Combat Ratings at level 85 (Cataclysm) - Page 40

sp00n · 04/14/11, 4:23 AM

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.

Whitetooth · 04/22/11, 3:26 PM

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.

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.

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:

Rating	Level 60	Level 70	Level 80	Level 81	Level 82	Level 83	Level 84	Level 85
Resilience(Player Damage Taken) (4.0.6)	9.58333	15.11218	31.42374	39.22359	48.95947	61.11195	76.28086	95.21492
Resilience(Player Damage Taken) (4.1.0)	7.96418	12.5589	26.11453	32.59655	40.68751	50.78676	63.3928	79.12785

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.

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)
  if not GetResilienceDataDB[res] then
    GetResilienceDataDB[res] = res..","..bonusOri..","..bonusDr
    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
    if not GetResilienceDataDB then
      GetResilienceDataDB = {}
    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:

Resilience	Damage Reduction before DR	Damage 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:

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.
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 DR			After DR
Resilience	Damage Reduction	Survivability	Survivability Increase	Damage Reduction	Survivability	Survivability 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)

landsoul · 09/03/11, 6:32 PM

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.

Bharlin · 01/07/12, 4:59 AM

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%?

Astrylian · 01/07/12, 4:26 PM

No; DR is constant, there's nothing progressive about it.

Bharlin · 01/07/12, 7:02 PM

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.

AceRider · 01/07/12, 9:09 PM

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.

sp00n · 01/08/12, 8:48 AM

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.

♦ arison · 07/13/12, 12:41 PM

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).

Hinalover · 07/16/12, 11:50 AM

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	0.885	235.5	0.0042462845010616	65.631440	0.01523660
Paladin	0.885	235.5	0.0042462845010616	65.631440	0.01523660
Death Knight	0.885	235.5	0.0042462845010616	65.631440	0.01523660
Monk	1.422	91	0.010989010989011	505	0.001980198019802
Druid	1.222	N/A	N/A	150.3	0.0066533599467731

Paladin/DK/Warrior formulas

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

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

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.

jekoh · 07/20/12, 2:01 AM

New armor formula lvl85+ (from me)

DR = Armor / ( Armor + 4037.5*level - 317117.5 )