[情報]0/21/40大炮術 火焰vs暗影 計算

[wizardfizban (瘋法師)]

NGA上有人翻譯了這一篇很不錯的文章。

http://forums.worldofwarcraft.com/thread.html?topicId=4821924693&sid=1

原作者:Arazan

NGA原文連結:http://bbs.ngacn.com/read.php?tid=1542111&fpage=1

譯者:黑暗神

文章內容:

Okay, I've always been interested in 0/21/40 warlocks but I was more
interested in playing fire, because it simply seemed more fun.
Immolate/conflag/incinerate weaving and such... it just reminded me of the
playstyle I loved with nuking rather than just binding one key to your one
damage ability and mashing it till it's broken. Anyway, with the change to
Emberstorm, I felt like I wanted to do the math to see how 0/21/40 fire stacks
 up with 0/21/40 shadow, so the following is a mathematical symposium.

Feel free to critique any errors you may find, and for shadow I will be doing
3 calculations of various ISB uptime... that way we can get an even better
gauge of how fire and shadow compete.

OK,我一直 對0/21/40犧牲毀很感興趣,但是火系魔法更深深地吸引著我,因為它們看起
來更有趣.獻祭/點燃/燒盡一直在提醒我,我所愛的遊戲方式絕不是將一個技能設定到一個
快捷鍵上,然後不停的按這個鍵直到這個鍵被按壞為止.無論如何,這次灰燼風暴的改動,
我感覺是時候要好好的計算一下對於0/21/40天賦, 究竟是火厲害還是暗影厲害了,下面
就是這次完整的計算.對於暗影箭,我會基於3個不同的概率,多次計算強化暗影箭這個天
賦對於暗影箭的提升,這樣更有助於 我們比較暗影箭與燒盡的DPS能力.如有錯誤敬請指出.

第一部分

First, the assumed spec:

http://0rz.tw/993Mv

首先,我們假定天賦如下:

http://0rz.tw/993Mv

The 2 points in intensity can be moved elsewhere, I just like the knockback
resist for pulse aoe. Note that this build can do EVERYTHING currently that
0/21/40 shadow does, it just picks up the points to max out fire's
capabilities as well. Also note that the point in demo of improved imp can be
put anywhere... as a matter of fact most of the points in the first few tiers
of demo can be rearranged as they don't change dps, so they're just preference
 and don't affect the calculations.

2 點天賦:強烈,可以隨便加到別的地方,我加強烈只是為了防止被週期性的AOE打斷我的
施法.注意這一個天賦可以同時滿足暗影和火的需要,並且對於兩者來說,都是在DPS方面
最完美的.另外要注意的是,強化小鬼的那一點天賦也可以隨便加到哪里.這些可以隨便
加的天賦都不會影響本次計算.

Okay, first we need some assumptions and a summary, so here's a list of
assumptions:

Personal:
+15% fire/shadow damage (DS)
+10% fire damage (Emberstorm)
+20% Incinerate/Shadowbolt coefficient (SnF)
200% crits (Ruin)
+8% crit (Backlash/Devastation)
5/5 ISB
5/5 Bane
5/5 Improved Immolate
-10% incinerate cast time
71.43% base Incinerate coefficient
2.25 second Incinerate cast time
85.71% base Shadowbolt coefficient
2.5 second Shadowbolt cast time
20% Immolate DD coefficient *
65% Immolate DoT coefficient *
42.86 Conflagrate coefficient
It is also assumed that incinerate will never hit without receiving the
immolate damage bonus

OK,我們要先擬定一些計算的前提.下面是本次計算用到的前提條件:

個人方面:
+15% 火焰/暗影傷害 (惡魔犧牲)
+10% 火焰傷害 (灰燼風暴)
+20% 暗影箭/燒盡受到的法傷加成 (暗影烈焰)
200% 暴擊傷害 (毀滅)
+8% 暴擊率 (反沖+破壞)
5/5 強化暗影箭
5/5 災禍
5/5 強化獻祭
-10% 燒盡施法時間
71.43% 燒盡受到基礎法傷加成
2.25秒 燒盡施法時間
85.71% 暗影箭受到基礎法傷加成
2.5秒 暗影箭施法時間
20% 獻祭初始傷害加成
65% 獻祭DOT傷害加成

42.86 點燃受到基礎法傷加成
我們還假設所有的燒盡都受到了獻祭效果的加成.
/*譯者注:作者後面的計算中,一個獻祭後面只打6個燒盡,確實每一個燒盡都可以享受到獻
祭的加成*/

Raid:
+15% fire damage (Mage: Improved Scorch)
+10% fire/shadow damage (Warlock: CoE/CoS)
+10% shadow damage (Priest: Shadow Weaving)

Technical:
+5% shadow damage (for 25% ISB uptime calcs)
+10% shadow damage (for 50% ISB uptime calcs)
+15% shadow damage (for 75% ISB uptime calcs)

+20% shadow damage (for 100% ISB uptime calcs)

And for later on, we're going to assume the following gear stats for some
calculations:

+16% hit
33% crit
+1100 spelldamage

(Note: I'm taking an educated guess on that gear level. If it seems like it's
too good or not good enough for a decent t5/6'ish destro warlock, let me know.)

團隊方面:
+15% 火焰傷害 (火法的強化灼燒)
+10% 火焰/暗影傷害 (元素/暗影詛咒)
+10% 暗影傷害 (暗牧的暗影之波)

技術方面:
+5% 暗影傷害 (25%的時間享受強化暗影箭)
+10% 暗影傷害 (50%的時間享受強化暗影箭)
+15% 暗影傷害 (75%的時間享受強化暗影箭)
+20% 暗影傷害 (100%的時間享受強化暗影箭)

另外,我們假定人物裝備為以下水平:
+16% 命中
33% 暴擊率
+1100 法術傷害

(注意:這個裝備水平是我對T5和T6級別犧牲毀術士的平均估計,如果這水平太高了或太
低了,請告訴我)

For the mathematical calculations, the following abbreviations are constant,
in order to keep track of the complex arithmetic:

SD- Spell Damage
BC - Base Coefficient
SF- Shadow and Flame
DS- Demonic Sacrifice
ES- Emberstorm
CS- Curse of Shadow
CE- Curse of Elements
MS- Improved Scorch
SW- Shadow Weaving
IS- Improved Shadowbolt

為了簡化後面的計算,我們為下面的辭彙設定簡稱:

SD - 法術傷害
BC - 基礎加成
SF - 暗影烈焰
DS - 惡魔犧牲
ES - 灰燼風暴
CS - 暗影詛咒
CE - 元素詛咒
MS - 強化灼燒
SW - 暗影之波
IS - 強化暗影箭

Nuke Comparisons:

Incinerate:

( 0.7143 BC + 0.2 SF ) * 1.15 MS * 1.1 ES * 1.1 CE * 1.15 DS = 1.4631 or
146.31% true coefficient, making it 65.03% per second.


Shadowbolt (25% ISB uptime):

( 0.8571 BC + 0.2 SF ) * 1.1 SW * 1.1 CS * 1.15 DS * 1.05 IS = 1.5445 or
154.45% true coefficient, making it 61.78% per second.


Shadowbolt (50% ISB uptime):

( 0.8571 BC + 0.2 SF ) * 1.1 SW * 1.1 CS * 1.15 DS * 1.1 IS = 1.6181, or
161.81% true coefficient, making it 64.72% per second.


Shadowbolt (75% ISB uptime):

( 0.8571 BC + 0.2 SF ) * 1.1 SW * 1.1 CS * 1.15 DS * 1.15 IS = 1.6916, or
169.16% true coefficient, making it 67.64% per second.


Shadowbolt (100% ISB uptime):

( 0.8571 BC + 0.2 SF ) * 1.1 SW * 1.1 CS * 1.15 DS * 1.2 IS = 1.7651, or
176.51% true coefficient, making it 70.60% per second.

火力比較:

燒盡:
( 0.7143 BC + 0.2 SF ) * 1.15 MS * 1.1 ES * 1.1 CE * 1.15 DS = 1.4631 或
146.31% 實際加成, 每秒加成65.03%.

暗影箭 (25%享受強化暗影箭):
( 0.8571 BC + 0.2 SF ) * 1.1 SW * 1.1 CS * 1.15 DS * 1.05 IS = 1.5445 或
154.45% 實際加成, 每秒加成61.78%.

暗影箭 (50%享受強化暗影箭):
( 0.8571 BC + 0.2 SF ) * 1.1 SW * 1.1 CS * 1.15 DS * 1.1 IS = 1.6181 或
161.81% 實際加成, 每秒加成64.72%.

暗影箭(75%享受強化暗影箭):
( 0.8571 BC + 0.2 SF ) * 1.1 SW * 1.1 CS * 1.15 DS * 1.15 IS = 1.6916 或
169.16% 實際加成, 每秒加成67.64%.

暗影箭(100%享受強化暗影箭):
( 0.8571 BC + 0.2 SF ) * 1.1 SW * 1.1 CS * 1.15 DS * 1.2 IS = 1.7651 或
176.51% 實際加成, 每秒加成70.60%.

So we see that at some ISB uptime between 50% and 75%, shadowbolt overtakes
incinerate. In fact, we can calculate where with:

( .7143 IBC + 0.2 SF ) * 1.15 MS * 1.1 ES * 1.1 CE * 1.15 DS / 2.25 = (
0.8571 + 0.2 SF ) * 1.1 SW * 1.1 CS * 1.15 DS * X IS / 2.5

And solving for X (where X is the %damage increase from ISB)-


0.65026667 = 0.58838186 * X

X = 1.105178

This means the damage contribution from ISB must be 1.105178, which
translates to 52.589% ISB uptime.

我們可以看到,暗影箭享受的加成超過燒盡的地方是在強化暗影箭享受50%和75%之間的某
一處.
實際上,我們可以這樣計算一下:

( .7143 IBC + 0.2 SF ) * 1.15 MS * 1.1 ES * 1.1 CE * 1.15 DS / 2.25 = (
0.8571 + 0.2 SF ) * 1.1 SW * 1.1 CS * 1.15 DS * X IS / 2.5

並且解出X的值, (X表示強化暗影箭貢獻的傷害百分比)

0.65026667 = 0.58838186 * X

X = 1.105178

這表示暗影箭要想在享受的加成上超過燒盡,強化暗影箭為我們帶來的實際加成應該大
於1.105178, 實際上就是要有52.598%以上的機率享受強化暗影箭.



第二部分:DPS/DPM比較

Okay, condensing the damage increases, we get that fire spells get a general
1.600225 multiplier buff to their damage + coefficient, and shadow spells get
a 1.3915 multiplier buff to their coefficient + damage, NOT counting ISB.

So, let's set up a few rotations and calculate some dpm and dps using the
previously mentioned gear stats. First, shadow:

OK,讓我們來考慮傷害加成,我們算出火系法術從各類buff上得到1.600225的加成,暗影
法術如果不考慮強化暗影箭的話,從各類buff上享受1.3915的加成.

那麼,讓我們基於前面提到的裝備水平來做一些dpm和dps方面的運算.

Shadowbolt spam:

{ [ ( 572 + 1.0571 * 1100 ) * 1.3915 * ISB ] * 1.33 (crit) } * 0.99:


         dps      dpm
25% ISB uptime      1335      7.947
50% ISB uptime      1399      8.325
75% ISB uptime      1462      8.703
100% ISB uptime      1526      9.081

暗影箭數據:
{ [ ( 572 + 1.0571 * 1100 ) * 1.3915 * ISB ] * 1.33 (crit) } * 0.99:
         dps   dpm
25%享受強化暗影箭      1335   7.947
50%享受強化暗影箭      1399   8.325
75%享受強化暗影箭      1462   8.703
100%享受強化暗影箭      1526   9.081

Corruption, Shadowbolt x7 (19.5 seconds total)

( 900 + .936 * 1100 ) * 1.3915 * ISB * .99 + ( { [ ( 572 + 1.0571 * 1100
 ) * 1.3915 * ISB ] * 1.33 (crit) } * 0.99 ) * 7:


         dps      dpm
25% ISB uptime      1341      7.901
50% ISB uptime      1405      8.277
75% ISB uptime      1469      8.654
100% ISB uptime      1533      9.030

腐蝕, 暗影箭 x7 (共19.5秒)

( 900 + .936 * 1100 ) * 1.3915 * ISB * .99 + ( { [ ( 572 + 1.0571 * 1100
 ) * 1.3915 * ISB ] * 1.33 (crit) } * 0.99 ) * 7:

         dps   dpm
25%享受強化暗影箭      1341   7.901
50%享受強化暗影箭      1405   8.277
75%享受強化暗影箭      1469   8.654
100%享受強化暗影箭      1533   9.030

/*譯者注:這裏顯示出,在這個裝備水平下,保持腐蝕對DPS有提高的作用*/

And now, Fire:

Immolate, Incinerate x6 (15 seconds total)

[ ( 327 + 0.2 * 1100 ) * 1.600225 * 1.25 * 1.33 * .99 ] + ( 615 + .65 * 1100 )
 * 1.600225 *.99
+
[ ( 599 + .9143 * 1100 ) * 1.600225 * 1.33 * .99 ] * 6

dps: 1589
dpm: 9.256

下面來看看火系魔法:

獻祭,燒盡 x6 (共15秒)

[ ( 327 + 0.2 * 1100 ) * 1.600225 * 1.25 * 1.33 * .99 ] + ( 615 + .65 * 1100 )
 * 1.600225 *.99
+
[ ( 599 + .9143 * 1100 ) * 1.600225 * 1.33 * .99 ] * 6

dps: 1589
dpm: 9.256

Immolate, Incinerate x6, Conflagrate (16.5 seconds total, note: you will only
get 4/5 immolate dot ticks with this rotation)

[ ( 327 + 0.2 * 1100 ) * 1.600225 * 1.25 * 1.33 * .99 ] + ( 615 + .65 * 1100
) * 1.600225 *.99 * .8
+
[ ( 599 + .9143 * 1100 ) * 1.600225 * 1.33 * .99 ] * 6
+
( 650 + .4286 * 1100 ) * 1.600225 * 1.33 * .99

dps: 1562
dpm: 8.95

獻祭, 燒盡 x6, 點燃 (共16.5秒, 注意:你的獻祭DOT會少跳一下)

[ ( 327 + 0.2 * 1100 ) * 1.600225 * 1.25 * 1.33 * .99 ] + ( 615 + .65 * 1100 )
 * 1.600225 *.99 * .8
+
[ ( 599 + .9143 * 1100 ) * 1.600225 * 1.33 * .99 ] * 6
+
( 650 + .4286 * 1100 ) * 1.600225 * 1.33 * .99

dps: 1562
dpm: 8.95

Immolate, Incinerate x4, Conflagrate (12 seconds total, note: you will only
get 3/5 immolate dot ticks with this rotation)

[ ( 327 + 0.2 * 1100 ) * 1.600225 * 1.25 * 1.33 * .99 ] + ( 615 + .65 * 1100 )
 * 1.600225 *.99 * .6
+
[ ( 599 + .9143 * 1100 ) * 1.600225 * 1.33 * .99 ] * 4
+
( 650 + .4286 * 1100 ) * 1.600225 * 1.33 * .99

dps: 1505
dpm: 8.322

At this level of gear in 0/21/40 fire, casting Conflagrate is a waste of time
and mana... no matter whether you force it and cast it whenever it's up, or
simply use it to eat the last immolate dot tick, you will do more damage
simply casting immolate and incinerate, and do so at better DPM.

獻祭, 燒盡 x4, 點燃 (共12秒, 注意:你的獻祭DOT會少跳2下)

[ ( 327 + 0.2 * 1100 ) * 1.600225 * 1.25 * 1.33 * .99 ] + ( 615 + .65 * 1100 )
 * 1.600225 *.99 * .6
+

[ ( 599 + .9143 * 1100 ) * 1.600225 * 1.33 * .99 ] * 4
+
( 650 + .4286 * 1100 ) * 1.600225 * 1.33 * .99

dps: 1505
dpm: 8.322

這裏可以看出,在這個裝備水平下,0/21/40犧牲毀天賦,施放"點燃"法術去結束獻祭是浪
費時間又浪費魔法的行為,不管你何時施放它.

Summary: At +16% spellhit, 1100 spelldamage, and 33% crit, shadow 0/21/40
casting corruption and spamming shadowbolt with 100% ISB uptime will deal
LESS damage per second than 0/21/40 fire using an immolate / incinerate x6
rotation, AND do said less damage with remarkably worse damage per mana!

總結: 在+16%命中,1100法傷,33%暴擊,0/21/40天賦的情況下,放腐蝕和暗影箭的輸出方式
,即使100%享受強化暗影箭效果,也還是不如放獻祭和燒盡的方式dps和dpm高.

--
「你要我做什麼？我不能......哦，可惡......」哈普羅一把抓住本資費，他正徒勞無功
地想把自己和雷桑拉上飛船。「你那隻龍呢？」哈普羅把老人拉上來，焦急地問他。

「基隆？」本資費像個被嚇呆的貓頭鷹，對著哈普羅猛眨眼睛。「好主意！聽說那裡的夜
巿不錯── 」
　　　　　　　　　　　　　　　　　　　　　　　　　　　　死亡之門─精靈之星

--
※ 發信站: 批踢踢實業坊(ptt.cc) 
◆ From: 140.128.140.193
推 RpRp:純推  但是玩術士還是喜歡有暗影的感覺  黑黑的很酷
推 PTTjoker:好文 不過毀術都要超強裝備才能玩 真可惜- -
推 foodfood:ㄧ個問題...灰燼風暴到底改了啥??
→ fewhy:漂亮的計算... 隨便一改火系果然大有可為....
→ fewhy:施法速度-10%
推 jerryou:sry 我end了..
推 stevey:什麼時候改的?還是是PTR上面的改動?
→ fewhy:2.4 即將改變
→ Gunsroses:第二部分看不大懂..
→ fewhy:簡單來說 第一部分在算哪個法傷加成吃比較大
→ fewhy:基本上來說如果秒傷加成太差的 到後期都會變很難用
→ fewhy:像是現在的燃盡
→ fewhy:第二部分就是去考慮實際的攻擊循環 以及法術的基礎傷害
→ fewhy:或是一些固定值的加成(譬如燃盡在獻祭時會多打xx)
→ fewhy:就可以算出實際上用哪系的效率(dps, dpm)會比較好
→ fewhy:結論是火系都強一點 但是暗系還有團隊buff效果
推 Gunsroses:推
推 fewhy:推一下好了
→ crecent:為何要放腐蝕阿??
→ crecent:看到了 眼殘