Combat Ratings at level 80 - Page 10

nightcrowler · 09/23/08, 5:09 AM

It could be interesting to notice if talents like survival of the fitness (feral druid, +6% all stats) or Blessing of Kings once multiplied by the base agility are affected by diminushing returns or not (aka, 87 base agility +SoF+BoK = 101 agility, 101-87 = 14, are those 14 agility affected by diminushing returns?).

Whitetooth · 09/23/08, 7:41 AM

The following level 80 warrior data when compared to my level 60 warrior data, shows that the cap $a$ does not change with level, so for the same class, the same formula and cap can be used for all levels.

Build: 8970
Name: Imbamoo
Level: 80
Class: Warrior
Base Defense: 300
Base Agi: 108

Defense	Dodge%	Parry%	Increased Dodge%	Increased Parry%
400	4.9323997497559	5.0000000000000	0.0000000000000	0.0000000000000
419	5.7202720642090	5.7817568778992	0.7878723144531	0.7817568778992
437	6.4537920951843	6.4987540245056	1.5213923454284	1.4987540245056
453	7.0955438613892	7.1176638603210	2.1631441116333	2.1176638603210
474	7.9235496520996	7.9048829078674	2.9911499023437	2.9048829078674

Build: 8970
Name: Whitetooth
Level: 60
Class: Warrior
Base Defense: 300
Base Agi: 83

Defense	Dodge%	Parry%	Increased Dodge%	Increased Parry%
400	7.0076994895935	5.0000000000000	0.0000000000000	0.0000000000000
419	7.7955713272095	5.7817568778992	0.7878718376160	0.7817568778992
437	8.5290918350220	6.4987540245056	1.5213923454285	1.4987540245056
453	9.1708440780640	7.1176638603210	2.1631445884705	2.1176638603210
474	9.9988489151	7.9048829078674	2.9911494255066	2.9048829078674

The variances in Increased Dodge% is the result of IEEE754 rounding effect.

Whitetooth · 09/23/08, 8:26 AM

Now we have everything we need, we're ready to do some multi stat calculations.

Current Stats:
Level 60 warrior
Base defense: 300
Base dodge%: 7.0076994895935
Base parry%: 5
Dodge rating: 0
Parry rating: 0
Base Agility: 83

Put on some gear which gives
+8 Defense
+24 Dodge Rating
+20 Parry Rating
+21 Agility

How much Dodge% and Parry% do I have now?

Solution:
For a level 60 Warrior
1 Defense = 0.04% Dodge + 0.04% Parry (the rest are not important for this problem)
12 Dodge Rating = 1% Dodge
15 Parry Rating = 1% Parry
1 Agility = 0.0427% Dodge

$Dodge=8*0.04+\frac{24}{12}+21*0.0427=3.2167$
$Parry=8*0.04+\frac{20}{15}=1.653333333$

Dodge Cap $C_D=88.131540$
Parry Cap $C_P=47.003518$

$Dodge_{DR}=\frac{1}{\frac{1}{C_D}+\frac{0.956}{Dodge}}=3.241011307$
$Parry_{DR}=\frac{1}{\frac{1}{C_P}+\frac{0.956}{Parry}}=1.668054461$

Add the base values and we have:
Dodge = 10.2487108
Parry = 6.668054461

Answer: (These are the values taken in game)
Dodge = 10.248710632324
Parry = 6.6680541038513

jowyattreides · 09/23/08, 11:59 AM

Originally Posted by Whitetooth

1 Defense = 0.04% Dodge + 0.04% Parry (the rest are not important for this problem)

Does this mean, that miss chance from defense is not subject to diminishing returns?

Selmarix · 09/23/08, 12:22 PM

Originally Posted by jowyattreides

Does this mean, that miss chance from defense is not subject to diminishing returns?

Miss is very likely subject to diminishing returns. But unlike dodge and parry there is no easy function to get the values after diminishing returns.
So we'd need someone getting hit a lot of times at one defense value to determine the cap in the formula (the $a$ ) and a lot of times at another defense value to confirm that it uses the same formula.

Rhî · 09/23/08, 1:56 PM

I guess, Paladins have another Dodge and Parry Cap? If yes, do you need some data to evaluate it?

Muphrid · 09/23/08, 1:57 PM

Okay, based on Whitetooth's results, we can conclude that the % increase in average time-to-live is given by the following expression:

$1+\Delta T/T = \left (h-a \right ) \left (h- \left (\frac{1}{a_c}+\frac{n}{a_u+\Delta a_u} \right )^{-1} - a_0 \right )^{-1}$

Where h is the chance to be hit before the generalized avoidance factor a is accounted for, a_c is the cap, n is the constant in the neighborhood of .956%, and a_u is the avoidance above base before diminishing returns, and a_0 is the base avoidance.

As $\Delta a_u$ increases, this quantity increases, indicating faster-than-exponential growth. So, in my mind, Blizzard has still not come close to fixing the problem. Avoidance is still better the more you stack it, particularly since the different avoidance stats don't share DRs. The only thing this will accomplish is encouraging tanks to stack a variety of avoidance stats, which for some is impossible.

Selmarix · 09/23/08, 2:11 PM

Originally Posted by Rhî

I guess, Paladins have another Dodge and Parry Cap? If yes, do you need some data to evaluate it?

They might, but they can dodge, parry and be missed like warriors so they don't really need a higher dodge cap like druids.
Some data to evaluate it will help though. With the formula known now few data points are enough to determine the caps. My guess is that they will be equal or close to the warrior values.

Deathknights should be interesting though. With their strength to parry conversion they might have a higher parry and a lower dodge cap.

Rhî · 09/23/08, 2:30 PM

Originally Posted by Selmarix

They might, but they can dodge, parry and be missed like warriors so they don't really need a higher dodge cap like druids.
Some data to evaluate it will help though. With the formula known now few data points are enough to determine the caps. My guess is that they will be equal or close to the warrior values.

Deathknights should be interesting though. With their strength to parry conversion they might have a higher parry and a lower dodge cap.

Valid Datapoints should look like? I can give you some with my lvl 70 Paladin.

Selmarix · 09/23/08, 2:58 PM

First the data without any equipment (base values), then several with different amounts of defense gear without agility on it. Then some with agility.

Rhî · 09/23/08, 3:27 PM

LVL70 Bloodelf Paladin
AGI Defense Dodge R. Dodge % Parry R. Parry %
79 350 0 6,45 0 5
79 366 44 9,45 0 5,66
79 371 74 11,16 0 5,86
79 379 97 12,57 0 6,18
87 403 97 13,72 0 7,12
92 412 97 14,21 0 7,46
109 429 131 16,87 0 8,09
109 502 288 25,03 75 13,02

No idea how to format it, sry.

Malazaar · 09/23/08, 3:33 PM

Originally Posted by Rhî

No idea how to format it, sry.

Use the table tag:

LVL70 Bloodelf Paladin

AGI	Defense	Dodge R.	Dodge %	Parry R.	Parry %
79	350	0	6.45	0	5
79	366	44	9.45	0	5.66
79	371	74	11.16	0	5.86
79	379	97	12.57	0	6.18
87	403	97	13.72	0	7.12
92	412	97	14.21	0	7.46
109	429	131	16.87	0	8.09
109	502	288	25.03	75	13.02

Whitetooth · 09/23/08, 3:53 PM

Originally Posted by Rhî

Valid Datapoints should look like? I can give you some with my lvl 70 Paladin.

For those that would like to contribute with data, may I suggest using the following command I formated for obtaining more precise data(because 2 decimal places isn't really useful):

/print select(1, UnitDefense("player"))+select(2, UnitDefense("player")).." "..GetDodgeChance().." "..GetParryChance().." "..GetCombatRating(CR_DODGE).." "..GetCombatRating(CR_PARRY).." "..select(1, UnitStat("player", 2))

This will print your stats in your chat frame, that looks like this:
"274 4.1817655563354 6.6373481750488 0 33 92"
Which is Defense, Dodge%, Parry%, Dodge Rating, Parry Rating, Agility in that order.

The /print command is provided by AceConsole-2.0, if you have any ace2 addons you can use it.
Another helpful addon is Chatter, it gives you a button at the bottom right corner of your chat frame click on it to open a window that you can select text and use ctrl+c to copy out your test results.

And if possible, use gear with only 1 DR stat, like pure agi(no defense dodge parry) or pure defense (no agi dodge parry, but block is fine), it simplifies the calculations quite a bit.

This is how I would do it:
1. Remove all equipped items, and reset talents to 0/0/0
2. Find some pure defense gear, no agi, dodge or parry, but block is fine.
3. Put them on one by one and print the data with the command.
4. Remove all equipped items, find some pure agi gear, take the data
5. Remove all equipped items, find some pure dodge gear, take the data
6. Remove all equipped items, find some pure parry gear, take the data

Rhî · 09/23/08, 4:05 PM

Ok, I will do that. And how I use that table tag?

Whitetooth · 09/23/08, 4:12 PM

Originally Posted by Rhî

Ok, I will do that. And how I use that table tag?

You can find how to use it here: Elitist Jerks - vB Code List

Rhî · 09/23/08, 4:50 PM

Defense	Dodge %	Parry %	Dodge Rating	Parry Rating
350	6,4521999359	5	0	0	79
350	8,5035847515869	5	38	0	79
350	21,867946624756	5	338	0	79
350	8,7512865066528	5	0	0	135
350	8,5910511016846	5	0	0	131
350	6,4521999359	6,9091701507568	0	45	79
367	7,1578016281128	5,7006936073303	0	0	79
377	7,5676093101501	6,1031923294067	0	0	79

It's not much. I hope it can help. Write, if you need more data. Defense, Dodge and Agility should not be a problem. Parry rating is rare.

Scurn · 09/23/08, 5:56 PM

How does this diminishing returns affect activated abilities like Evasion? Does it add 50% on top of the current value or the base and then the effects from gear are diminished? I'm assuming that the 50% isn't diminished itself which could also be the case. I'm not sure if any other class has a built in avoidance increase like that other than Lichborne but miss is hard to test like you said above.

Whitetooth · 09/24/08, 12:44 AM

Thanks to the paladin data from Orbitus and Rhî, I've been able to varify that the cap values for both dodge and parry for paladins are the same as that of warriors.

sp00n · 09/24/08, 8:11 AM

Some data points from my rogue. Hope they are not too chaotic.
Also I had zero items with parry rating, so increase in parry is only due to defense.

Agility only

Defense	Agility	Dod Rate	Dodge %	Parry %
350	163	0	7.5600004196167	9
350	207	0	9.7531709671021	9
350	232	0	10.9700965881350	9
350	265	0	12.5451583862300	9
350	297	0	14.0395107269290	9
350	353	0	16.5795726776120	9
350	385	0	17.9898128509520	9
350	440	0	20.3467864990230	9
350	474	0	21.7631397247310	9
350	546	0	24.6649265289310	9
350	587	0	26.2607574462890	9
350	587	0	26.2607574462890	9
350	609	0	27.1008186340330	9
350	627	0	27.7799091339110	9

Dodge Rating & Agility

Defense	Agility	Dod Rate	Dodge %	Parry %	Note
350	163	0	7.5600004196167	9
350	163	38	9.5645303726196	9
350	182	57	11.4627943038940	9
350	207	73	13.4434757232670	9
350	207	373	26.8053054809570	9	Moroes' Trinket
350	207	73	63.4434776306150	9	Evasion
350	207	373	76.8053054809570	9	Moroes + Evasion

Defense & Agility

Defense	Agility	Dod Rate	Dodge %	Parry %
350	163	0	7.5600004196167	9
355	199	0	9.5565271377563	9.2021484375000
361	263	0	12.8653888702390	9.4439859390259

Defense & Dodge & Agility

Defense	Agility	Dod Rate	Dodge %	Parry %	Note
350	163	0	7.5600004196167	9
356	175	25	9.7150039672852	9.2425098419189
360	223	40	12.9347238540650	9.4037351608276
367	287	57	16.9279708862300	9.6850204467773
367	287	95	18.6843452453610	9.6850204467773
367	306	114	20.3504829406740	9.6850204467773
367	331	130	22.0919513702390	9.6850204467773
374	395	130	24.8851947784420	9.9652166366577
379	431	130	26.4372673034670	10.1646947860720
379	479	130	28.2508735656740	10.1646947860720
379	511	130	29.4313697814940	10.1646947860720
379	562	130	31.2673358917240	10.1646947860720
379	633	130	33.7343673706050	10.1646947860720
379	681	130	35.3463897705080	10.1646947860720
379	718	130	36.5595855712890	10.1646947860720
379	772	130	38.2859992980960	10.1646947860720
379	794	130	38.9747772216800	10.1646947860720
379	809	130	39.4396820068360	10.1646947860720	+Scroll of Agility
379	829	130	40.0536956787110	10.1646947860720	+Warp Burger
379	794	430	98.0570907592770	10.1646947860720	Evasion + Trinket without Scroll & Food
379	829	430	98.9718322753910	10.1646947860720	Evasion + Trinket with Scroll & Food
379	864	130	41.1124114990230	10.1646947860720	+Major Agility
379	864	430	99.8707809448240	10.1646947860720	Evasion + Trinket with Scroll, Food & Elixir
379	984	430	102.838478088380	10.1646947860720	+1x Mongoose & Evasion + Trinket

// Edit
I added Elixir of Major Agility and a Mongoose proc. The game shows values above 100%, even in the character sheet:

Selmarix · 09/24/08, 8:47 AM

Originally Posted by sp00n

Dodge Rating & Agility

Defense	Agility	Dod Rate	Dodge %	Parry %	Note
350	163	0	7.5600004196167	9
350	163	38	9.5645303726196	9
350	182	57	11.4627943038940	9
350	207	73	13.4434757232670	9
350	207	373	26.8053054809570	9	Moroes' Trinket
350	207	73	63.4434776306150	9	Evasion
350	207	373	76.8053054809570	9	Moroes + Evasion

Both with and without Moroes' Trinket Evasion seems to add exactly 50%. So Evasion is a non diminished flat addition similar to base dodge.
That means unlike the Sunwell Radiance solution, this solution to avoidance allows rogues to evasion tank.

Whitetooth · 09/24/08, 10:14 AM

Originally Posted by sp00n

Some data points from my rogue. Hope they are not too chaotic.
Also I had zero items with parry rating, so increase in parry is only due to defense.

Thanks for all the data, I've been able to calculate both caps for dodge and parry, but I've also found something odd in here.

First,

Dodge Cap $C_d =$ 145.5604076
Parry Cap $C_p =$ 144.9275362319

Dodge% per Agi = 0.0483805

Now, in TBC we have 0.04% dodge/parry per Defense, and 0.05284524% dodge per dodge rating at level 70.
I tried to use those values at first but that did not work out, so I had to calculate them like dodge per agi.

Lv70 Rogue	WotLK	TBC	ratio
Dodge per Defense	0.038705	0.04	0.967625
Parry per Defense	0.038705	0.04	0.967625
Dodge per Dodge Rating	0.05113465	0.052845524	0.967625

I wonder whats the Dodge% per Agi for a 70 rogue in TBC, can you run 2 data points for dodge/agi with 13 decimal places on live?

sp00n · 09/24/08, 10:15 AM

I added an Elixir of Major Agilty and a Mongoose Proc above.

Mongoose adds 120 agility. Without it (and an activated Moroes' Trinket + Evasion) I have a 99.87% dodge chance. With the added 120 agility, I'm at 102.84%. This means, those 120 agility are worth only 2.97% dodge, or 40.44 agility is needed for 1% dodge at that level.
The normal conversion rate at level 70 for a rogue is 20 agility per 1% dodge. It more than doubled.

sp00n · 09/24/08, 11:30 AM

Originally Posted by Whitetooth

I wonder whats the Dodge% per Agi for a 70 rogue in TBC, can you run 2 data points for dodge/agi with 13 decimal places on live?

Defense	Agility	Dodge Rate	Dodge %	Parry
Live:
350	166	0	8.710000038147	5
350	639	0	32.360000610352	5
PTR:
350	163	0	7.5600004196167	9
350	627	0	27.7799091339110	9

On Live I have skilled Vitality for 2% increased agility, additionally there is a 1% dodge bonus from Quickness. Both have been removed/replaced on the PTR.
On PTR, I have skilled for an additional 4% parry.

Additionally I have made a test with avoidance gear (but without consumables):

Defense	Agility	Dodge Rate	Dodge %	Parry	Note
Live:
379	810	130	48.939918518066	6.1599998474121
379	810	430	114.79357147217	6.1599998474121	Evasion + Trinket
PTR:
379	794	130	38.9747772216800	10.1646947860720

Interestingly, parry through defense seems to be slightly higher than on live if you subtract the 4% through talents.

Muphrid · 09/24/08, 11:58 AM

I think, as a consequence of the dodge and parry diminishing returns, you actually get more benefit from the stats for a very limited time. This was something I noticed (and found strange as well) in the other data sets.

Whitetooth · 09/24/08, 2:09 PM

With the new data gather by sp00n, it appears that my original assumption that $k$ =0.956 is constant is not true.

$\frac{1}{x'} = \frac{1}{c}+\frac{k}{x}}$

So far we only know that for a 70 rogue, $k$ =0.988, and for a 60 warrior, $k$ =0.956

Does k change with class or level? I think I need to go back and take a closer look, more test data from different classes and levels would be helpful.

Edit: Checked again with data from 80 warrior, and confirmed that $k$ =0.956 for warriors.
It seems that k is also dependent on class but not level.

Edit2:
A quick recap on what we know about the DR formula:

$\frac{1}{x'} = \frac{1}{c}+\frac{k}{x}}$

$x'$ is the diminished stat before converting to IEEE754.
$x$ is the stat before diminishing returns.
$c$ is the cap of the stat, and changes with class.
$k$ is is a value that changes with class.

Warrior and Paladin:
$k$ =0.956
$C_d=\frac{1}{0.011347}=88.1290208866$
$C_p=\frac{1}{0.021275}=47.0035252644$

Druid:
$k$ =0.972
$C_d=\frac{1}{0.008555}=116.8907071888$

Death Knight:
$k$ =0.99356050
$C_d=\frac{1}{0.011347}=88.12902089$
$C_p=\frac{1}{0.021690}=46.10419548$

Rogue:
$k$ =0.988
$C_d=145.5604076$
$C_p=144.9275362319$