Elitist Jerks Combat Ratings at level 85 (Cataclysm)

04/14/11, 4:23 AM   #586
sp00n
Bald Bull

Night Elf Rogue

Wrathbringer (EU)
 Originally Posted by Cards Thanks for the macro. I have tried it and gotten 1.8 attack speed though not 2.0.
Ok, that may have changed then. Last time I actually used it was back in ICC.

Stopped Playing

04/22/11, 3:26 PM   #587
Whitetooth
Piston Honda

Orc Warlock

Ner'zhul
4.1 Resilience Diminishing Returns(DR) Machanics
 Originally Posted by 4.1 Patch Notes Resilience scaling has been modified for linear returns, as opposed to increasing returns. Under the new formula, going from 30 resilience to 40 resilience gives players the same increase to survivability as going from 0 to 10. Resilience now scales in the same way armor and magic resistances do. A player with 32.5% damage reduction from resilience in 4.0.6 should see their damage reduction unchanged in 4.1. Those with less than 32.5% will gain slightly. Those with more will lose some damage reduction, increasingly so as their resilience climbs.
I've edited the first post with the final results, this post is about how I arrived at those results. So when I saw those patch notes, I thought well, this sounds like something I could do.
1. Loaded up a PTR client and started digging through the game files, and if I were lucky I could find the formula written in the lua files. Sadly, as with the avoidance diminishing returns formula, it too is implemented in a C code API.
2. Continue digging through the DBC files, I found that the Resilience conversion values for all levels has scaled down by a constant(this is before the new DR kicks in), meaning more damage reduction per Resilience point when in 4.0.6:
RatingLevel 60Level 70Level 80Level 81Level 82Level 83Level 84Level 85
Resilience(Player Damage Taken) (4.0.6)9.5833315.1121831.4237439.2235948.9594761.1119576.2808695.21492
Resilience(Player Damage Taken) (4.1.0)7.9641812.558926.1145332.5965540.6875150.7867663.392879.12785
Divide any 4.0.6 value with the 4.1.0 value results in a constant, using level 85 for example:
$95.21492/79.12785=1.203304778$
This value is actually pretty strange, because in the past when they want to change the numbers a bit they would pick a "pretty" number like 1.25 or 1.2. So why 1.203304778? I will answer this by deriving the number at the end of this post.
3. Before I can start to derive the Resilience DR formula, I will need a decent amount of data to work with. Blizzard gave us 2 APIs: GetCombatRating(16) returns your current resilience rating, and GetCombatRatingBonus(16) returns the damage reduction percentage of your current resilience rating after DR. After updating my lua library LibStatLogic with the new values I found in step 2, I can use StatLogic:GetEffectFromRating(resilience, 16) to get the damage reduction percentage of a given resilience rating before DR.
So I wrote a little addon to help me collect data while I equip and unequip my pvp gear trying to generate as many resilience values I can. Here's the addon code:
function SaveData()
local res = GetCombatRating(16)
local bonusDr = GetCombatRatingBonus(16)
local bonusOri = StatLogic:GetEffectFromRating(res, 16)
print("Resilience: "..res..", "..bonusOri..", "..bonusDr)
end
end

local f = CreateFrame("Frame")
f:RegisterEvent("PLAYER_ENTERING_WORLD")
f:RegisterEvent("COMBAT_RATING_UPDATE")

local function OnEvent(self, event, ...)
if event == "PLAYER_ENTERING_WORLD" then
end
else
SaveData()
end
end
f:SetScript("OnEvent", OnEvent)
Here's the raw data I gathered from the current PTR build 4.1.0.13914:
ResilienceDamage Reduction before DRDamage Reduction after DR
0 0 0
20 0.252755525 0.253705169
40 0.50551105 0.506766674
60 0.758266575 0.75918615
72 0.909919891 0.910330315
80 1.011022101 1.010965224
100 1.263777626 1.262105522
120 1.516533151 1.512608664
140 1.769288676 1.762476266
160 2.022044201 2.011709942
179 2.26216195 2.247896264
180 2.274799726 2.260311181
191 2.413815265 2.396773118
200 2.527555251 2.508281941
220 2.780310777 2.755623352
240 3.033066302 3.002337478
326 4.11991506 4.056095155
361 4.562237229 4.481665514
460 5.813377078 5.675227718
626 7.911247937 7.643178884
880 11.12124311 10.57519803
952 12.031163 11.38925986
1005 12.70096514 11.9837598
1007 12.72624069 12.00611523
1079 13.63616058 12.80715097
1104 13.95210499 13.08357858
1215 15.35489815 14.30037521
1238 15.64556701 14.55036532
1287 16.26481804 15.08052477
1306 16.50493579 15.28521084
1406 17.76871342 16.35440017
1440 18.19839781 16.71484162
1463 18.48906666 16.9577902
1560 19.71493096 17.97462151
1599 20.20780424 18.37993174
1707 21.57268407 19.49190962
1718 21.71169961 19.6043128
1766 22.31831287 20.09296689
1815 22.93756391 20.5887381
1826 23.07657945 20.69961144
1942 24.54256149 21.85942518
1945 24.58047482 21.88919504
2014 25.45248138 22.57076243
2042 25.80633912 22.84564252
2070 26.16019685 23.11954529
2193 27.71464333 24.31129227
2204 27.85365887 24.41696677
2261 28.57401212 24.96219626
2343 29.61030977 25.73966833
2369 29.93889195 25.9844985
2462 31.11420515 26.85364613
2505 31.65762952 27.2520529
2562 32.37798277 27.77683108
2581 32.61810052 27.95091317
2670 33.74286261 28.76078721
2700 34.1219959 29.03172013
2741 34.64014472 29.40033249
2827 35.72699348 30.16730947
2860 36.1440401 30.45939674
2878 36.37152007 30.6182035
2899 36.63691337 30.80301754
2985 37.72376213 31.5547561
2997 37.87541544 31.65899849
3104 39.2276575 32.58150188
3116 39.37931082 32.68418053
3200 40.44088402 33.39856574
3258 41.17387505 33.88740181
3357 42.4250149 34.71352131
3392 42.86733707 35.00310677
3408 43.06954149 35.13506147
3417 43.18328147 35.20916713
3465 43.78989473 35.60297315
3474 43.90363472 35.67654425
3510 44.35859466 35.96999153
3539 44.72509018 36.20540678
3542 44.7630035 36.22971113
3584 45.29379011 36.56899171
3591 45.38225454 36.62536433
3599 45.48335675 36.68972642
3621 45.76138783 36.86638714
3646 46.07733223 37.06654032
3718 46.98725213 37.63944261
A plot of the data:
4. Now here's the fun part, figuring out how to arrive at B with A. I was first mislead by the patch notes into believing that the new formula would be similar to the armor and resistance forumlas, and that the results would be linear in terms of TTL, this was not the case. Then I tried the avoidance DR formula but that didn't work either. What we're looking for is something new. We notice that for values smaller then 1, the output is greater then the input, so for input of 1 the output is likely to also be 1. And after a few cups of coffee, I came up with:

$x'=100-100\times0.99^x$

where
$x'$ is the damage reduction after DR.
$x$ is the damage reduction before DR.

When compared to the results from the in game API, its correct to the 4th decimal place.
5. Now the patch notes mentioned that a damage reduction of 32.5% in 4.0.6 should stay the same when in 4.1.0. So how much damage reduction before DR should we have for a 32.5% damage reduction after DR?
Solve: $32.5=100-100\times0.99^x$
$100\times0.99^x=67.5$
$0.99^x=0.0675$
$x\log(0.99)=\log(0.0675)$
$x=\frac{\log(0.0675)}{\log(0.99)}=39.10740833$
Now when we divide 39.10740833 with 32.5 we get:
$39.10740833/32.5=1.203304872$
Which is why the resilience conversion value was divided by 1.203304 from 4.0.6 to 4.1.0!

Even after applying the new scaling formula, resilience still gives increasing returns in terms of survivability.

Before DRAfter DR
ResilienceDamage Reduction SurvivabilitySurvivability IncreaseDamage Reduction SurvivabilitySurvivability Increase
20 0.252755525 1.00253396 0.000127342 0.253705169 1.002543505 0.000127499
40 0.50551105 1.005080794 0.506766674 1.005093479
100 1.263777626 1.012799534 0.000129966 1.262105522 1.012782382 0.000128801
120 1.516533151 1.01539886 1.512608664 1.015358399
220 2.780310777 1.028598227 0.000134058 2.755623352 1.028337097 0.000130779
240 3.033066302 1.031279388 3.002337478 1.030952679
3646 46.07733223 1.854507652 0.000442098 37.06654032 1.588979861 0.000202748
3718 46.98725213 1.886338739 37.63944261 1.603577713

Example:
The Survivability for 20 Resilience after DR is calculated as: 1/(1-0.253705169/100)=1.002543505
The Survivability increase of resilience from 20 to 40 after DR is calculated as: (1.005093479-1.002543505)/(40-20)

Last edited by Whitetooth : 04/22/11 at 6:53 PM.

Hotdogee@Ner'zhul US <Bahamut>
Author of RatingBuster

 09/03/11, 6:32 PM #588 landsoul Myrmidon Champion     Landsoul Worgen Warrior   Alterac Mountains Cataclysm Strength to Parry: This is now 27% instead of 25% after agility to dodge was removed. However, not all strength is allowed to be ocnverted. The Strength pool that is allowed to be converted is non-naked strength. For example a level 85 naked Worgen has 192 strength which is the amount that cannot be converted by the 27%. Any bonus from equipment, plate spec, buffs, etc. can be converted. >--Coaching Site--< Private coaching / Warrior Resource >--Stream--< Tues, Wed, 7 Eastern.
 01/07/12, 4:59 AM #589 Bharlin Glass Joe   Bharlin Dwarf Priest   Die Silberne Hand (EU) New to tanking and trying to understand how exactly DR on Parry/Dodge works. Let's assume a Paladin (85) has 20% Parry and 10% Dodge. According to \frac{1}{x'} = \frac{1}{c}+\frac{k}{x}} this would result in a DR value of 15.8% Parry. So let's say such Paladin parries the first attack. My understanding is, that his chance to parry the second attack will be 15.8% and to dodge the second attack would be still 10%. Is this correct so far? So now two scenarios: 1) The second attack again is parried. Parry then drops to 13,2% for the third attack, while dodge remains at 10%. 2) The second attack is dodged. Dodge drops to 9.02% - and parry? Does it go back to 20% or does it remain at 15.8% until an attack actually hits? Now, let's say two in a row are parried and the third attack actually hits - is the parry chance for the fourth attack then back up to 20%?
 01/07/12, 4:26 PM #590 Astrylian Rawr     Celestrylian Night Elf Monk   Stormrage No; DR is constant, there's nothing progressive about it. Rawr!
01/07/12, 7:02 PM   #591
Bharlin
Glass Joe

Dwarf Priest

Die Silberne Hand (EU)
 Originally Posted by Astrylian No; DR is constant, there's nothing progressive about it.
Meaning what? Perhaps you could provide some more detail and use an example in your answer.

01/07/12, 9:09 PM   #592
AceRider
Von Kaiser

Blood Elf Mage

Chamber of Aspects (EU)
 Originally Posted by Bharlin Meaning what? Perhaps you could provide some more detail and use an example in your answer.
The diminishing returns on dodge and parry are not about how many times you are hit but about how many stats are required to get the same effect. A random number example would be that with 0 DR 100stat + 100stat will always mean you dodge/parry 1%, but with DR 100stat + 100stat would mean you dodge/parry 1.5% as the more you have of each the less gain you receive.

Last edited by AceRider : 01/08/12 at 6:40 AM.

I used to be an Arcane Mage, then I took a Fireball to the knee.

 01/08/12, 8:48 AM #593 sp00n Bald Bull   Surprise Night Elf Rogue   Wrathbringer (EU) Random events in WoW don't have a memory, such things as the combat mechanic or boss loot aren't influenced by previous random events. So you won't get punished for a lucky streak of swings (say crits, or dodges), but neither does the chance increase of that one item dropping for which you've been farming for the last three weeks. The chance to drop is just the same, only your probability of actually seeing it increases the more kills you invest (although sometimes it really does feel like the game just wants to mess with you). The same is true for hits, crits and avoidance. You don't magically avoid less because the last 6 hits of that bad boss were all dodged by you lucky bastard. Stopped Playing
07/13/12, 12:41 PM   #594
arison
King Hippo

Pandaren Hunter

Windrunner
Thread necro, I guess. Here are the 86-90 numbers currently in the beta as of build 15799.

 Rating Level 60* Level 70& Level 80* Level 85* Level 86 Level 87 Level 88 Level 89 Level90 Dodge 13.8 21.76154 45.25019 176.7189 335.00000 430.00000 545.00000 700.00000 885.00000 Parry 13.8 21.76154 45.25019 176.7189 335.00000 430.00000 545.00000 700.00000 885.00000 Block 6.9 10.88077 22.62509 88.35944 112.00000 143.00000 182.00000 233.00000 295.00000 Hit 9.37931 14.79045 30.75475 120.1088 130.00000 166.00000 211.00000 269.00000 340.00000 Spell Hit 8 12.61539 26.23199 102.44574 130.00000 166.00000 211.00000 269.00000 340.00000 Crit 14 22.07692 45.90599 179.28004 228.00000 290.00000 370.00000 470.00000 600.00000 Haste 10 15.76923 32.78999 128.05716 162.00000 208.00000 264.00000 336.00000 425.00000 Expertise 2.34483 3.69761 7.68869 30.0272 130.00000 166.00000 211.00000 269.00000 340.00000 Mastery 14 22.07692 45.90599 179.28004 228.00000 290.00000 370.00000 470.00000 600.00000

Currently missing are PVP conversions (which I don't immediately have on hand).

It actually looks like the numbers changed at 85 and other levels as well, which isn't reflected above; 60-85 in this chart are current live values (borrowed from the OP) and 86+ are extracted from simcraft (which extracts them from the game's data files).

The consistent use of even numbers is a bit of a change from previous tiers, and generally is only true for 86+ (the new scaling factors at 85 are still non-integers, just different than they are now).

<Temerity> - Always recruiting. 12 hrs PST schedule - Valen#1972

07/16/12, 11:50 AM   #595
Hinalover
Piston Honda

Pandaren Monk

Kil'Jaeden
DR for cata

Verified by Theck over at Sacred Duty

All Agility based classes will have a 951.158596 Agility to Dodge rating at lvl 90. For Paladins, DKs, and Warriors, there is a 951.158596 Strength to Parry conversion at lvl 90. Monks will not have the Strength to Parry conversion.

$k$$C_p$$1/C_p$$C_d$$1/C_d$
Warrior 0.885235.5 0.004246284501061665.631440 0.01523660
Death Knight0.885235.5 0.004246284501061665.631440 0.01523660
Monk 1.42291 0.0109890109890115050.001980198019802
Druid 1.222N/A N/A 150.30.0066533599467731

${totalDodge}= {baseDodge} + \left (\frac{1}{C_d}+\frac{k}{preDodge} \right )^{-1}$

${totalParry}= {baseParry} + \frac{baseStr}{Q} + \left (\frac{1}{C_p}+\frac{k}{\frac{{totalStr}-{baseStr}}{Q} + {preParry}} \right )^{-1}$

Monk/Druid

${totalDodge}= {baseDodge} + \frac{baseAgi}{a} + \left (\frac{1}{C_d}+\frac{k}{{preDodge}+\frac{{Agi}-{baseAgi}}{a}}\right )^{-1}$

Monk Only

${totalParry}={baseParry}+ \left (\frac{1}{C_p}+\frac{k}{preParry}\right )^{-1}$

All classes have a 3% dodge baseline. Monks also have a 8.01% parry rating. DK's, Paladin's, and Warriors have a 3% parry rating baseline (Prot Paladin's get an extra 2% parry from Sanctuary), and Pallies and Warriors have a 3% Block rating. Block Rating according the GC does not have a DR component to it.

Last edited by Hinalover : 08/19/12 at 11:46 AM.

 07/20/12, 2:01 AM #596 jekoh Glass Joe   jekoh Human Paladin   Eitrigg (EU) New armor formula lvl85+ (from me) DR = Armor / ( Armor + 4037.5*level - 317117.5 )

 Elitist Jerks Combat Ratings at level 85 (Cataclysm)