# MoP Beta Mitigation Stat Weights – b15983

The last few days have seen a flurry of beta activity, but none of the builds have done anything to change our survivability calculations.

There was one significant survivability change: SotR was finally adjusted to grant the mitigation buff on-cast rather than on-hit, to the relief of tankadins everywhere. Without that change, we would have been essentially forced to cap hit and expertise before seeking any other stats just to make our active mitigation work reliably. Luckily, Ghostcrawler recognized the inequity this would produce between different tanks (given that Shield Block and Savage Defense don’t have the same drawback), and it looks like they’ve implemented that change, at least for paladins.

This is a Very Good Thing(tm), because it allows active mitigation to exhibit “skill scaling.” A good tank that’s careful with their SotR usage should be able to take less damage than a less skilled tank that plays sloppily. That goes out the window if your active mitigation ability is shackled to the RNG, though. Which means you either live (or die) with the RNG, or you cap hit and expertise to eliminate that possibility. The latter isn’t an interesting choice, because it’s hands-down better than risking a flubbed SotR at the wrong time.

So the old mechanics would have essentially imposed a 7650-rating penalty on paladins and monks – 2550 for hit-cap and 5100 for expertise hard-cap – before they could even think about pursuing other, potentially better mitigation stats. The new mechanics are far better, because they at least give us a choice. We may still gear for hit/exp to improve Holy Power generation and increase our survivability, but we’re not arbitrarily forced to by the mechanics.

But enough soapboxing. The point of bringing up that anecdote was to mention that this change has no effect whatsoever on the calculations we performed last time. Either version of the mechanics gives the same steady-state SotR buff uptime, so our formulas are still perfectly valid. We can forge ahead with these equations and start looking at how these mechanics affect our play, particularly in the gearing arena.

Avoidance Scaling

For starters, let’s consider a newly-minted L90 that has no rating from gear. He’s got 55k armor, 5% dodge, 3% parry, 8% mastery, and 0% hit, expertise, and haste. Note that these are all character sheet values since that’s what we see, but don’t worry – the code properly subtracts out boss avoidance and block negation, so the numbers we’re getting will be genuine. The stat block below summarizes all of these input conditions, and then gives the stat weights, individual mitigation factors $F_{ar}$, $F_{av}$, $F_{b}$, and $F_{s}$, and the final value for total damage reduction $1-D/D_0$:

Ar=55000, Dodge=5.0%, Parry=3.0%, mastery=8.0%
hit=0.00%, exp=0.00%, haste=0.00%

$3\Delta_{ar}= 1.1184$
$\Delta_d= 0.5423$
$\Delta_p= 0.5423$
$\Delta_\Sigma= 0.5298$
$\Delta_m= 0.5022$
$\Delta_h= 0.2254$
$\Delta_e= 0.1449$
$\Delta_s= 0.1494$

Far=0.5149, Fav=0.9950, Fb=0.9489, Fs=0.8694

TDR=61.963%

Remember that these mitigation factors $F_i$ represent the damage we take, so a value of one means its mitigating no damage. The lower the number, the more mitigation we’re getting from that mechanic. So we start out with 61.963% damage reduction, primarily from armor and Shield of the Righteous ($F_{ar}$ and $F_{s}$). Avoidance does very little because we only have 0.5% dodge and no parry, and block is only a moderate contributor because we only have ~17% block after boss negation.

The stat weights here seem to say that avoidance and mastery are far ahead of hit, expertise, and haste. And that’s certainly the case in the “no rating” scenario. Let’s see what happens if we stack some avoidance. We’ll bring our player up to 10% dodge and 20% parry on the character sheet:

Ar=55000, Dodge=10.0%, Parry=20.0%, mastery=8.0%
hit=0.00%, exp=0.00%, haste=0.00%

$3\Delta_{ar}= 0.8880$
$\Delta_d= 0.4628$
$\Delta_p= 0.4658$
$\Delta_\Sigma= 0.4550$
$\Delta_m= 0.3987$
$\Delta_h= 0.1789$
$\Delta_e= 0.1150$
$\Delta_s= 0.1186$

Far=0.5149, Fav=0.7900, Fb=0.9489, Fs=0.8694

TDR=69.800%

So we gained a little under 8% absolute TDR from 18% parry and 7% dodge. Note that this is actually a reduction of our relative damage intake by about 20.5% though [math: 100*(69.8-62.0)/(100-62.0) = 20.5%]. The avoidance mitigation factor reflects the fact that all of this extra TDR came from avoidance, as it should.

But increasing avoidance made the stat weights of everything a little smaller. That illustrates the competition between avoidance and other stats that we discussed back when the new blocking mechanics were announced. While the new mechanics make every stat’s relative mitigation independent of one another, their absolute mitigation values are intimately tied. Stacking more avoidance means you take fewer un-avoided attacks that are eligible for block, SotR, or armor mitigation. Subsequently, this means that stacking avoidance on your gear undermines all of the armor, hit, expertise, haste, and mastery you have by reducing the effectiveness of those stats.

To better illustrate the difference between absolute and relative value, consider this example: You stack some dodge to go from 10% avoidance to 40% avoidance. If you have 30% block chance, then before the change you were blocking 30% of all unavoided attacks, so out of every 100, you’d block (100-10)*0.3=27 attacks. After the change, you’re still blocking 30% of all unavoided attacks (i.e., the same relative mitigation), but there are fewer unavoided attacks to begin with. So instead of blocking 27 attacks out of every 100, you’ll block (100-40)*0.3=18 attacks. That means the absolute mitigation value of block went down.

You might ask, “OK, but why do we care? We’re still taking less damage, right?” And you’d be right, you are taking less damage. The catch is that you could be taking even less damage if you could shift any of that (now weaker) hit, expertise, or haste over into dodge and parry. Instead of encouraging a balanced gear progression, where you want to have a mixture of avoidance, mastery, and resource generation stats, it encourages picking one type stat and sticking to it. In this case, that stat is avoidance – you get your ideal mitigation by stacking dodge/parry as high as you can at the expense of the other stats.

Diminishing returns will ensure that there’s an upper limit to this, at least for dodge. The parry DR equation is forgiving enough that I doubt it will ever fall behind enough to dissuade you from stacking it, though. We can check that by simply graphing the effects as we vary dodge and parry:

These plots show pretty much what we expected from the equations: as we stack avoidance, other stats get less effective. The DR on dodge is harsh enough that it declines more rapidly than the other stats, leading to an intersection with the mastery line somewhere around 16% dodge. That’s actually good – it would at least encourage increasing both dodge and mastery.

The parry scaling isn’t as accommodating though. It decreases more slowly than the other stats, making it a “king stat.” The more of it you get, the better it is relative to everything else. At this point, one could imagine an expansion full of super-spiky tanks that stack avoidance and strength to the sky, all the while praying to the RNG gods that they don’t take multiple-hit streaks.

Active Mitigation Scaling

However, that’s not the whole story either. We could go the other way. What if we stack some hit and expertise? Let’s add 7.5% hit and 7.5% expertise to the mix:

Ar=55000, Dodge=10.0%, Parry=20.0%, mastery=8.0%
hit=7.50%, exp=7.50%, haste=0.00%

$3\Delta_{ar}= 0.8681$
$\Delta_d= 0.4525$
$\Delta_p= 0.4553$
$\Delta_\Sigma= 0.4449$
$\Delta_m= 0.4276$
$\Delta_h= 0.1789$
$\Delta_e= 0.1150$
$\Delta_s= 0.1363$

Far=0.5149, Fav=0.7900, Fb=0.9489, Fs=0.8500

TDR=70.474%

Interesting. First, note that the value of hit and expertise didn’t change. The simulation enforces the caps, but that isn’t borne out in the analytical expressions we’re using for the stat weights. To do that properly, we would have needed to use piecewise functions in the derivation, which makes things messier than they already were. We can enforce those stat weights ourselves, though, by simply not stacking more than 7.5% hit and 15% expertise.

But in any event, the point here is that hit and expertise increase survivability linearly up to their respective caps, a concept that Weeby astutely noted in an earlier discussion. There’s no soft-cap on expertise in terms of survivability. It’s worth the same amount all the way up to the hard-cap of 15%. Hit is more valuable thanks to Judgment, but it follows the same linear scaling up to its cap of 7.5%.

Note also that the stat weights of avoidance went down, while the stat weights of mastery and haste went up. Again, this is an expected consequence of the new blocking model. More hit/exp means more SotR uptime, which means normal melee attacks are less dangerous, on average. Less dangerous melee attacks make avoidance less important. Similarly, the more hit and expertise we have, the better returns we get from mastery and haste; the latter becomes more effective at increasing SotR uptime, and the former makes that SotR uptime less dangerous by making SotR more effective.

I could generate and show you hit and expertise scaling plots, but it turns out that the scaling with these particular stats is fairly weak. So we’ll skip them and move on to something more interesting. So far we’ve ignored mastery, so let’s address that. We’re not likely to be stuck at the base 8%, that’s for sure. Let’s add 12% mastery to bring it to a nice round 20% and see what that does:

Ar=55000, Dodge=10.0%, Parry=20.0%, mastery=20.0%
hit=7.50%, exp=7.50%, haste=0.00%

$3\Delta_{ar}= 0.7910$
$\Delta_d= 0.4123$
$\Delta_p= 0.4149$
$\Delta_\Sigma= 0.4053$
$\Delta_m= 0.3841$
$\Delta_h= 0.2272$
$\Delta_e= 0.1460$
$\Delta_s= 0.1730$

Far=0.5149, Fav=0.7900, Fb=0.9156, Fs=0.8026

TDR=73.099%

Mastery had a pretty big effect. Dodge and parry dropped pretty dramatically (around 10% of their value), while hit, expertise, and haste all went up significantly. Most of the logic from the last few paragraphs still applies here – making white attacks less dangerous devalues dodge/parry, while the extra mitigation boosts haste/hit/exp. Mastery actually goes down for the same reason that dodge/parry does – weakening an already weak melee hit isn’t as important as turning more strong (unmitigated) melees into weak melee hits (which is what hit/haste/exp do).

To see just how significant an effect this is, let’s look at the mastery scaling plot:

Whoa. These stat weights are really sensitive to mastery. It’s still not enough to bring haste and expertise up to the level of dodge and parry, but it certainly narrows the margin. That said, it’s unlikely we’re going to be able to reach 50 mastery any time soon.

The one stat we haven’t really looked at is haste. Haste happens to be one of our cheaper stats, so let’s add 15% haste and see what happens:

Ar=55000, Dodge=10.0%, Parry=20.0%, mastery=20.0%
hit=7.50%, exp=7.50%, haste=15.00%

$3\Delta_{ar}= 0.7618$
$\Delta_d= 0.3971$
$\Delta_p= 0.3996$
$\Delta_\Sigma= 0.3904$
$\Delta_m= 0.4158$
$\Delta_h= 0.2613$
$\Delta_e= 0.1680$
$\Delta_s= 0.1730$

Far=0.5149, Fav=0.7900, Fb=0.9156, Fs=0.7730

TDR=74.091%

Haste and mastery show a lot of synergy here. Fifteen percent haste was enough to boost mastery to our #1 stat, and that’s after stacking 20% of it (remember that mastery is self-deprecating, it’s the emo kid of our stats). Let’s see how the plot of that looks:

The strong synergy between haste, mastery, hit, and expertise is even more apparent here. Again, it’s not enough to make hit or expertise catch up to the avoidance juggernaut, but it does vault mastery ahead.

Out of curiosity, what if we knock our avoidance back down a notch and put more itemization into these synergistic stats. We’ll drop parry down to 10% and dodge down to 7% to simulate getting very little dodge and parry from gear (Strength alone is probably enough to give us 10% parry). We’ll bump haste up to 25% and mastery up to 25% as well, and keep our 7.5% hit and expertise:

Ar=55000, Dodge=7.0%, Parry=10.0%, mastery=25.0%
hit=7.50%, exp=7.50%, haste=25.00%

$3\Delta_{ar}= 0.8249$
$\Delta_d= 0.4066$
$\Delta_p= 0.4069$
$\Delta_\Sigma= 0.3975$
$\Delta_m= 0.4897$
$\Delta_h= 0.3589$
$\Delta_e= 0.2307$
$\Delta_s= 0.2186$

Far=0.5149, Fav=0.9200, Fb=0.9033, Fs=0.7286

TDR=71.946%

Now, these are just rough estimates of stat levels, but you can already see what’s happening. The positive feedback between mastery, haste, hit, and expertise are bringing all of them up and bringing dodge and parry down. The TDR value isn’t as high as when we were emphasizing dodge and parry, but this setup would give us more consistent, and perhaps more importantly, more controllable mitigation.

Talents

And for those that are curious, here’s what Divine Purpose does to that situation:

Ar=55000, Dodge=7.0%, Parry=10.0%, mastery=25.0%
hit=7.50%, exp=7.50%, haste=25.00%

$3\Delta_{ar}= 0.7224$
$\Delta_d= 0.3561$
$\Delta_p= 0.3564$
$\Delta_\Sigma= 0.3481$
$\Delta_m= 0.5899$
$\Delta_h= 0.4785$
$\Delta_e= 0.3076$
$\Delta_s= 0.2915$

Far=0.5149, Fav=0.9200, Fb=0.9033, Fs=0.6381

TDR=75.430%

Divine Purpose heavily supports the mastery/haste machine, further devaluing dodge and parry. While it’s not the most attractive talent in terms of overall mitigation, it has a huge effect on our stat weight priorities.

For completeness, here’s what the stat weights looks like under Holy Avenger. Note that this is only during the period when Holy Avenger is active, it’s not a time-weighted average of on/off cycles:

Ar=55000, Dodge=7.0%, Parry=10.0%, mastery=25.0%
hit=7.50%, exp=7.50%, haste=25.00%

$3\Delta_{ar}= 0.5095$
$\Delta_d= 0.2512$
$\Delta_p= 0.2513$
$\Delta_\Sigma= 0.2455$
$\Delta_m= 0.7982$
$\Delta_h= 0.0000$
$\Delta_e= 0.0000$
$\Delta_s= 0.0000$

Far=0.5149, Fav=0.9200, Fb=0.9033, Fs=0.4500

TDR=82.672%

Hit, expertise, and haste lose all value in this situation because SotR maintains 100% uptime. It’s no surprise that mastery wins in that scenario, or that dodge and parry suffer badly.

And finally, here’s what Sanctified Wrath does (again, this is during the uptime, it’s not a time-weighted average):

Ar=55000, Dodge=7.0%, Parry=10.0%, mastery=25.0%
hit=7.50%, exp=7.50%, haste=25.00%

$3\Delta_{ar}= 0.7287$
$\Delta_d= 0.3592$
$\Delta_p= 0.3595$
$\Delta_\Sigma= 0.3512$
$\Delta_m= 0.5838$
$\Delta_h= 0.4614$
$\Delta_e= 0.1730$
$\Delta_s= 0.2870$

Far=0.5149, Fav=0.9200, Fb=0.9033, Fs=0.6436

TDR=75.216%

Sanctified Wrath is fairly similar to Divine Purpose. It shifts the rotation around some (J>CS becomes the new priority for holy power generation), and the higher Holy Power income rate boosts SotR uptime, which buffs mastery/haste/hit/exp.

Conclusions (?)

That’s all I’m going to say on the topic for now. Mel has promised me he was going to make a post about gearing in this paradigm, and I don’t want to steal his thunder. The main points I wanted to illustrate in this article were that:

1. Our stat weights were quite volatile, subject to shuffling depending on what stats we already have, and
2. There is a constant tug-of-war between avoidance and the “active mitigation” stats: haste, mastery, hit, and expertise.

Suffice to say, the volatility in our stat weights give us a lot of options to choose from when determining which stat allocation scheme we want to pursue. We’ll see if there’s anything more for me to add after Mel has said his piece.

I made the comment earlier that the active mitigation stats might give us more “reliable” mitigation, but didn’t back that up with data. These calculation give us very good estimates of the mean value of each stat, but give us no information about the standard deviation. And deviation/variance statistics are the way you’d evaluate the reliability or “smoothness” of damage intake. The Monte-Carlo code is the ideal tool for that, so in the meantime I hope to get the Monte-Carlo code updated so that we can do some analysis of the variances

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### 46 Responses to MoP Beta Mitigation Stat Weights – b15983

1. Zaephod says:

ANOVA…ewww. Nothing against my stats classes, but it just completely disconnected from the world once we got to that part (even though I know it was the most relevant part, I just couldn’t ground it).

Theck, given that there is one easy way to prevent all parry, disarming, is there any of that to worry about in MOP?

• Theck says:

I don’t think any bosses have had a disarm effect in Cataclysm. I don’t expect they would in MoP either. PvP is another story, but at that point this analysis is mostly irrelevant anyhow.

2. Weebey says:

“Mastery actually goes down for the same reason that dodge/parry does – weakening an already weak melee hit isn’t as important as turning more strong (unmitigated) melees into weak melee hits (which is what hit/haste/exp do).”

I’m not sure I agree with this explanation; in fact, I think mastery and avoidance exhibit diminishing returns(*) for rather different reasons. For avoidance, the explanation is purely the explicit diminishing returns curve built into the statistic. To see this, suppose we “turn off” the diminishing returns part of avoidance, so that our (say) dodge was simply r_d/f_d. Then the derivative of D with respect to dodge rating would be

$dD/dr_d = D_0*S*F_{ar}*F_b*F_s/f_d$

None of the expressions on the right hand side depend on dodge, so the derivative is constant.

As for mastery, we currently have diminishing returns on block, so we would expect a similar effect. However, given that block is a relatively small component of mastery’s value, and the DR curve is not that steep at low levels, this doesn’t seem an adequate explanation for the mastery curve. In fact, you would see negative second derivative, even if the block change were reverted and the DR curve removed.

To see this, it helps to focus on the component of the mastery derivative coming from SoTR mitigation. That term of the derivative looks like

$D_0*S*F_{ar}*F_{av}*F_b*U_s/f_m$

where U_s is SoTR uptime. Unlike the case of avoidance, these terms are NOT all independent of mastery. The block mitigation factor F_b obviously also depends on mastery, and its presence in the above equation gives the negative second derivative. Similarly, the block derivative with respect to mastery, in addition to the explicit DR factor, has another factor, F_s, which also decreases as mastery increases. If, say, Blizzard completely removed the block component of mastery, the mastery curve would be constant.

So the TLDR would be: avoidance sees a downward sloping curve entirely because of the explicit diminishing returns on the rating to stat value conversion, while mastery sees one because it affects two different sources of damage mitigation, which interact multiplicatively.

Now, this is probably purely academic; all that really matters for gearing purposes is what happens, the why is less significant. Still, I for one was not expecting the downward sloping mastery curve, so I wanted to figure out what was going on.

(*) In an absolute sense; I actually prefer to think in relative terms (e.g. dD/D), but that would get incredibly confusing when comparing statements to the OP.

• Theck says:

“For avoidance, the explanation is purely the explicit diminishing returns curve built into the statistic.”
This is probably a misunderstanding borne of poor wording on my part. What I was saying is that mastery’s stat weight value goes down *as you increase mastery* for the same reason that dodge/parry’s stat weight value goes down *as you increase mastery*. It should be fairly clear that increasing mastery has no effect on the diminishing returns formula for dodge or parry, so that doesn’t explain the scaling I was addressing in that part of the text.

Your analysis of mastery is correct though – mastery diminishes for two reasons. The first is its own diminishing returns curve, which *is* relevant to this discussion. However, it’s also the minority contributor. The bigger effect is the interaction between block and mastery. If we write the derivatives out explicitly:
$frac{dDelta_m}{dm} propto -frac{d^2D}{dm^2} propto-frac{dPhi_b}{dm}B_vF_s -Phi_bBvfrac{dF_s}{dm}-frac{dF_b}{dm}U_s \ propto – 2Phi_bfrac{m-kbeta}{m}B_vF_s – 2Phi_b B_v U_s&s=2$.
The first term is the second derivative of $F_b$, which is the diminishing returns component. The second term is from the product of $frac{dF_b}{dm}frac{dF_s}{dm}&s=2$, one factor each from the second and third terms in $frac{dDelta_m}{dm}&s=2$. The second derivative of $F_s$ is identically zero.

It’s trivial to show that the same is true of the dodge stat weight.
$frac{dDelta_d}{dm} propto frac{d(F_bF_s)}{dm}&s=2$,
which will give the same sorts of factors.

I’m not sure the wording of my rationalization was strictly correct, though. The basic gist is that as you get more mastery, the white hits that were dangerous before become less dangerous. But the mechanic is a little more complicated than that, because it requires the interaction of block and SotR. It’s not enough to just have SotR, because the second derivative of $F_s$ is zero. In the absence of DR, the second derivative of $F_b$ would go to zero as well; DR is the only reason that term survives. But even without DR, the cross terms *do* survive, and those are the terms that dominate the negative scaling of mastery.

• Weebey says:

Exactly, and that explains the misunderstanding. I was going to comment on the cross-derivatives, but I was worried it was going to get too ugly without proper tex formatting. Also, $e^{/pi i } +1 = 0$,

• Weebey says:

Well, close enough

3. Weebey says:

On a side note, remind me again how to format tex expressions on this blog? I was under the impression that dollar signs were sufficient, but that is obviously not the case.

• Theck says:

Nope, it’s dollar sign followed by “latex.” In other words, $.latex expression$ without the period (no space between $and latex). It irritates the hell out of me too, but then again, it would probably be just as irritating (if not more) for the other bloggers if their posts got mangled every time they decided to chip in their$0.02.

4. Erik says:

a question, was that calculated with all buffs, or without (specifically the haste plots and melee 10% haste buff)

• Theck says:

It’s not assuming any buffs, necessarily. Keep in mind that there is no 10% melee haste buff. It’s a 10% *attack speed* buff, and thus only affects white swings.

• Erik says:

oh right, forgot that. thought sanctity worked like before with spell haste, but now with melee haste instead. Do you think there’s any chance tanks will get 7.5% expertise passive (when infront) for quality of life ?

• Theck says:

Sanctity does work with melee haste, just like it used to with spell haste. The difference is in the raid buff, not the ability.

As far as a parry QoL change, I wouldn’t bet on it. But you never know.

5. Ayashi says:

Seems to me that exp no longer double-diping by reducing parry and dodge at the same time really killed it’s growth. It’s pretty much always the last stat for us now, or the stat to reforge out of.

• Theck says:

Actually, that just brought it in line with hit. When Judgment was still a spell, hit and expertise were exactly equivalent for survival. That’s clear in older versions of the derivation (pre-15961).

What “killed” expertise was Judgment returning to a melee attack that can’t be dodged or parried. That introduced the asymmetry between hit and expertise, because it meant that expertise no longer affected a significant portion of our HP generation. It also eliminated the “soft-cap” of expertise as far as survival goes.

• Ayashi says:

I still wonder why don’t they just fuse hit and expertise into one stat and be done with it… Heck, for that matter dodge and parry are pretty much the same too.
With two less stats we’d have more room for haste, or even crit on tanking gear (with appropriate passive to make crit somewhat useful i guess)

6. Nooska says:

I’m thinking it would be good for a legend in regard to the different deltas, as to what they are representing – the 2 I am confused about (though I think I have them right) at $Delta_s$ and $Delta_h$ – I think I figured out that h is hit and s is haste (speed?) – but others that may not have read the previous ones in detail could probably also get confused by $Delta_Sigma$ being strength.
(I hope I did the latex correctly)

• Theck says:

Perhaps. They’re defined in the previous post for b15961, but I guess not everyone will go back and read through that.

• Nooska says:

And even though I read it, I missed it *cough*

7. Ayashi says:

Amusing tidbit : 170 STR bracer enchant can be BiS for tanking XD

On a more on topic subject: what’s the best way to compare the DR of dodge and parry directly as they grow on our gear ?
I mean, to see grafically the result of $.D_d and$.D_p as two variable at the same time instead of just one at a time as you shown in the first two grafs of the blog post.
A 3D graf with x=$.D_d, y=$.D_p and z= resulting TDR ?

• Ayashi says:

…testing … $.latexD_d • Ayashi says: yeah well, i’ll forget the nice formulas thing XD • Nooska says: no period, Theck just used it to make the result NOT latex • Nooska says: So you want a graph result of $D_d$ and $D_p$ as simultaneous variables, and a 3d graph of $x=D_d, y=D_p, z=TDR$ (Hope I didn’t screw the last latex there) • Ayashi says: testing: $D_d • Ayashi says:$latex D_d • Ayashi says: $D_d$ • Ayashi says: Aha! found it ! Thx, both of you (^_^) • Theck says: You could certainly make a 3-D graph showing TDR as a function of post-DR dodge and parry. Though you’d get the same effect by plotting $Phi_d$ and $Phi_p$, like this: https://sites.google.com/site/sacreddutyfiles/files/dodge_parry_surf.png However, if you’re only interested in comparing the DR of dodge and parry, that’s a little overkill. All you really need to know is the equation of the intersection of those two planes on the graph, which I’ve done in an earlier blog post: http://sacredduty.net/2012/07/06/avoidance-diminishing-returns-in-mop-part-3/ 8. Ayashi says: Humph, i should have guessed there was a reason to keep reading those articles (event if I couldn’t understand half of the first one… the second totally lost me >_>). Got to save that equation somewhere, thx. So, if i understand correctly, the intersec of $Phi_d$ and$Phi_p\$ which are the post-DR value of dodge and parry ratings would be the highest point of TDR avaliable given the minimal total dodge+parry rating. I’m a bit bluffed that that intersec seem to be decreasing as dodge+parry rating go up… but i guess it could just be a recycled image you used to make the point and not the actual thing.
(not that a blame you for not doing a 3d graph just for … idk, my pretty eyes i guess XD)

9. Ayashi says:

Wait no. Z is TDR in absolute value, where 1=100% damage taken. Our mitigation value. Of course we’d want that to decrease as more rating is spent to hopefully take less damage.

10. Ayashi says:

More on topic: Am i readying the 1st image correctly if i say that the crossing point between $D_d$ and $D_m$ is the point at which dodge DR makes mastery better than dodge?
If so, shouldn’t it be ~16% instead of 12% here:
“The DR on dodge is harsh enough that it declines more rapidly than the other stats, leading to an intersection with the mastery line somewhere around 12% dodge.”

12% would be, maybe, the point for $D_Sigma$ ?

I’m asking because 16% post DR dodge would be a bit over 10k dodge rating.
And if i’m reading the last graph on avoidance DR in mop part 3 correctly, where i’m seeing a 2.2parry:dodge ratio, so for the 11% dodge from rating (+5% base dodge) gives ~24%parry from rating, then that would mean that dodge+parry avoidance would suck pretty much every rating avaliable on our gear.
BUT, that would also mean that, at 16%dodge and 27%parry, mastery becomes more valuable point per point than avoidance. And in opposition your 2nd graph, TDR parry scaling, clearly shows that mastery “never” becomes better than parry, and specially not at 27%…
So, i’m a bit lost on what to think here. Am I simply miss-reading the graphs ?

• Theck says:

No, you’re right. It should be 16%. I’ll edit the text to reflect that.

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12. Noblesoft says:

Just curious if this macro is a correct representation of your formula to determine how much parry you need on your character sheet based on how much dodge you have on your character sheet:

/script DEFAULT_CHAT_FRAME:AddMessage(“Needed Parry to match Dodge: “..string.format(“%.2f”, (3.67+(235.5/65.631440)*(GetDodgeChance() – 5.01)) ))

One issue… I am coming up with lower numbers (slightly) from this macro as compared to when I calculate it myself using an ‘out of game’ calculator and the actual character sheet values. I anticipate this may be because the character sheet rounds numbers to the nearest hundredth… and the GetDodgeChance() returns a much more accurate number. Example

Char sheet dodge = 12.49%
Macro returns 30.52% Parry needed
Calculator returns 30.509…% Parry needed

Which number should I trust?

• Theck says:

The discrepancy is definitely partly due to rounding. The other part is that the 235.5 value for $C_p$ isn’t as accurate as it could be. Our latest “best estimate” is 236.1. Here’s the macro I’ve been using:
/run ChatFrame1:AddMessage(format(“Ideal pre-dr parry/dodge ratio: 3.597, yours is %.3f%%, if too high reforge more parry to dodge”,(GetParryChance()-3.67)/(GetDodgeChance()-5.01)))

Note that if you’re copy/pasting from here, the quotation marks don’t translate properly, so you’ll have to re-type them in WoW.

• Noblesoft says:

Great, thanks much Theck! That does indeed simplify the equation.

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