AST Card cycles help

[Rongway]

Did some more maths in response to a question from someone in the Novice Network regarding Extended Balance versus Expanded Balance with Celestial Opposition.

Let a, b, c, and d be the four party members' DPS values.



Extended Balance, without Celestial Opposition

  (a DMG/s + b DMG/s + c DMG/s + 1.2 d DMG/s) × 30 s    (Balance)
+ (a DMG/s + b DMG/s + c DMG/s + 1.2 d DMG/s) × 30 s    (Extended)
+ (a DMG/s + b DMG/s + c DMG/s +     d DMG/s) × 10 s    (No buff)
= 70 (a + b + c) DMG + 82 d DMG



Light Party Expanded Balance, without Celestial opposition

  (    a DMG/s +     b DMG/s +     c DMG/s +     d DMG/s) × 30 s    (No buff)
+ (1.1 a DMG/s + 1.1 b DMG/s + 1.1 c DMG/s + 1.1 d DMG/s) × 30 s    (Expanded Balance)
+ (    a DMG/s +     b DMG/s +     c DMG/s +     d DMG/s) × 10 s    (No buff)
= 73 (a + b + c + d) DMG
= 73 (a + b + c) DMG + 73 d DMG



Extended Balance, with Celestial Opposition

  (a DMG/s + b DMG/s + c DMG/s + 1.2 d DMG/s) × 30 s    (Balance)
+ (a DMG/s + b DMG/s + c DMG/s + 1.2 d DMG/s) × 30 s    (Extended)
+ (a DMG/s + b DMG/s + c DMG/s + 1.2 d DMG/s) × 10 s    (Celestial Opposition)
= 70 (a + b + c + 1.2 d) DMG
= 70 (a + b + c) DMG + 84 d DMG



Light Party Expanded Balance, with Celestial Opposition

  (    a DMG/s +     b DMG/s +     c DMG/s +     d DMG/s) × 30 s    (No buff)
+ (1.1 a DMG/s + 1.1 b DMG/s + 1.1 c DMG/s + 1.1 d DMG/s) × 30 s    (Expanded Balance)
+ (1.1 a DMG/s + 1.1 b DMG/s + 1.1 c DMG/s + 1.1 d DMG/s) × 10 s    (Celestial Opposition)
= 74 (a + b + c + d) DMG
= 74 (a + b + c) DMG + 74 d DMG



Should I Extended Balance (no Celestial Opposition),
      or Expanded Balance (no Celestial Opposition)?

Extended Balance only:  70 (a + b + c) DMG + 82 d DMG
Expanded Balance only:  73 (a + b + c) DMG + 73 d DMG
                        =============================
                       + 3 (a + b + c) DMG -  9 d DMG
                     
The two are equal when
     3 (a + b + c) = 9 d
   3/9 (a + b + c) = d
0.3333 (a + b + c) = d

Let T0 be total of party's DPS values.
T0 = a + b + c + d
T0 = a + b + c + 0.3333 (a + b + c)
T0 = 1.3333 (a + b + c)

d = 0.3333 (a + b + c)
d = x T0
x = d / T0
x = 0.3333 / 1.3333
x = 0.25



Should I Extended Balance (no Celestial Opposition),
      or Expanded Balance with Celestial Opposition?

Extended Balance only:          70 (a + b + c) DMG + 82 d DMG
Expanded Balance + Opposition:  74 (a + b + c) DMG + 74 d DMG
                                =============================
                               + 4 (a + b + c) DMG -  8 d DMG
                     
The two are equal when
     4 (a + b + c) = 8 d
   4/8 (a + b + c) = d
   0.5 (a + b + c) = d

Let T1 be total of party's DPS values.
T1 = a + b + c + d
T1 = a + b + c + 0.5 (a + b + c)
T1 = 1.5 (a + b + c)

d = 0.5 (a + b + c)
d = x T1
x = d / T1
x = 0.5 / 1.5
x = 0.3333



Should I Extended Balance with Celestial Opposition,
      or Expanded Balance with Celestial Opposition?

Extended Balance + Opposition:  70 (a + b + c) DMG + 84 d DMG
Expanded Balance + Opposition:  74 (a + b + c) DMG + 74 d DMG
                                =============================
                               + 4 (a + b + c) DMG - 10 d DMG

The two are equal when
   4 (a + b + c) = 10 d
4/10 (a + b + c) = d
 0.4 (a + b + c) = d

Let T2 be total of party's DPS values.
T2 = a + b + c + d
T2 = a + b + c + 0.4 (a + b + c)
T2 = 1.4 (a + b + c)

d = 0.4 (a + b + c)
d = x T2
x = d / T2
x = 0.4 / 1.4
x = 0.2857

Noting that Extended Balance and serial Balance + Balance are mathematically equivalent, this leads to...


Summary

Is Celestial Opposition Available?
|
+-- Yes -- Is one person doing more than 28.57% of total party damage?
|          |
|          +-- Yes: Use Balances and Extended Balances on best DD
|          |
|          +-- No: Use Expanded Balance with Celestial Opposition
|
|
+-- No  -- Is one person doing more than 25% of total party damage?
           |
           +-- Yes: Use Balances and Extended Balances on best DD
           |
           +-- No: Use Expanded Balance

So as you can see, for Expanded Balance to be worthwhile in a light party, all four party members need to be doing pretty much equal shares of the party damage. As this is rarely the case, it's better to avoid Expanding your Balances in a light party.

[Lyrica_Ashtine]

Did some more maths in response to a question from someone in the Novice Network regarding Extended Balance versus Expanded Balance with Celestial Opposition.

I've done something similar like 8 months back. I'll just drop a link here as an addition to yours. As I haven't compared expanded with Extended/Enhanced as expanded has significantly more variables due to it's AoE nature.
Original topic
Post with the spreadsheet in question
Or just click on this link for the spreadsheet if you can't be bothered to skim through the topic:
http://i.imgur.com/qFFxkTn.png