In terms of mitigation, there have only been a few changes since we last looked at this topic (build 15739). Most of the previous derivation still works. Here’s a quick rundown of the changes we did see:

- Block was changed twice, first to remove the diminishing returns, then again to re-implement it. The new DR equation has a slightly different cap.
- We’ve determined that the avoidance diminishing returns equations are no longer symmetric. That means that dodge and parry each have slightly different stat weights, and we need to address them separately.
- Since we also have a parry contribution from Strength, it will have its own stat weight.
- Judgment is now back to being a melee attack that cannot be dodged/parried. That means that hit and expertise are no longer symmetric, and will have individual stat weights.
- Now that SotR mechanics are well-understood, we can refine our treatment of them.
- We have all of the constants required to evaluate the calculation for level 90 characters.
- Blessed Life no longer generates consistent Holy Power for prot, so I’ve removed it from the derivation.

In this post, I’m going to work through the entire calculation one more time, so that we have the whole thing in one place with all of the proper equations. You might note that some portions of the text haven’t changed much since the last version of this post – that’s because I shamelessly copy/pasted the old text, and just modified the parts that changed.

**1. The Incoming Damage Formula**

The incoming damage formula can be expressed in the following form:

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

$D$ 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, which we’ll be defining in the next few sections. To see how damage varies with different stats, we’ll want to perform implicit differentiation on $D$:

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

We divide through by $D_0$ and $S$ to normalize since they don’t depend on any of the variables we’re interested in. As with the previous calculations, we’ll define each of the $F_i$ and evaluate derivatives until we express $dF_i$ in terms of the individual rating contributions $r_i$.

**2. Armor Mitigation Factor**

The armor factor is very simple. A character with $Ar$ armor has a mitigation percentage of

$\large M_{ar} = Ar / (Ar + K)$,

where $K$ is the armor constant (58370 for a level 93 boss). The armor factor is then

$\large F_{ar} = 1-M_{ar} = K/(Ar+K)$,

and differentiating we get

$\large dF_{ar} = -dAr K / (Ar+K)^2 = \frac{-dAr}{f_{ar}}F_{ar}$.

We’ve defined $f_{ar}=(Ar+K)$ to put this in a similar form to the other expressions we’ll be deriving. You can think of $f_{ar}$ as a “rating-to-percent” conversion factor for armor, since that’s what $f_i$ will represent for rating $r_i$ throughout the calculation.

**3. Avoidance Mitigation Factor**

Avoidance has changed a little, because we now have to account for dodge and parry. We’ll represent our total avoidance $A$ as:

$\large A = A_{0}+A_d+A_p$

where $A_d$ and $A_p$ are the dodge and parry gained from sources subject to DR (rating and strength), and $A_{0}$ represents avoidance from all other sources (including base dodge and parry and the parry from base strength). The avoidance mitigation factor is then:

$\large F_{av} = 1-A$

and differentiating this gives us

$\large dF_{av} =-dA_d-dA_p$

To express the post-DR differentials in terms of rating, we need to differentiate the diminishing returns equation which links pre-DR avoidance $x$ to post-DR avoidance $X$:

$\large \frac{1}{X} = \frac{1}{C} + \frac{k}{x}$.

Differentiating, and substituting to eliminate $x$, we get:

$\large dX = \frac{dx}{k}\left ( 1-X/C \right )^2$.

$C$ and $k$ in this expression are the diminishing returns coefficients. The scale factor $k$ has the same value for both dodge and parry, $k=0.885$. However, the avoidance cap $C$ is different for each type of avoidance, so we’ll represent it with subscripts to indicate which one we mean. The cap for dodge is $C_d=0.65631440$, while the cap for parry is $C_p \approx 232$.

We can simplify the expression for $dF_{av}$ slightly by introducing avoidance dependency factors $\Phi_{d}$ and $\Phi_{p}$ based on the DR equation:

$\large \Phi_{d} = \frac{1}{k}\left ( 1-\frac{A_d}{C_d} \right )^2$

$\large \Phi_{p} = \frac{1}{k}\left ( 1-\frac{A_p}{C_p} \right )^2$

such that $dF_{av}$ is

$\large dF_{av} = -\left ( \frac{dr_d}{f_d} \right ) \Phi_{d}-\left ( \frac{dr_p}{f_p} + \frac{d\Sigma}{f_\Sigma} \right ) \Phi_{p}$.

This expression makes our earlier definition of $f_{ar}$ a little clearer, since $f_d$ and $f_p$ are our rating-to-percent conversion factors for dodge and parry (e.g., $a_d = r_d/f_d$), and $f_\Sigma$ is the strength-to-parry conversion factor. $f_d=f_p=885$, while $f_\sigma = 951.2/1.05 = 905.9$ after Kings.

**4. Block Mitigation Factor**

The block mitigation factor is pretty simple now that it’s independent of SotR. The expression for $F_{b}$ is

$\large F_{b} = 1 – B_c B_v$,

where $B_c$ is our block chance and $B_v$ is our block value. $B_v$ is constant now (30%), so the differential $dF_{b}$ only has one term:

$\large dF_{b} = -B_v dB_c$.

To evaluate $dB_c$, we need to account for diminishing returns. Let’s express $B_c$ as

$\large B_c = B_0 + \beta$,

which splits our block chance into two parts: $B_0$ covers block chance that isn’t subject to DR (base block, Guarded by the Light) and $\beta$ covers the diminished block gained through mastery. The DR equation for block can be written

$\large \frac{1}{\beta} = \frac{1}{C_b}+\frac{k}{m}$,

where $k$ is the same as in the avoidance equations and $C_b=1.491$ is the block DR cap. While we could perform the same manipulations we did for the avoidance differentials to eliminate the pre-DR value, there’s really no need. Our pre-DR block value is much more accessible than our pre-DR avoidance because it’s just our mastery. So we can skip the middle man and just solve for $dB_c$ in terms of both $\beta$ and $m$:

$\large dB_c = d\beta = dm\frac{k}{m^2}\left ( \frac{1}{C_b} + \frac{k}{m} \right )^{-2} = dm \frac{k \beta^2}{m^2}$.

If we define a block dependency factor $\Phi_b$:

$\large \Phi_b = \frac{k B_v \beta^2}{m^2}$,

we have a nice expression for $dF_{b}$:

$\large dF_{b} = -\left (\frac{dr_m}{f_{m}}\right ) \Phi_b$.

In this expression, $f_{m}$ is the mastery rating-to-percent conversion factor ($f_{m}=600$).

**5. SotR Mitigation Factor**

SotR’s mitigation is a little more involved simply because it depends on more than one stat. The expression for $F_{\rm SotR}$ is very simple though:

$\large F_{\rm SotR} = 1 – U_{s} M_{S}$

where $U_{S}$ is the uptime of the SotR mitigation buff and $M_{S}$ is the mitigation it provides in decimal form. Differentiating this is also quite simple:

$\large dF_{S} = -dU_{S} M_{S} – U_{S} dM_{S}$

We’ll need expressions for $U_{S}$ and $M_{S}$ to complete the derivation. Since $M_{S}$ is easier, we’ll start with that one.

**5.1 SotR Mitigation Factor – Mastery Contribution**

SotR gives a baseline 30% DR plus 1% for every percent of mastery, so we can write the following expression for $M_{S}$:

$\large M_{S} = 0.3 + m = 0.3+r_m/f_m$

where $r_m$ is our mastery rating and $f_{m}$ is the mastery-rating-to-percent conversion factor. The derivative of $M_{S}$ is clearly $dr_m/f_{mm}$, which is all we need to complete the mastery half of the SotR mitigation factor.

**5.2 SotR Mitigation Factor – Hit/Exp/Haste Contribution**

Since $U_{S}$ is the SotR buff uptime, it will depend on our SotR cast rate and subsequently our holy power generation rate. $U_{S}$ is quite simply the product of our SotR cast rate and the SotR buff duration,

$\large U_{S} = R_{\rm SotR} T_{\rm buff} = 3R_{\rm SotR}$,

with the caveat that $U_{S}$ has an upper bound of unity. Since both factors are positive, $U_{S}$ will always have a value between zero and one (i.e. $0<S<1$). $R_{\rm SotR}$ can be related to our holy power generation (HPG) rate by the equation

$\large R_{\rm SotR} = R_{\rm HPG}/3 + \alpha_{\rm DP}R_{\rm SotR}$,

where $\alpha_{\rm DP}$ is the Divine Purpose proc rate (0.25 if talented and 0 if not). This can be trivially re-arranged to find $R_{\rm SotR}=R_{\rm HPG}/3(1-\alpha_{\rm DP})$.

Plugging this into the expression for $U_{s}$ reveals an interesting fact:

$U_{s} = 3R_{\rm SotR} = R_{\rm HPG}/(1-\alpha_{\rm DP})$

In other words, in the absence of Divine Purpose (which we may not take, since both Holy Avenger and Sanctified Wrath are appealing talents), **our Shield of the Righteous uptime is simply our holy power generation rate**. That’s pretty convenient for players who want to do napkin math about how much hit and expertise they need/want.

The expression for $R_{\rm HPG}$ is a little more complicated, having the form,

$\large R_{\rm HPG} = (1+s)(1+\alpha_{\rm GC})\theta_m R_{\rm CS} + (1+s)\theta_r R_{\rm J}$

where $s$ is our decimal spell haste (to account for Sanctity of Battle), $\alpha_{\rm GC}$ is the proc rate of Grand Crusader, $R_{\rm CS}$ and $R_{\rm J}$ are the Crusader Strike and Judgment cast rates, and $\theta_m$ and $\theta_r$ are our melee and “ranged” hit factors defined below for $\mu$ chance to miss, $\delta$ chance to be dodged, and $\rho$ chance to be parried (each 7.5% for a level 93 boss):

$\large \theta_m = 1 – (\mu – h) – (\delta + \rho – e)$

$\large \theta_r = 1 – (\mu -h)$

It is clear from these expressions that $d\theta_m= dh+de$ and $d\theta_r = dh$. Differentiating $R_{\rm HPG}$ gives us

$\large dR_{\rm HPG} =ds \left [ (1+\alpha_{\rm GC})\theta_m R_{\rm CS} +\theta_r R_{\rm J} \right ] + d\theta_m (1+s)(1+\alpha_{\rm GC})R_{\rm CS} + d\theta_r (1+s) R_{\rm J}$

and substituting $d\theta_m$ and $d\theta_r$ to express this in terms of hit and expertise derivatives gives us

$\large dR_{\rm HPG} = ds \left [ (1+\alpha_{\rm GC})\theta_m R_{\rm CS} + \theta_r R_{\rm J} \right ] \\ + dh (1+s)\left [(1+\alpha_{\rm GC})R_{\rm CS} + R_{\rm J} \right ] \\ + de (1+s)(1+\alpha_{\rm GC})R_{\rm CS}$

Combining all of the equations in this section, we can write an expression for $dU_{S}$:

$\large dU_{S} = ds\sigma_s + dh\sigma_h + de\sigma_e$,

where $\sigma_s$, $\sigma_h$, and $\sigma_e$ are

$\large \sigma_s = \frac{(1+\alpha_{\rm GC})\theta_m R_{\rm CS} + \theta_r R_{\rm J}}{(1-\alpha_{\rm DP})}$

$\large \sigma_h = \frac{(1+s)\left [(1+\alpha_{\rm GC})R_{\rm CS} + R_{\rm J}\right ]}{(1-\alpha_{\rm DP})}$

$\large \sigma_e = \frac{(1+s)(1+\alpha_{\rm GC})R_{\rm CS}}{(1-\alpha_{\rm DP})}$

Which completes the calculation of the hit, expertise, and haste contributions.

**5.3 SotR Mitigation Factor – Combining Terms**

Combining the results of the previous two sections, we can write a final expression for $dF_{S}$:

$\large dF_{S} = – \frac{dr_s}{f_s}\Phi_s -\frac{dh}{f_h}\Phi_h-\frac{de}{f_e}\Phi_e- \frac{dr_m}{f_{mm}}\Phi_m$,

where

$\large \Phi_s = \sigma_s M_{S}$

$\large \Phi_h = \sigma_h M_{S}$

$\large \Phi_e = \sigma_e M_{S}$

$\large \Phi_m = U_{S}=R_{\rm HPG}/(1-\alpha_{\rm DP})$

It may seem a little overkill to define these $\Phi$ factors, but you’ll see the reason why I did in the next section.

**6. Bringing It All Together**

If we plug our expressions for $dF_{\rm ar}$, $dF_{\rm av}$, $F_{\rm b}$, and $dF_{\rm SotR}$ into the expression for $dD/D_0 S$, we get:

$\large \begin{align}

\frac{dD}{D_0S} &= -\frac{dAr}{f_{ar}}F_{ar}F_{av}F_{b}F_{S} – \frac{dr_d}{f_d}F_{ar}\Phi_{d}F_{b}F_{S} – \left ( \frac{dr_p}{f_p} + \frac{d\Sigma}{f_\Sigma} \right ) F_{ar}\Phi_{p}F_{b}F_{S} \\

&~~- \frac{dr_m}{f_{m}}F_{ar}F_{av}\Phi_{b}F_{S} – \frac{dr_s}{f_s}F_{ar}F_{av}F_{b}\Phi_s – \frac{dr_h}{f_h}F_{ar}F_{av}F_{b}\Phi_h \\

&~~-\frac{dr_e}{f_e}F_{ar}F_{av}F_{b}\Phi_e- \frac{dr_m}{f_m}F_{ar}F_{av}F_{b}\Phi_m

\end{align}$

Now the definitions for $\Phi_i$ should be a little more obvious – they’re each a replacement for one of the $F_i$. If we combine terms we can get fairly simple expressions for the damage reduction scale factors $\Delta_i$:

$\large \frac{dD}{D_0S} = -dAr\Delta_{ar}-dr_d\Delta_{d} – dr_p\Delta_{p} – d\Sigma\Delta_\Sigma \\-dr_m\Delta_m-dr_h\Delta_h-dr_e\Delta_e-dr_s\Delta_s$,

where

$\large \Delta_{ar} = \frac{1}{f_{ar}}F_{ar}F_{av}F_{b}F_{S}$

$\large \Delta_{d} = \frac{1}{f_d}F_{ar}\Phi_{d}F_{b}F_{S}$

$\large \Delta_{p} = \frac{1}{f_p}F_{ar}\Phi_{p}F_{b}F_{S}$

$\large \Delta_{\Sigma} = \frac{1}{f_\Sigma}F_{ar}\Phi_{\Sigma}F_{b}F_{S}$

$\large \Delta_m = \frac{1}{f_{m}}F_{ar}F_{av}\left (\Phi_b F_{S} + F_b\Phi_m\right )$

$\large \Delta_h=\frac{1}{f_h}F_{ar}F_{av}F_{b}\Phi_h$

$\large \Delta_e=\frac{1}{f_e}F_{ar}F_{av}F_{b}\Phi_e$

$\large \Delta_s = \frac{1}{f_s}F_{ar}F_{av}F_{b}\Phi_s$

**7. Plugging In Numbers**

It’s a fairly simple matter to plug in numbers and see how these values compare. I’ve updated the old derivations.m script to match the above derivation and incorporate some of the new changes in recent beta builds. I won’t bore you with all of the constant factors (I defined most of them earlier in this post, and you can just take a look at the code to see them anyhow), but our test paladin has 50k armor, 30% avoidance (20% dodge, 10% parry, no miss since bosses negate that anyway), 5% hit, 5% expertise, 5% haste, and 20 mastery, which works out to a 32.6% chance to block on the character sheet after diminishing returns (13% from base+spec, the rest from mastery). Note that we lose 4.5% dodge, parry, and block against a boss, so we subtract 4.5% from each of those numbers (e.g. in our definitions of $A$ and $B_c$). I’m also turning off Divine Purpose for these numbers.

For a fair comparison, we’ll multiply the armor factor by 4, since we get 4 armor per itemization point compared to one of any type of rating. If we plug the above numbers into the calculation, we get the values below (multiplied by $10^5$ for simplicity):

$\large 4\Delta_{ar} = 1.1528$

$\large \Delta_{d} = 0.4308$

$\large \Delta_{p} = 0.4335$

$\large \Delta_{\Sigma} = 0.4235$

$\large \Delta_{m} =0.4029$

$\large \Delta_{h} =0.2496$

$\large \Delta_{e} =0.1604$

$\large \Delta_{s} =0.1732$

What’s interesting about this result is just how close the top four stats are to one another (ignoring armor, which is far and away our best stat). Dodge and parry are neck and neck, and which one takes the lead will depend on your dodge:parry ratio. Strength will always trail parry, but only barely. Mastery isn’t very far behind in terms of TDR, though its value depends fairly significantly on hit and expertise (it’s considerably worse at low hit/exp, and gets better as we approach the cap).

Hit, expertise, and haste all fall behind a bit in TDR calculations, though it’s worth noting that the interdependence of these stats has a big effect. I’ll talk more about that in the next blog post, in which I’ll be analyzing what happens as we change the initial conditions.

**8. A Note on TDR**

I would be remiss if I didn’t include the same disclaimer about TDR as last time:

You might ask how relevant a TDR-based stat calculation will be for tanking in Mists of Pandaria. After all, we’ve harped on the relevance of TDR in severalearlierblogposts. And the truth is that we don’t really know yet, because we don’t know what raiding will look like in MoP. It depends fairly intimately on game balance and encounter design. TDR tends to be important in a few select scenarios, specifically cases where bosses don’t stress tank EH but do stress healer mana. We’ve seen that happen fairly rarely, even in Cataclysm, but there are several healing changes (including a more constrained mana pool) that may make those situations more common in Mists.

On the other hand, we’ve noted before that sometimes stamina is a more effective way to conserve healer mana than damage reduction, simply based on healer psychology. The healer who feels like they have more time to react will be able to use more of their slower, mana-efficient heals. The healer that feels like their tank is in danger of spike death will call in the big guns regardless of mana cost. That’s a difficult (if not impossible) theory to quantify, but it’s not hard to see the logic in it.

In a practical sense, this means that we should take these numbers with a grain of salt. Yes, dodge, parry and mastery will be our prime TDR stats, but we’ll have to see what the encounter landscape looks like before we can say whether they’re still attractive

survivabilitystats. For example, Mel and I have been discussing this issue for a few weeks now, and one point that’s come up several times is that TDR may undervalue hit/exp/haste. Having 75% DR on SotR instead of 60% isn’t necessarily better for survivability than having 60% DR and using the skill more often (via faster HPG). From a healer’s perspective, maybe 60% DR is “enough.” The tank with 60% DR but higher hit/exp will turn more 100k hits into 40k hits, which may be preferable to a tank that converts fewer of those 100k hits into 25k. Luckily, thatissomething we can quantify, either numerically with the Monte-Carlo or analytically with the formalism I’ve put forth in this post. I’ll hopefully get to revisit that question in a later blog post. So you hit/exp enthusiasts shouldn’t give up hope just yet!

I’m still planning on revisiting this topic once I fix up the Monte-Carlo simulation, which will let us see exactly what sort of “smoothing” effect hit/exp/haste/mastery have. But before we get to that, I want to look at how the stat weights change under different initial conditions. For example, how different are the stat weights for a player with Divine Protection talented than for one who has Holy Avenger? Or for a player who caps hit and expertise compared to a player with very low hit and expertise? That will be the topic of my next post, hopefully later this week.

Excellent update post Theck, was looking forward to this with the new builds, been a fan of your number crunching for a while. If you need any particular data for further analysis I have a plethora of WoL from almost every beta raid (10/25 normal and heroic), just pm me on maintankadin or the Midwinter site.

Slootbag

I’m mildly surprised how much better mastery is than avoidance as a TDR stat (once you factor in a level 75 talent.) Given that the factors not captured in, TDR pretty clearly favor mastery, it seems more interesting from a tuning perspective to make avoidance a much better TDR stat. A trade-off between TDR and other considerations is at least potentially an interesting gearing decision, but as it stands there is nothing appealing about avoidance.(*)

Something else I am curious about seeing in the next post: my intuition is that, as gear scales up, avoidance will start to seriously fall behind the other stats, especially mastery, as avoidance suffers from diminishing returns, whereas you have two sources of increasing returns for mastery (a linear conversion to damage reduction, and good scaling with hit/expertise/haste). My guess is that even a 13 ilevel increase would lead to a very large shift in the relative stat weights.

(*) Conditional, of course, on the initial values; we will see on Thursday, but I assume at a very low hit and avoidance levels avoidance pulls significantly ahead.

Er, avoidance deltas are at 0.43, mastery is at 0.40 but mastery is much better than avoidance ?

If anything it’s the opposite.

Maybe at hit/exp cap since those push mastery value up via HPG and SoRuptime, but we don’t have the numbers for that just yet. So i really don’t see what you base your conclusion upon.

Weebey said “when you factor in a level 75 talent”

Oh, missed that.

Well… TDR point of view, DP “only” buffs mastery up to being ~16% above avoidance stats. I mean sure it’s nice, but hardly something to write home about (ie: I have 3:1 stat weights on my SV hunter main toon atm!)

Also, TDR may undervalue hit/exp/haste, but it does also mastery. After all a 75% SoR instead of a 60% might mean more HPG, but also -15% block chance !

actually that’s too big of a trade : 15 mastery = 9000 rating = 27% exp+hit, =overhardcapped by 5% (1690rating). At most you can trade 12 mastery between touch hardcapped and 0%/0%.

So, does that 12mastery decrease translate into a flat +12% SoR uptime ? does +15%exp/+7.5%hit increase HPG by more than 12% ? I belive it does not, my napkin math says it’s about a +10% SoR

(flat increase, as in “SoR is up for an extra 10% of the whole fight”. Not multiplicative SoR uptime increase)

I don’t know where you are getting 16% from. If you look at the derivation, $U_{s} is increased by a constant factor of $/frac{1}{1-/alpha_{DP}}$, which is a 33% increase when $/alpha_{DP} = .25$. Obviously this doesn’t affect the block component of mastery, but the SoTR factor is the bulk of the value. I don’t feel like searching for it, but Theck posted preliminary numbers are on Maintankadin that showed mastery over 25% ahead of avoidance in this gear set.

Directly from the stat weight formulas, it’s napkin math so i could very well be wrong:

Delta_m = frac{1}{f_{m}}F_{ar}F_{av}left (Phi_b F_{S} + F_bPhi_mright )

Since what we look for is DP effect, anything not affected by DP is constant and can be eliminated if it’s multiplicative.

Variables are F_{ar}, F_{av}, F_{S} and F_{b}. Armor, avoidance, and block value are unaffected by selecting DP talent, and are therfor constant in this case. Only F_{S} changes.

DP effect in a direct increase of 25% of U_(s) since U_(s) = X / (1- 0.25) = 1.25 * X which means F_{S} increases by 25% ergo Delta_m by 25% too.

Delta_m non DP is 0.4029 => Delta_m with DP is 0.5036.

0.5036 / 0.4308 (dodge)= 1.17 => mastery becomes 17% more valuable than dodge

0.5036/ 0.4335 (parry)= 1.16 => mastery becomes 16% more valuable than parry

So we have a lot more parry than dodge so i went with ~16%. 16-17% would have been more apropriate ?

Anyway, assuming i’m wrong and it’s mastery = 1.25 avoidance stats on tdr point of view, i guess you do have a point.

Having mastery be:

- the “best” stat in TDR if DP talented,

- affect our survival versus magical damage (SoR buffing WoG),

- providing both a powerful flash cd (single SoR versus stuff like madness empale)

- lol-holy avenger 21s 100% SoR uptime (which could potencially go up to 70-74% physical damage reduction in t14 gear);

is … well, i’d agree if you say it might be too much, and will “force” mastery stacking again.

Erm: [i]For a fair comparison, we’ll multiply the armor factor by 4, since we get 4 armor per itemization point compared to one of any type of rating[/i]

MoP armor pot = 12000armor, STR pot = 4000STR. Alchimy shows a 3 to 1 ratio instead which pushed armor down to 0.8646. Still the “best stat”, pitty there’s no reforging into armor or armor gems!

Interesting. In Cata, armor was itemized at a 4:1 ratio. It looks like that’s been reduced to 3:1 in MoP (elixirs are also a 3:1 ratio to other secondary stats). There are no armor trinkets to compare with at this point.

I have an amusing question on mastery cap and softcaps:

My napkin elementary level math shows that mastery hardcap (100% block rate) happens at around 55k rating.

There’s also the mastery softcap of 100% physical damage reduction on SoR buff cap. Around 37k mastery, might go as low as 32k with t14 4p bonus. Maybe reachable by HC t16 full BiS if blizzard delivers on their promise of inflated stat creeping.

Now, the 1’000’000$ question is, what’s last mastery softcap value ? Which amusingly is not linked to mastery rating but to haste. I can’t wait to be able to say that mastery soft cap is XxX haste !

Or how much haste rating do we need to have 100% HPG with DP talent, 5%raidbuff (??), 7.5% hit and 15% expertise (exp may or may not be required as this blog post shows haste as more valuable than expertise)

I have noooo idea how to pump that number out of your or any equation i found so far (like i said: elementary level math )

Okay forget this, i managed to get a napkin that was whiter and longer than the average dishcloth or napkin and got something ridiculous like 52k haste at lvl 85 . Also requires some crazy 0.77s GCD lol

Yeah, Mel and I were discussing this a few days ago, and it took around 240% haste to get 100% uptime on SotR (without DP, I think).

Note: I just noticed you assume 30% block value.

Are we expected to gem the 2% armor meta, or was the 1% meta forgotten ?

I’m ignoring both metas for the purpose of this math. It’s easy enough to calculate which is better, but it would have complicated the math even further. Better to do a separate “which meta is better” calculation where you can ignore all of the other differentials.

For some reason I can’t respond directly to Ayashi’s comment, but: you at one point write that X/(1-.25) = 1.25 * X. This if of course wrong; it is equal to 1.33 * X (repeating, of course.)

This mistake is common. For instance, you sometimes see direct comparisons between the ICC buff and the DS nerf, which isn’t quite accurate. Increasing player power by 30% is not the same as reducing boss power by 30%, but instead corresponds to 1/1.3 = ..77, or a 23% reduction. DS at 25% was more “nerfed” than ICC at 30%.

Calculus aside: for |x| < 1, we have the power series expansion 1/(1-x) = 1 + x + x^2 + … So for x sufficiently small, 1/(1-x) ~ 1+x. So e.g. a 1% increase in raid dps is roughly the same as a 1% decrease in boss health, which I think is the source of the error.

Sorry to get didactic; there is nothing worse than a know-it-all…

Well, you got my mistake indeed. You do have a point, I guess we should be expecting some nudge downwards on our mastery by some point before MoP goes live.

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Question about Block mechanics, coming from Theck’s Blog.

frac{1}{beta} = frac{1}{C_b}+frac{k}{m}

is ‘m’, mastery on the tooltip (8% base for example) or Mastery Rating?

It would be great if they would tell us that they are removing or (re)implementing DR.

I was hoping I could copy-paste the formula, failure obviously

$latex m$ is mastery (i.e. 8%). Rating is always $latex r_i$ in my notation

Thanks

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