a real encounter.
It's not really possible to simulate a tank going out of range of healers. Siming healers going oom - possible, and probably should be included, since it's crucial to see in which model healers go oom faster. And cooldowns - if you're not using them on spikes, you're brain dead as well. Simulating people's ability to play isn't really doable.
And if we simulate a perfect world where everyone plays perfectly - we shouldnt need simulations then, because it would be impossible to die. :/

theckhd wrote:I realize I'm sounding pretty harsh here, and I don't want you to think I'm being unkind. Your sim seems to do a great job of modeling the limited combat environment it set out to do, and it does give us some useful information. But you have to be really careful when drawing conclusions from such a model. "Mastery increases expected TTL more than Stamina under conditions X" would be a reasonable conclusion, "Mastery is better than Stamina" or "Mastery wins" would not.
I don't think you're harsh or anything, your all points are valid. Some could be debated, but still valid.
And I do agree that I probably stated it wrongly, and shouldve stated "Mastery increases expected TTL more than Stamina under conditions X".

theckhd wrote:What I've always wanted to see, and never had the time to do myself, is a simulation like this that tries to model real healers and real tanks. One of the major limitations of every simulator I've seen before is that it treats every tank and every healer like an automaton rather than a human being. It wouldn't have to be a very complex model to start out with; anything would be better than "I cast Generic Heal (Rank 4) over and over." Refining the model could be a longer-term project.

That sort of model (with some tweaking) would allow for a little bit of healer reaction; when the tank gets low, he starts ramping up to higher HPS in an effort to counter the incoming damage. Similarly, you could write a simple tank model such that he starts popping available cooldowns when he drops below a certain threshold (40%?).

Again, this is still very limited. For example, it doesn't account for a second healer helping to cover the tank during spikes, which almost certainly happens in real raid situations. But it's an order of magnitude better than another generic heal-bot and tank-bot simulation.
Then adding healer's mana is needed as well, since healer can't spam indefinately. It just doesn't happen. Adding regen and etc. Then it becomes a real combat simulator. And too many factors WILL skew the stat values. They WON'T BE accurate. For example - simulator decides that the healer wants to heal dps who's low, ignoring the fact that a damage spike is inc and tank doesnt have a cooldown. Bam dead.
On the other hand what could be done is having a healing model, 1 healer with X different spells, healer's mana pool, several abilities that do damage to tank, and tank stats to compare. That should give more insight without skewing the data too much. Or at least give us a breaking point when the healer goes oom or a tank dies.
And even then you could argue that I'm not including spirit or healer cooldowns to increase the time for them going oom. (Which is actually not really relevant)

Then again - comes the alternative:
Taking existing logs with their tank stats, and swapping that tank with new stats. And rerunning the logs to see what changes. That's much more realistic than real encounter simulation.

At any rate I will have time in weekend again, so I'll work on something, just need to decide on what :)
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Re: Simulation: Stamina vs Mastery

Postby theckhd » Wed Jan 19, 2011 11:03 am

Onewinged wrote:Yes, in my opinion cooldowns should be ignored while simulating. Because they do not change much in the STA vs MAS miniwar. You're taking damage anyways, be it reduced or not, and at any rate I don't think (yet again, imo) that there's a tank that uses cooldowns when they go off cd. Since anyways you will be using them somehow - they do impact DTPS, however they do not impact how STA scales vs MAS, because they don't increase your health pool percentagely nor they increase your block chance/value. They *just* reduce the damage taken. Basically just doing the same as adding more healing, which doesnt cost mana.


A cooldown is significantly different than just reducing damage taken in real combat scenarios though. A cooldown does increase your effective health pool, because it makes every point of stamina more effective. A 50% cooldown is essentially the same as doubling your health pool for the duration of the cooldown, and also makes every point of healing twice as effective.

This is especially relevant in the type of simulation you're running. A death in your simulation will almost always be the direct result of a string of unblocked/unavoided hits. That's a situation where incoming DTPS is temporarily larger than incoming HPS. Popping a cooldown extends that period, giving healers time to react.

Mathematically, mastery and stamina act differently in that situation. Your chance to take N unavoided hits in a row is:
(1-A)^N
and your chance to take N unblocked hits in a row is:
(1-A-B)^N

Adding mastery increases B, but adding Stamina increases N. Popping a cooldown increases N multiplicatively. There's no reason to expect that 20k health and 10% block would give you mathematically identical results with and without cooldowns active, because they're not linear effects.

For example, let A=0.25 (25%) and B=0.4 (40%). You have the option of taking +18k health or dB=+10% block (which are equal itemization amounts, 10% block from mastery should be ~18.4k HP if converted to stamina). Here's what the probabilities work out to be:
Code: Select all
N   (1-A)^N     (1-A-B)^N   (1-A-B-dB)^N
1    0.7500      0.3500      0.2500
1.5  0.6495      0.2071      0.1250
2    0.5625      0.1225      0.0625
2.5  0.4871      0.0725      0.0312
3    0.4219      0.0429      0.0156
3.5  0.3654      0.0254      0.0078
4    0.3164      0.0150      0.0039
4.5  0.2740      0.0089      0.0020
5    0.2373      0.0053      0.0010


Adding 18k health increases N by some proportion of a boss attack. If that increases N by half a boss hit on average (dN=0.5), then for small N, it's generally more effective than the mastery at keeping you alive. At larger N values, it falls behind mastery as expected. At that point though, the simulation is wandering into unrealistic territory, since your healer has 6-10 seconds to react to the spike.

To make that a little clearer, let's look at some specifics. If the boss hits for 50k unblocked, and N=1 unblocked attack will kill you but one blocked attack (30k) will not, you're sitting between 30.001k and 50.001k health. So the overkill on that hit will be between 0 and 20k.

Adding 18k health in that situation is pretty significant. It covers almost all of the overkill, which means that a good portion of the time, you can survive that unblocked hit. It pushes N closer to 2, and gives you a much better chance of surviving that unblocked hit than the 10% block from mastery would. As you let your initial health pool get bigger (increasing N), mastery starts to pull ahead because of the exponential form of the expression.

Now consider a 50% cooldown. If you were between 30k and 50k health, but the boss now hits for 25k, you can definitely survive 1 unblocked hit, and possibly 2 (if you were at 50.001k initially). So it takes somewhere around N=2 hits to kill you on average. Adding 18k pushes that much closer to N=3, again giving you a better chance of living than the mastery rating. Again, if you start at a higher threshold (N=2 without cooldown, N=4 with), the mastery starts to pull ahead, just like before.

However, think about how you actually use cooldowns. As you said:
Onewinged wrote:and at any rate I don't think (yet again, imo) that there's a tank that uses cooldowns when they go off cd.

Onewinged wrote:And cooldowns - if you're not using them on spikes, you're brain dead as well.

In other words, you don't pop them as soon as they're available. You use them in emergency situations, which means "low health." So cooldown usage itself generally tends towards the situations where it only takes 1-2 boss attacks to kill you. That means that generally, you use cooldowns in situations where the extra stamina is more helpful than the extra mastery.

The take-home message here is that not only are cooldowns not irrelevant from the standpoint of this sort of simulation, but also that the way you implement them has a significant effect on which stat they favor. And remember, this is all ignoring the most important detail about cooldowns, which is that they increase the reaction time available to your healers, something that we can't even begin to address with this limited model.


Onewinged wrote:It's not really possible to simulate a tank going out of range of healers.

Why not? It's just a period where the healer stops healing. There's nothing complicated about that. The hard part is figuring out how often you want to include that occurrence, which would depend on the type of fight you're modeling. Some fights it doesn't happen at all, others it might happen frequently.

Onewinged wrote:And if we simulate a perfect world where everyone plays perfectly - we shouldnt need simulations then, because it would be impossible to die. :/

I don't think "more realistic" necessarily means "everyone plays perfectly." A raid group undergearing a fight can play perfectly and still have healers run oom, tanks run out of cooldowns, and players get incapacitated by encounter mechanics.


Onewinged wrote:Then adding healer's mana is needed as well, since healer can't spam indefinately. It just doesn't happen. Adding regen and etc. Then it becomes a real combat simulator. And too many factors WILL skew the stat values. They WON'T BE accurate. For example - simulator decides that the healer wants to heal dps who's low, ignoring the fact that a damage spike is inc and tank doesnt have a cooldown. Bam dead.

I'm not sure I understand your argument here. Adding things to make the combat simulator more realistic may skew the stat values, but that won't make them less accurate unless you do it incorrectly. For example, the sim should never decide that the tank healer decides to heal a DPS instead if you don't tell it to do that.


Onewinged wrote:On the other hand what could be done is having a healing model, 1 healer with X different spells, healer's mana pool, several abilities that do damage to tank, and tank stats to compare. That should give more insight without skewing the data too much. Or at least give us a breaking point when the healer goes oom or a tank dies.

That's sort of the direction I was suggesting, yes.

In the end though, I'm not sure it's worth the time spent. I suspect the answer will still be "stamina and mastery are both pretty good, and both strong in different situations." I don't think you'll ever get a single numerical value to represent the relationship between the two, because there are simply too many variables involved. That's part of the reason I'm a little skeptical of these sorts of limited TTL simulations - they only give you a part of the story. There are so many factors that have to be ignored to be able to write the simulation in a reasonable amount of time that it's hard to make the results relevant in any general sense.
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Re: Simulation: Stamina vs Mastery

Postby Rasmfrackn » Wed Jan 19, 2011 1:04 pm

To be fair I'd say that a flat % reduction cooldown scales everything approximately equally, not just stamina. Taking half damage also makes the blockable damage look much more attractive to mastery gearing since it reduces hit size compared to health pool.

It's all that darned unblockable spike damage that messes things up.

Per your slightly more sophisticated healing model, theck, that was my first idea as well. At this point I'm tending towards a TTL check instead of a health % check as something that might be more realistic, but I'd love to get some more input on that since technically the health % is what healers see on the bar.

E.g.
Code: Select all
if tank.TTL>8 seconds
   cast Heal
elseif tank.ttl>4 seconds
   cast Greater Heal
elseif tank.ttl>2
   cast Flash Heal
else
   cast Instant and pray
end


Either way for choosing a heal, it wouldn't be that difficult to add a mana pool, a regen rate, mana costs, and then maybe some rudimentary regen-cooldown usage.

My main concern about modeling healers is that while they all have this toolbox of the 3 baseline heals, I don't think they use them much compared to their class/spec-specific heals. It's rejuvs/swiftmends, riptides, shocks, pennance, PWS, etc. especially compared to the actual efficient Heal class heals. I don't see any healer using those like ever.
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Re: Simulation: Stamina vs Mastery

Postby theckhd » Wed Jan 19, 2011 1:50 pm

Rasmfrackn wrote:To be fair I'd say that a flat % reduction cooldown scales everything approximately equally, not just stamina. Taking half damage also makes the blockable damage look much more attractive to mastery gearing since it reduces hit size compared to health pool.

I think that would only be the case if the cooldown were active with 100% uptime. That's the reason that Mastery "catches back up" as N gets larger in the example I gave; starting at higher health (more hits before death) is essentially longer cooldown uptime in that example.

In other words, they only scale equally for net damage taken calculations, not for discrete attacks. When you're down to the last 1 or 2 hits, the discretization becomes significant. A cooldown acts differently in that situation than it does when you're at 90% health, because there's less room for other effects (i.e. fewer chances to break up the string of hits).

If I had to put a more mathematical description on it, I'd guess that it's closely related to binomial statistics. What you're essentially doing here is integrating the area under that distribution from k=x to k=infinity, where x is the number of hits you can survive without dying. The binomial distribution changes significantly between N=1 trials and N=5 trials in such a way that increasing x from 0 to 1 for N=1 is a much bigger reduction than increasing x from 1 to 2 for N=2, from 2 to 3 for N=3, and so on.

Rasmfrackn wrote:Per your slightly more sophisticated healing model, theck, that was my first idea as well. At this point I'm tending towards a TTL check instead of a health % check as something that might be more realistic, but I'd love to get some more input on that since technically the health % is what healers see on the bar.

E.g.
Code: Select all
if tank.TTL>8 seconds
   cast Heal
elseif tank.ttl>4 seconds
   cast Greater Heal
elseif tank.ttl>2
   cast Flash Heal
else
   cast Instant and pray
end


My main concern about modeling healers is that while they have this toolbox of the 3 baseline heals, I don't think they use them much compared to their class/spec-specific heals. It's rejuvs, riptides, shocks, pennance, PWS, etc. especially compared to the actual efficient Heal class heals. I don't see any healer using those like ever.


Yeah, there are a number of hurdles involved in modeling healing. Not least of which is modeling different healer types, because each plays and heals a little differently. And even restricting oneself to a single type (say Holy Paladins), two different players likely won't even heal the same way. I'll admit that I have no idea how realistic the "3 baseline heals" model is, but I'd be willing to bet that it's closer than robo-heal-9000 just spamming Holy Light.
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Re: Simulation: Stamina vs Mastery

Postby Kelaan » Wed Jan 19, 2011 2:06 pm

Rasmfrackn wrote:At this point I'm tending towards a TTL check instead of a health % check as something that might be more realistic, but I'd love to get some more input on that since technically the health % is what healers see on the bar.

I think that the last part is important: healers rarely know your expected TTL, but can always see your health (plus expected short-term heals).
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Re: Simulation: Stamina vs Mastery

Postby Rasmfrackn » Wed Jan 19, 2011 3:15 pm

theckhd wrote:
Rasmfrackn wrote:To be fair I'd say that a flat % reduction cooldown scales everything approximately equally, not just stamina. Taking half damage also makes the blockable damage look much more attractive to mastery gearing since it reduces hit size compared to health pool.

I think that would only be the case if the cooldown were active with 100% uptime. That's the reason that Mastery "catches back up" as N gets larger in the example I gave; starting at higher health (more hits before death) is essentially longer cooldown uptime in that example.

In other words, they only scale equally for net damage taken calculations, not for discrete attacks. When you're down to the last 1 or 2 hits, the discretization becomes significant. A cooldown acts differently in that situation than it does when you're at 90% health, because there's less room for other effects (i.e. fewer chances to break up the string of hits).

If I had to put a more mathematical description on it, I'd guess that it's closely related to binomial statistics. What you're essentially doing here is integrating the area under that distribution from k=x to k=infinity, where x is the number of hits you can survive without dying. The binomial distribution changes significantly between N=1 trials and N=5 trials in such a way that increasing x from 0 to 1 for N=1 is a much bigger reduction than increasing x from 1 to 2 for N=2, from 2 to 3 for N=3, and so on.

Yeah, I think I'm mostly in agreement. The case of blowing a cooldown late when you're already at low health is a tricky case to consider, though. I also think the reality of cooldown usage is closer to what you're saying... I still think that simply scaling damage by a % should affect most stats close to equally but they're generally used in situations where not all stats apply. There's the occasional frenzy/berserk that'll up melee damage intake, but we're usually using cooldowns when our avoidance/blocking fails us, so it really is only multiplying stamina's value, not anything else's.
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Re: Simulation: Stamina vs Mastery

Postby Kihra » Wed Jan 19, 2011 3:16 pm

theckhd wrote:A cooldown acts differently in that situation than it does when you're at 90% health, because there's less room for other effects (i.e. fewer chances to break up the string of hits).


While this is definitely true, in this raid tier I find myself using cooldowns when I'm at high health far more often than when I'm at low health. This tier is full of telegraphed attacks and/or danger periods where you find yourself wanting to mitigate the damage even if you enter the danger phase with full health.

Examples include:

Magmaw - Mangle.
Maloriak - Engulfing Darkness (heroic).
Chimaeron - Feud Periods (heroic). Double Attacks. The sub-20% Mocking Shadows burn (heroic).
Nefarian - Shadow Breaths. Electrocutes.

Halfus - Furious Roar.
Ascendant Council - Fire guy's flames. Lighting guy's shock. Late in the P2 burn.
Cho'gall - Conversion stacks. If you're stuck tanking with Fury because your co-tank keeps dying! ;)

Conclave - Permafrost.
Al'akir - Electrocute.

Cooldown use for me has been less about low health emergencies and more about well-known danger periods that I'm often entering topped off. The purpose of the CD is to reduce risk of death during a spike period or to just alleviate strain on the healers by enduring the dangerous phase without losing too much health.
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Re: Simulation: Stamina vs Mastery

Postby theckhd » Wed Jan 19, 2011 4:07 pm

Kihra wrote:While this is definitely true, in this raid tier I find myself using cooldowns when I'm at high health far more often than when I'm at low health. This tier is full of telegraphed attacks and/or danger periods where you find yourself wanting to mitigate the damage even if you enter the danger phase with full health.


Sure, but those telegraphed attacks are another thing that's absent in this simulation. In practice, what this means is that you're committing some of your cooldowns to those predetermined periods, and thus have fewer free for the panic situations. As long as you're not using all of your cooldowns to cover telegraphed stuff, you should have a couple free for panicking.

This also brings up another interesting question: are you more likely to die during those predictable bursts, even with cooldowns up, than you are in the periods between? This simulation probably does a good job of simulating a predictable burst situation with the right combination of parameters (incoming DTPS higher than HPS, hit size chosen so that it only takes about 3 unblocked hits to kill a tank; coincidentally that is a case where the cooldown could be irrelevant, since it might be up 100% of the time).

<edit> On the other hand... I suppose I should point out how many of those burst situations involve magical damage...
Kihra wrote:Magmaw - Mangle.
Maloriak - Engulfing Darkness (heroic).
Chimaeron - Feud Periods (heroic). Double Attacks. The sub-20% Mocking Shadows burn (heroic).
Nefarian - Shadow Breaths. Electrocutes.

Halfus - Furious Roar.
Ascendant Council - Fire guy's flames. Lighting guy's shock. Late in the P2 burn.
Cho'gall - Conversion stacks. If you're stuck tanking with Fury because your co-tank keeps dying! ;)

Conclave - Permafrost.
Al'akir - Electrocute.


It's no wonder that the reports from tanks working on heroic modes have pretty consistently been not to ignore Stamina and blindly stack Mastery.

As a quick example, take two of the paladin tanks near the head of progression:
MT's own Treckie
Lazeil
Both of these guys have a few pure stam gems floating around, and go 20/30 mast/stam in green sockets rather than 40 mastery. I'd be willing to bet that you'll see a similar methodology on other tanks that are at similar levels of progression.
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Re: Simulation: Stamina vs Mastery

Postby Hrobertgar » Wed Jan 19, 2011 5:15 pm

As someone with both a Pally healer Main and an often used Pally Tank alt (long story involving multiple servers), I can say that my experience is that once a tank reaches a health pool such that he will not be 2-shot by the boss, mitigation (physical or magical depending on the fight) almost always trumps health pool.

If you are tanking a magic dmg intensive boss, you are probably far better of using the resistance elixir than the stam flask.

Just prior to Cata, I joined a 25m Algalon attempt. 5 Heals, 2 Tanks. Tank #1 was a pally with 82k buffed health (impressive back then). Tank #2 was a bear with 78k buffed health. Again, this was outside ICC and its 30% bonus. My experience was that the Pally tank with his outrageous health pool would die if I stoppped spamming Divine Light on him for more than 3 seconds = tank caused OOM. On the other hand, the lower health bear tank (surely a contradiction) would still be alive after I stopped healing him for a full 5 seconds. Unfortunately the inspect bug, prevented me from evaluating Pally tank's gear, but a friend told me after he was wearing mostly dps/PvP gear. So health <> success.

For other fights, when I'm on my tank I consider sources of dmg. A health flask that is 1.5%-3% max health increase is not always better than a resistance flask that reduces incoming dmg by 10%.

I ask those of you sporting HM gear the following question. If you could (through converting dodge/parry or some other means like the Mastery elixir) become advoidance capped through Block, would that make your encounters easier?

Again, a tank does need a base health pool sufficient to absorb a couple boss hits, but after that, saving healer mana is more important. I do not believe I have ever seen a tank die because their total health pool was not 1% larger. But I see them die all the time because they took too much dmg, or because the tank or dps actions caused me and/or other healers to go OOM.
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Re: Simulation: Stamina vs Mastery

Postby inthedrops » Wed Jan 19, 2011 5:55 pm

Do not compare prior content to current game. It's not a valid or useful comparison.

Take the following combat log for heroic CoW on Nezir as an example of why the Mastery strategy becomes questionable.

Permafrost is an ability that without cooldowns or resist hits for roughly 50k every second for 3 seconds. In other words, 150k in 3 seconds. Very often, the last tick of Permafrost coincides with a melee hit between 30k and 50k. In other words, 200k damage in 3 seconds.

Code: Select all
[23:15:32.764] Paperplate casts Divine Protection
[23:15:33.154] Nezir Permafrost Paperplate 23914 (R: 14600)
[23:15:34.369] Nezir Permafrost Paperplate 31960 (R: 5058)
[23:15:35.182] Nezir Permafrost Paperplate 24983 (R: 15252)
[23:15:36.308] Nezir hits Paperplate 23575 (B: 15717)
[23:15:42.744] Paperplate's Divine Protection fades from Paperplate


Now, the above numbers only show 104k damage lasting a bit longer than 3 seconds. So you might ask yourself...."That's not so bad? Surely mastery would be fine?"

But I'm setting you up :)
First, I was at 285 resist during the fight (using resist elixir). Second, I had my divine protection glyphed for 40% magical damage reduction. Third, I step out of melee range near the end of the breath to try to buy an extra 0.5 second or so for a heal to land before he hits me.

(BTW, would love to see some discussion about the merits or not with those two combined)

I guess it's relevant to note that my fully buffed health in this example was 183k. Healing is extremely intense. There are two healers healing me during this crap. And more often than not one has to move out of a frost patch. Meaning that there are times where only one healer can really get the job done.

There is nothing this dangerous in the regular version of the fights that I can think of off hand.

Stamina really is an important stat and not to be dismissed.

Sorry for the derail.
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Re: Simulation: Stamina vs Mastery

Postby theckhd » Wed Jan 19, 2011 6:08 pm

inthedrops wrote:Sorry for the derail.

Not at all. I think your insight is probably more relevant to this discussion than even mine is.
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