Tankadin Meta Gems – Detailed Analysis

So far, we’ve been assuming that the Austere Primal Diamond was our go-to meta gem. With the massive changes to blocking in 5.0, the flat 1% block value afforded by the Eternal Primal Diamond can’t hold a candle to 2% increased armor, right?

This week, I received a private message from an EJ user asking exactly that question. They provided some quick-and-dirty numbers that compared the damage reduction of 1% extra block to the damage reduction of 2% extra armor. The extra armor mitigated more raw damage on a 100k hit than the extra block value did, and of course that’s not even accounting for the fact that block isn’t guaranteed. But there was still the extra avoidance granted by the Eternal diamond to consider, and they weren’t sure how to handle that.

As such, I figured it was time to break out the calculus and treat the problem properly.

We can start with the damage taken equation we developed all the way back in August:

$D = D_0 S F_{ar} F_{av} F_{b} F_{S}\large$

In this expression, $D$ is net damage taken after all mitigation effects, while $D_0$ is the boss’ raw (unmitigated) damage output. $S$ is the Sanctuary mitigation factor ($S=0.9$). $F_{ar}$, $F_{av}$, $F_{b}$, and $F_{S}$ are the armor, avoidance, block, and SotR damage mitigation factors, respectively. For now, I’m not going to repeat the definitions of the different mitigation factors, since they’re exhaustively in that earlier post.

To calculate the effect of the block or armor meta gems, we differentiate this expression to determine the change in damage intake $dD$ that each gives us.

Armor Meta

The armor meta essentially multiplies our armor by a factor of 1.02. There are some details there we’re glossing over (for example, this factor isn’t applied to armor from enchants or elixirs), but it’s such a minor correction that we can safely ignore it in this analysis. Since it has no other effect, it won’t change the factors $F_{av}$, $F_{b}$, or $F_{S}$, so our differential is simply:

$dD = D_0 S F_{av} F_{b} F_{S} dF_{ar}\large$

and we know from that earlier post that $dF_{ar} = \frac{dAr}{f_{ar}}F_{ar}$. $dAr$ is the change in armor, which is just $0.02Ar$, while $f_{ar}=Ar+K$ is the effective “rating-to-percentage” conversion factor for armor (again, see the August post for details on why we defined that value). Thus, the net change in damage taken is just:

$dD = \frac{0.02 Ar}{Ar + K} D\large$

Block Meta

The block meta gives us 1% extra block value and 432 avoidance rating. Thus, it will change the values of $F_{av}$ and $F_{b}$, but not $F_{ar}$ or $F_{S}$. This means that wen we differentiate, we get two terms:

$dD = D_0 S F_{ar} F_{S} \left ( F_{b}dF_{av} + F_{av}dF_{b} \right )\large$

The avoidance term is pretty easy, since its a dodge rating bonus – we can use the already-calculated result of

$dF_{av} = -\left ( \frac{dr_d}{f_d} \right ) \Phi_d\large$

where $dr_d$ is the amount of dodge rating added (432), $f_d$ is the dodge rating-to-percent conversion factor, and $\Phi_d$ is a factor defined in the August post that encapsulates the effects of diminishing returns.

The block term is also pretty easy. Starting with the definition of $F_{b}=1-B_v B_c$, with $B_v$ and $B_c$ representing our decimal block value and block chances respectively, we simply differentiate:

$dF_{b} = -dB_v B_c = -0.01*B_c\large$

Combining these two, we get:

$dD = -D_0 S F_{ar} F_{S} \left ( \frac{432}{f_d} F_{b}\Phi_d + 0.01*B_c F_{av} \right ) \large$

Plugging in Numbers

To see which of these has the largest effect, we plug in some numbers. I’ve put my current stats on Theck into my 5.1 Tankadin Stats Sheet, which spits out the numbers of interest:

$F_{ar}=0.5068$
$F_{av}=0.8150$
$F_{b}=0.9266$
$F_{S}=0.8009$
$\Phi_d = 1.0323$
$B_c = 0.2448$
$Ar=56815$
$K = 58370$
$f_d = 88500$

Plugging those into the expressions above, we get the following results.

Armor meta: $dD/D_0 = 0.2721\%$
Block meta: $dD/D_0 = 0.2435\%$

Surprisingly, the gap isn’t as large as we originally thought. The majority of the block meta’s mitigation comes from the avoidance (~0.17%, compared to ~0.07% for the block value increase). However, there are some other factors that make the armor meta hands-down superior to the block meta.

First, we have to note that the mitigation of the block meta is the combination of the dodge rating and the block value effect. However, the 2% armor bonus isn’t the only thing the armor meta gives you. It also gives you a nice chunk of stamina, which we value pretty highly, especially in a control gearing scheme.

Second, if you’ve been following this blog for any significant amount of time, you already know that we don’t put much stock in total damage reduction. We’re more interested in what makes you a better tank, and generally that means making you easier to heal and less likely to become a puddle on the floor. So it’s not just the amount of damage reduction that matters, but also how that damage reduction is applied. The armor meta is the quintessential smoothing mechanic – it applies to every single attack that gets through your avoidance, no matter what else happens.

On the other hand, the block meta is more erratic. It gives its damage reduction in chunks – an extra avoided attack here, or a little extra mitigation on a blocked attack there. By its nature, it’s “spiky” damage reduction. Even if the block meta gave slightly higher damage mitigation, we might shy away from it and favor the smooth mitigation of the armor meta, for exactly the same reason we choose control gearing strategies over avoidance gearing strategies.

Conclusions

In short, our intuition about our meta gem choices this tier were correct. The Austere Primal Diamond provides more overall damage mitigation than the Eternal Primal Diamond, does so in a “smoother” manner, and also gives a nice chunk of stamina. What’s surprising is just how close the mitigation values are – I don’t think many of us realized exactly how much mitigation that ~0.5% avoidance on the Eternal was worth. But either way, there’s just no compelling reason to pick up the Eternal diamond – it falls short in all of the categories we care about, and just ends up being the weaker option for survivability. If the Eternal option increased block chance by 1% in addition to increasing block value, it would at least pull ahead of the Austere in raw TDR, though that still isn’t enough to offset the stamina disparity in my mind.

I’ve updated the 5.1 Tankadin Stat Sheet to include the meta gem comparison above, even though it’s not something we’re likely to change. But at least you can play around with stats that way to see what it would take to push the block meta ahead in raw TDR. I’ll also note that I’ve used a more careful calculation for the spreadsheet. Since the sheer amount of avoidance granted by the Eternal diamond is enough to significantly affect the amount of diminishing returns experienced, I’ve instead calculated the actual damage mitigation values before and after equipping each meta rather than using differentials.

You may notice that I didn’t mention the Effulgent Primal Diamond at all in this analysis. I don’t think that it’s particularly compelling for the majority of encounters in this tier. For that meta to become attractive, you’d need around 30%-40% of your total damage taken to be magical in nature. Luckily, it’s a drop-in replacement for the Austere diamond, so you can just swap them around for fights that do satisfy that constraint (Lei Shi being an obvious one).

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8 Responses to Tankadin Meta Gems – Detailed Analysis

  1. Jav says:

    Hey Theck

    What do you think of the recent bug fix to Paladins:
    “The area of effect component of Hammer of the Righteous will no longer activate Seal of Insight or Seal of Justice.”?

    It feels like a HUGE nerf to us. It’s going completely destroy our healing on fights like Wind Lord Heroic, making Paladins worthless.

    Also, could you do a post on how sacred shield/seal of insight scales with vengeance?

    Thanks and Merry Christmas!

    Jav

  2. Vayacondios says:

    “Worthless” is a bit extreme, even with that bug fix we’re super powerful for that fight. SoTR alone is a huge deal, add in the fact that our CDs are by far the best in the game for that type fight and that SoI still does a huge amount of healing, we’re in a very good place.

    Also remember that most of that healing that was being done was huge over heals, I sit at around 650k hp, one hit from the bugged AoE SoI was about 400k HP, thing is my healers almost never let me drop below 450k HP (I chain CDs so that when we have two packs+boss I ALWAYS have a CD of some kind) so at the best of times that 400k heal was at least 50% over healing.

    I didn’t even feel a change on Wind Lord this week, felt about the same on my damage taken/healing done as the last few kills.

    • Jav says:

      Good to hear. The sky isn’t falling!

      I overreacted and completely forgot that Glyph of the Battle Healer procs off damage dealt and not SoI.

      However, I’ll probably feel it a bit on Empress Heroic. It might be worth me tanking the 2 big adds, leaving the small ones to my druid OT from now on.

  3. Angelflavor says:

    Thanks for Maths Again : )
    This is the first expac I felt having 2 prot specs is worthless since the introduction of Duel Spec, because how easy you can change one talent to the other. So… I now have a Off-spec Ret. I’m finding ret to be almost as fun as prot. I see it’s your off-spec too and was wondering if you ever math out ret before?

    • Theck says:

      I don’t really math out Ret at all – the EJ & Simcraft guys do a pretty good job of that. In theory, I’d like to add Ret to the MATLAB DPS code because it would be easier than trying out rotations in Simcraft, but it’s one of those projects that’s on the back burner for lack of time.

  4. Wrathblood says:

    t15 set bonuses (on PTR) have been announced. Casting WoG now grants us +40% Block for 5 seconds per HoPo used. If nothing else, I see this improving the value of the +block meta.

  5. Haziel says:

    Ghostcrawler posted this:
    “Paladin
    - For Protection, we do have plans to try and lower the value of haste relative to dodge and parry. We don’t want to make haste terrible for paladins, but we agree that it’s odd for it to be better than more traditional tank stats. It might require a nerf to Shield of the Righteous to do this, but our goal is not to nerf survivability overall. We just wanted to provide you some context if you see odd changes to tanking abilities.”
    Source: http://us.battle.net/wow/en/forum/topic/7593740975?page=45#884

    Could it be our haste set, it’s gonna be inferior probably when compared to a mastery set ? :S (on 5.2? Hope not)

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