# Fun with math! Computing Resilience and Defense Rating

I had a very nice reader question mailed in that I thought was very relevant considering yesterdays’ mammoth bear tank gear post.

Sköll of Aerie Peak wrote in;

I want to thank you for the awesome post “Gearing your bear tank from
70 to Karazhan!”

I downloaded Rawr and made a few customizations to my gear and bearing in mind the defense cap, here are the stats I came up with

Defense Rating: 136
Resilience: 18
Dodge: 37.6434%
Miss: 6.666667%
Mitigation: 72.53479%
Dodge + Miss: 44.31007%
Total Mitigation: 82.77659%
Damage Taken: 17.22341%
Chance to be Crit: -0.123253%

with both Glyph of the Defender and exalted Scryers inscription.

As you can see the report says I’m uncrittable by raid bosses (mouseover shows 7 Defense Rating or 4 Resilience over the crit cap)

After making the calculation manually (136*0.423)+350=407/415.

I know there is some Resilience, but I don’t think it will make me crit immune together with the Defense Rating.

Best Regards!

Thanks for your email, Sköll, I appreciate it. And it is a very timely comment to make.

If you want to compute your actual Defense from Defense Rating manually, then you are correct, you can use the formula;

(DR*0.423)+350= Defense

But what you need to do to be completely accurate, is to add in the equivalent value of Resilience to the Defense Rating in that formula.

Now, we’ve covered this in other places before, but let’s go over the basics.

While Resilience and Defense also do other things, we are ONLY concerned with their function to remove the chance to be critically hit. And with 3/3 talented in Survival of the Fittest, you need 415 Defense in order to be uncrittable to level 73 raid bosses.

With that firmly in mind,

59 Defense Rating = -1% Crit.
39.4 Resilience = -1% Crit.

Therefore, 59 DR = 39.4 Resilience.

So 1 Resilience = 1.497~ Defense Rating.

Remember, we need whole numbers. So round down when actually doing the math.

In your example above, you would have 136 Defense Rating, and 18 Resilience.

18 Resilience is equal to 26~ Defense Rating. Round it down to 26.

136+26 = an equivalency of 162 Defense Rating.

(162*0.423)+350 = 418 Defense. 3 Defense over the cap.

And as a cross check against Rawr, 3 Defense = 7.092 Defense Rating.

See?

I am very glad that people are not blindly assuming that Rawr is correct, and that you are doing your own math to determine the truth. That kicks ass.

I just hope that this will help to show you that the Resilience really does make that big of a difference, and help you in doing your own math so you can figure this out on your own, assuming you are crazy, OR are unable to run Windows .NET applications.

Oh, and can I just mention again how tired I am of needing to do math, even simple math like this, just to make sure I can correctly perform my role in raids?

Well, I guess only us min/maxers that want to optimize our builds need to do this. I should shut up and just enjoy having the tools to get our job done.

Have a great day folks!

PS: What I really need to do is contact Astrylian, and interview him on what level of genius it took to make Rawr in the first place. Hmm, idea for a future WoW Insider article. Cool.

## 12 thoughts on “Fun with math! Computing Resilience and Defense Rating”

1. Amendment:

After thinking about it, I guess the other hybrids could *technically* fill all four of those roles, if you account for a tanking Shammy or even a Pally who did nothing but Holy Shock. Far be it from me to exclude any innovative Shammies and Pallies out there. After all, Panzerkin tanking seems kinda cool in its own way.

But, druids are the only ones who are generally accepted in all four roles, even at high levels.

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2. >>Has anyone ever done any full-druid-Kara raids? Hm.

My husband and I were just discussing this last night. Druids are the only class that can fill all 4 traditional roles (tank, healer, melee DPS, ranged DPS), so it would definitely be cool to try. However, unless they were all WAY overgeared, I’m guessing there are some fights that just wouldn’t work. First one that came to mind was Maiden: no dispeller for Holy Fire. (Of course, she is optional…)

It would be so fun to be part of an all-druid Kara though, just to see how far it would get.

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3. Symbiode |

I created an excel spreadsheet that allows me to plug in my defense and resilience stats, and it tells me by what percent I’m over and how many points of each I can free up. I can post it after I get off work if anyone is interested.

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4. bigbearbutt |

Grats Heilerin!

And Novo, I believe I have seen the erroneous 60 value somewhere in Elitist Jerks, but I do not have time just this second to go see if I can figure out where.

As you may nkow, Elitist Jerks are some of the best and brightest, and the general assumption is 100% of everything there is gold.

I think if I remember right, I saw that one adding error in one post there, made a mental note, double checked my calculations, said “Wow, I never expected to see that” and moved on.

I also know I’ve seen it correct over there, too.

‘d imagine whereever you saw the 60 posted was just someone that took what they saw there and didn’t check.

Or… hell, I’m guessing here. Go with the 59, though.

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5. Totally OT, but I thought I’d mention it here because I am so happy and I know that a lot of druids read your blog and will understand my excitement: My druid got her 4th piece of T4 last night, Mags dropped the chest piece and I got it: she is at 32491 armor now 🙂

I’d like to apply to be part of the hardcore-druid-tank-circle. Where can I find that app? 🙂

Has anyone ever done any full-druid-Kara raids? Hm.

Anyway: /happydance!

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6. Novo |

Here’s what I don’t get, and maybe you can point me to the relevant (and most recent) theorycrafting.

In Rawr, and from your calculations, I get that I’m 1 point under the Def. Cap, at 414 (401 def + 22 res).

Using the in-game macro that Karlenn posted, I get a negative number — ie. that I am fine as far as the Def. Cap goes.

From what I can tell, this difference comes from two different values being used for the DR:Res equivalences. I’ve seen it stated two ways — first being the 59:39.4 ratio that you give, and second being a 60:39.4 ratio which seems to mirror the in-game macro.

Any idea on where these different numbers come from, and which one is accurate? I suppose I could try it in a raid and see if I get any crits on me, but I’d rather not put my healers through that 😉

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7. Given the itemization on leather, I’ve found it much easier to maintain crit immunity using resilience. With two pieces of gladiator’s, most of my requirements are taken care of, the difference easily made up by the Violet Signet, Shermanar Great Ring, and Heavy Clefthoof Legs (I think that’s all I need) allowing me to use trinkets for sta/avoidance and enchants for dps to up threat generation.
And, if you don’t want to do the math, just tooltip over the defense and resilience boxed in your character pane and make sure, when added, they list reduction in chance to be crit as over 2.6

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8. Earendil |

Not sure, if this works or if it helps at all, but I did some Math about this. As I am more of a PvP Player due to the lack of getting more than 5 people together my gear is more PvP gear. In addition, I play a Rogue, but this might work for a Druid, too.

You said you have to have 415 defense to be immune to critts. Ok, then the formula will look like:

415 = (x * 0.423) + 350; x is defense rating

x = z * 1.497; z is resilience rating

If you insert the second formula into the first one it looks like:

415 = (z * 1.497 x 0.423) + 350

Now, if you work on this a little you get:

z = … = 102.7

I.e. you need a resilience rating of 103 to be immune to critts.

Now, if you have a look at what is available on PvP gear that has not only resilience rating, but also some other nice stats, there should be a way to get the 103 Resilience without much of a loss on other stats.

This might be a good alternative to raiding and still get very good tanking gear.

However, as said before, I do not play a warrior nor a druid and therfore have no clue whether this is working or not…

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9. bigbearbutt |

Karlenn, I actually posted that in my massive guide to Expertise, Defense Rating and Hit Rating on WoW Insider.

As nice as that macro is, remember that it tests your currently equipped status. If you are unsure as to where you’re at, that is good to give you a flat yes/no, but it doesn’t give you results you can interpret as to HOW FAR over or under the cap you are.

Using Rawr, or using the raw math, you can plan in advance, and you can see how far over or under you are, and you can change things accordingly.

With the wealth of Defense Rating and Resilience on items and gems and enchants and Glyphs and such, we have a lot of options to mix and match. It pays to plan ahead 🙂

That said… everyone that tanks should read about Defense and understand how the combat system works.

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10. Karlenn |

Oops, I just screwed up your page margins. Fixed repost:

“Not sure if you mentioned this, but WoWWiki has a nice macro which checks your gear for “uncrittability.” Depending on how trusting you are of other’s work and such . . . YMMV.

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11. Karlenn |

Not sure if you mentioned this, but WoWWiki has a nice macro which checks your gear for “uncrittability.” Depending on how trusting you are of other’s work and such . . . YMMV.

(Assuming 3/3 SoF)
/script DEFAULT_CHAT_FRAME:AddMessage(2.6-(GetCombatRatingBonus(CR_DEFENSE_SKILL)*.04+GetCombatRatingBonus(CR_CRIT_TAKEN_MELEE)),1,0.5,0)

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