Strength vs mastery (or self healing vs mitigation)

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Strength vs mastery (or self healing vs mitigation)

Postby Cocosavage » Tue Jan 25, 2011 4:59 am

Strength is a good threat stat (after expertise and hit) and a poor avoidance stat (parry).

BUT: strength improves paladin self healing abilities (via AP and SP).

Let's assume you're tanking with seal of insight, spamming WoG, and you specced for maximizing self heal.

Empirical evidence gives the following result: a +40 str gem gives you +24 hps
(Theck pointed out that it's a bit less, approx. 21hps)

Let's assume you're taking 5k dps damage (after mitigation and avoidance).

One could consider it as a mitigation of 24/5000=0.48% incoming damage.

A +40 mastery gem gives you +0.5% block chance, that is 0.2% mitigation.

It seems that strength beats mastery if the incoming damage is <5000 dps, after mitigation.
That is roughly 25k dps of unmitigated physical damage.

One should consider also that mastery mitigate physical damage only, and strength gives you a threat boost, and a little avoidance.

Conclusion: stacking strength is a good idea if physical dps intake is low (<5000 dps): heavy magical fight or soloing old content.

I apologize for my very poor english and thank you for any criticism or advice.
Last edited by Cocosavage on Fri Jan 28, 2011 1:27 pm, edited 5 times in total.
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Re: Is strength a good mitigation stat?

Postby Durability » Tue Jan 25, 2011 7:51 am

Assuming your numbers are correct this is pretty interesting - what's your source on 40 str = 24 hps?
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Re: Is strength a good mitigation stat?

Postby theckhd » Tue Jan 25, 2011 9:13 am

There are a few inaccuracies here.

  1. First and foremost, Strength is not a mitigation stat. Healing is not the same as mitigation, and shouldn't be treated as such because there are important differences between the two. Mitigating X damage is better than X healing in almost every conceivable scenario. So Strength gives self-healing (through AP->WoG/SoI) and avoidance (through parry rating), but not mitigation.

  2. Your empirical estimate seems pretty far off. A 40 STR gem gives 84 AP and 25 SP after raid buffs. This should increase the size of a 3-point WoG by 104.27 points of healing, on average, and the size of a SoI heal by 18.4 healing, on average. Formulas here.
    • You get 1.23 3-point WoGs off every 9.35 seconds on average if you have Eternal Glory and cast 3-point WoGs whenever possible. That's 13.7 HPS.
    • Seal of insight is a 15 PPM mechanic. With raid-buffed haste, this means you should expect 15*melee_haste, or 15*1.1=16.5 procs per minute from auto-attacks. You also gain an additional (15*2.6/60)*3=1.95 procs every 9.35 seconds from CS, which is 12.5 procs. So on average you'll get 29 procs or 29*14.15=410.35 extra healing from that 40 STR every minute, or 6.8 HPS.
    Together, that's a total of about 20.5 HPS, a little smaller than your empirical estimate.

At current gear levels (let's say 36k armor, 30% avoidance, 55% block as a conservative estimate), how much mastery would it take to match this amount of self-healing?

According to the damage taken formulas, D=Do*Fa*[1-Av-0.4*B] and dD = -Do*Fa*[dAv+0.4*dB], where D is net DPS intake, Do is the raw boss DPS, dD is the change in incoming DPS, Fa is the armor mitigation factor, dAv is the change in avoidance (in decimal notation, not %), and dB is the change in block (again, in decimal notation). At 36k armor, Fa=0.475. At 30% avoidance and 55% block, Do=D/(Fa*[1-Av-0.4*B]) = 21.9k DPS.

40 Strength gives 10 parry rating, which is dAv=0.000352 (0.0352%) avoidance at this level of diminishing returns. That reduces DPS intake by 3.67 DPS. So our total estimate for STR is about 20.5 HPS and 3.7 DPS, or around 23 DPS in combination.

  • For dD=24 and Do=21.9k, dB=0.00552 or 0.552% block. That equates to 44.0 mastery rating.
  • A more realistic estimate for a raid situation might be D=10,000 DPS, which is Do=43.86k, dB=0.276%, in which case it takes only 22.0 mastery rating to reduce intake by 24 DPS.

In other words, even in a "best-case" for STR, a mastery gem reduces incoming DPS by almost as much as a STR gem would increase the sum of self-HPS and incoming DPS, and in a more realistic damage intake scenario the mastery gem is almost 2x better. And remember, the bulk of the STR gem's benefit is from self-healing, which is demonstrably less effective than mitigation in the majority of practical scenarios.
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Re: Is strength a good mitigation stat?

Postby Cocosavage » Tue Jan 25, 2011 9:15 am

I did some test on the boss training dummy with and without strength trinkets.

The results agree with the theory: WoG scale with strength by the following formula:

Str*2.6*0.6*1.05*1.05*1.06*1.06*1.1*1.1*1.185=2.77

(AP and SP, WoG formula, glyph of SoI, BoK, divinity, divinity, glyph of WoG, GbtL, Crit (RoL))

This gives Str*2.77/9*1.3=Str*0.4 hps (due to eternal glory).

So WoG hps should scale with 40% of Strength.

Here is the math for SoI:

Str*2.6*0.15*1.05*1.06*1.06=0.46

(AP and SP, SoI formula, BoK, divinity, divinity, SoI glyph doesn't affect SoI!)

The ppm is approx 25 (tested).

This gives: Str*0.46*25/60=0.192

Conclusion: hps should be scale by approx. 59% of strength. A +40 str gem gives in fact approx. 24 hps in my test.
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Re: Is strength a good mitigation stat?

Postby theckhd » Tue Jan 25, 2011 9:31 am

Hm... I neglected the STR->SP conversion, let me go back and fix that.

<edit> Fixed, mastery is still better. Here are the errors I see in your evaluation:

  • 5k DPS is a pitiful amount, and not realistic for a raiding scenario. At 150k hit points, you can survive 30 seconds without a single heal. That's not a boss, it's a level 85 non-elite world mob. Since block scales with damage intake and self-healing from STR does not, the mastery will quickly eclipse STR once you escalate DPS intake to mimic a raiding scenario, as we saw in my calculation.

    For a few simple benchmarks, Onyxia (10N) and Nefarian (10N) both do about 10k DPS in phase 1, and Nefarian increases slightly to arond 12k in phase 3. On Halfus (25H), I was tanking drakes the entire time and took an average of over 20k DPS on our kill, and you can see that in the early phases while I was tanking Time Warden and Whelps I was spiking between 20k and 30k. The tanks who spent part of their time tanking Halfus (who does less DPS) took around 14k DPS on average (20k while tanking a drake, probably 8-10k while tanking Halfus). In fact, the only time any tank dropped below 10k DTPS during that fight is when they're not actually tanking something because we're swapping drakes around.

    This is by far the biggest error in the calculation, because block scales very favorably with this while Strength does not. At reasonable damage intake levels (10k), mastery is back to being better than strength, and that disparity will only increase as intake goes up further.

  • WoG scaling is wrong - it's (0.2086*SP + 0.1984*AP)*(3 holy power)*(crit factor)*(divinity)*(GbtL)*(1+glyph.WoG+glyph.SoI), or (0.2086*0.6*1.05*STR + 0.1984*2*1.05*STR)*3*(1.1175)*(1.06^2)*(1.1)*(1+0.1+0.05) where STR is the value on the gem (i.e. 40). That gives me 2.6115 points of healing per point of STR, lower than the 2.77 you're predicting. Note that the two glyphs are not multiplicative with each other, and I'm not sure what your values of 0.6 and 1.185 are representing. This is an ~6% over-estimate of the HPS output of WoG in your calculations.

  • WoG HPS is calculated incorrectly for several reasons. You do not get 30% extra WoGs from Eternal Glory because of the 15-second internal cooldown. The more accurate estimate is 1+0.3/(1+0.3)=1.2308 WoGs. In addition, this doesn't occur in 9 seconds because the extra WoG costs a GCD, turning the rotation into a 9+1.5*0.3/(1+0.3)=9.35 second rotation. This accounts for about 10% over-estimate of the healing output of WoG in your calculations.

  • The combination of the previous two errors puts WoG's HPS scaling at 34.37% of STR.

  • SoI scaling is correct, but the base PPM of the enchant is definitely not 25. It's 15 PPM off of melee attacks, which is increased to around 29 by haste and procs from Crusader Strike. So the observed PPM of the enchant should actually be 29, higher than the 25 you're estimating. On a dummy, you should expect to see around 27 procs per minute without a 10% melee haste buff if you're following the rotation perfectly, which explains your estimate of 25.

  • Based on this, we should expect SoI HPS to be 0.46*29=13.34% of STR. I'm not sure how you got 19 in your calculation, as 0.46*25 is only 11.5%.

  • Combined, this puts total HPS scaling at about 47.7% of STR, about 11% less than your estimate and a 20% relative change in effectiveness.
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Re: Is strength a good mitigation stat?

Postby Cocosavage » Tue Jan 25, 2011 9:56 am

There is a mistake in my math:

The duration of a cycle is in fact 9.45 sec, due to eternal glory.

The scaling of WoG should be: 0.381*Str. This gives a scaling factor of 0.57.
A +40 str gem should give 23hps.

A remark:SoI procs on single target attacks, not only auto-attacks, and reckoning attacks.
The test on the dummy shows 25 ppm (without reck). Is this correct?

Thank you very much for the constructive criticism.
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Re: Is strength a good mitigation stat?

Postby theckhd » Tue Jan 25, 2011 10:54 am

Cocosavage wrote:A remark:SoI procs on single target attacks, not only auto-attacks, and reckoning attacks.
The test on the dummy shows 25 ppm (without reck). Is this correct?


No, it does not.

It procs off of CS. However, no seals proc off of HW/AS/Cons/Judge currently, and JotJ only procs SoT/SoR, not SoI. SotR procs SoT/SoR, and might proc SoI, but that's irrelevant for our analysis because we're using WoG as a holy power dump in this situation.

So at best, you get an addtional 3 procs every 9.35 seconds from CS.

My analysis assumes that you have 0/2 Reckoning and no parry-haste, since that's the condition you were simulating (dummy doesn't hit you, so you'd see neither effect). Adding 2/2 Reckoning and parry-haste has the effect of dropping your swing timer to 1.7456 seconds instead of the 2.3636 you'd get from just the 10% melee haste buff. That would increase the expected procs from melee attacks from 16.5 to 22.34, adding another 1.38 HPS to SoI procs. That's significant, but it should be clear by this point that it's nowhere near enough to make STR the winner against even the most trivial raid boss putting out 10k DPS.

Also, your estimates of the scale factors are still incorrect, for the reasons I outlined in the previous post. 57% STR scaling is still an over-estimate.
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Re: Is strength a good mitigation stat?

Postby Durability » Tue Jan 25, 2011 11:00 am

This is still a good thought where old solos are concerned - since in those cases both dmg and healing matter and you're taking relatively low incoming damage. I'll have to try out dancing with Sapphiron again in my ret set.
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Re: Is strength a good mitigation stat?

Postby Cocosavage » Tue Jan 25, 2011 11:06 am

I think my SoI computation is correct: Str*0.46 is the healing amount of one proc.
In one minute you have 25 procs => hps=Str*0.46*25/60=Str*0.19 hps.

Whatever, it's irrelevant: I've understood my BIG mistake, thanks to your explanation (differential calculus). I've considered the effect of mitigation of the mastery on the already MITIGATED damage, wich is obviously wrong. This explains the factor 2 discrepancy with your calculation.

Thank you!

PS: Stacking strength is definitely a bad strategy for raid, but
could it be good for soloing old bosses with enrage timers, with <5000 dps of incoming damage?
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Re: Is strength a good mitigation stat?

Postby theckhd » Tue Jan 25, 2011 2:13 pm

Cocosavage wrote:PS: Stacking strength is definitely a bad strategy for raid, but
could it be good for soloing old bosses with enrage timers, with <5000 dps of incoming damage?


Yes, it probably would be. Old bosses aren't likely to put out more than 5k DPS, so STR would be better than mastery at that point. Provided you aren't dying to the boss, you'd get slightly more threat out of hit-capping and expertise soft-capping than from STR, but if you're right on the borderline of survivability then all-out STR is probably better overall.

Which reminds me - we've ignored hit and expertise in these calculations. In practice, not all of your auto-attacks or Crusader Strikes will land, which should reduce the HPS of SoI accordingly. A better estimate for a raid-geared tank is probably around 85% of the value we have (2% hit, ~26 expertise).
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Re: Is strength a good mitigation stat?

Postby majiben » Tue Jan 25, 2011 7:14 pm

theckhd wrote:Which reminds me - we've ignored hit and expertise in these calculations. In practice, not all of your auto-attacks or Crusader Strikes will land, which should reduce the HPS of SoI accordingly. A better estimate for a raid-geared tank is probably around 85% of the value we have (2% hit, ~26 expertise).
16 expertise might be better since this assumes SoL usage and hence is 10 expertise lower than if SoT is used.
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Re: Is strength a good mitigation stat?

Postby theckhd » Wed Jan 26, 2011 6:05 am

majiben wrote:
theckhd wrote:Which reminds me - we've ignored hit and expertise in these calculations. In practice, not all of your auto-attacks or Crusader Strikes will land, which should reduce the HPS of SoI accordingly. A better estimate for a raid-geared tank is probably around 85% of the value we have (2% hit, ~26 expertise).
16 expertise might be better since this assumes SoL usage and hence is 10 expertise lower than if SoT is used.


Anything between 80% and 85% would probably be fine. The matlab model's default gear set has 2.x% hit and 16 expertise, which puts you at something around 82% (I don't have exact numbers handy). I just rounded up to an easy number and estimated how much hit/exp that would take.
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Re: Is strength a good mitigation stat?

Postby Cocosavage » Wed Jan 26, 2011 12:28 pm

1) The formula for damage intake shouldn't be:

D=Do*Fa*[1-Av-0.4*B]*0.9

because of Sanctuary talent?

In this case mastery would be 0.1 less effective: dD=-Do*Fa*0.4*0.9*dB (assuming Av is constant).

This isn't huge but it's interesting nevertheless.

2) I noticed that only half of the damage you took in the nefarian encounter was melee.
I think that in this case mastery is less effective in keeping the tank alive.

3) You consider an armor of 36k. This is a low value for a high level raid encounters. I think 40k is more appropriate. This gives a mitigation of 0.61, is it right?


So, strength not so bad after all?
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Re: Strength vs mastery (or self healing vs mitigation)

Postby Grae » Wed Jan 26, 2011 3:33 pm

Since you are purely focusing on spell power/HPS from Str, can you also add in how Int would fall into this?

i.e. 40 Int vs 40 Str (imagining a gem)
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Re: Is strength a good mitigation stat?

Postby theckhd » Wed Jan 26, 2011 6:35 pm

Cocosavage wrote:1) The formula for damage intake shouldn't be:

D=Do*Fa*[1-Av-0.4*B]*0.9

because of Sanctuary talent?

In this case mastery would be 0.1 less effective: dD=-Do*Fa*0.4*0.9*dB (assuming Av is constant).

This isn't huge but it's interesting nevertheless.


For actual calculations, yes, Sanctuary would be included. However, that's irrelevant to our problem here because it's also factored into the observed damage taken D. Thus, it cancels when you calculate dD as a function of D (I'll use S=0.9 as the Sanctuary factor):

Code: Select all
Do=D/(Fa*S*[1-Av-0.4*B])
dD=-Do*Fa*S*[dAv+0.4*dB] = D/(Fa*S*[1-Av-0.4*B])*Fa*S*[dAv+0.4*dB] = D*[dAv+0.4*dB]/[1-Av-0.4*B]


Alternatively, you can treat it as being wrapped into Do (i.e. our values of Do already include this factor of 0.9).

Cocosavage wrote:2) I noticed that only half of the damage you took in the nefarian encounter was melee.
I think that in this case mastery is less effective in keeping the tank alive.

3) You consider an armor of 36k. This is a low value for a high level raid encounters. I think 40k is more appropriate. This gives a mitigation of 0.61, is it right?

Yeah, 40k is probably a better estimate for a raid tank. Again though, armor cancels out here because we're basing it off of observed damage D, so that won't affect the results of our calculation.
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