Under some circumstances Offense set does more critical damage than CD set
In order to be equally comparable, the primaries and secondaries before applying the sets will be identical. There is no other way to tell if a set is better than the other without this assumption.
The starting formula is then this one:
[(Base*AbilityMultiplier)*(1+Off_Mods)]*(1+Off_Bonus)*(1.5+CD_Mods+CD_Bonus))
For the Off set, 0.15 will be added in the (1+Off_Mods) bracket
For the CD set, 0.3 will be added in the (1.5+CD_Mods+CD_Bonus) bracket
To make a comparison between both sets, we’ll equal both damages. We’ll call x to the Offense bracket and y to the CD bracket.
[(Base*AbilityMultiplier)*(x+0.15)]*(1+Off_Bonus)*y = [Base*AbilityMultiplier)*(x)]*(1+Off_Bonus)*(y+0.30)
Developing the formula, we get:
(Base*AbilityMultiplier)*(x+0.15)*(1+Off_Bonus)*y = (Base*AbilityMultiplier)*(x)*(1+Off_Bonus)*(y+0.30)
(x+0.15)*y = x*(y+0.30)
xy+0.15y = xy + 0.30x
0.15y = 0.30x
y = 2x Or x = 0.5y
So both sets can get to do same damage under the condition of Offense (before sets) equaling half the Critical Damage (before sets).
Also, we can see that Off Bonus from leadership, uniques and buffs don’t affect the result.
To make the following data easier to read I’ve used (Base*AbilityMultiplier) equal to 1. So it shows the amount of times that (Base*AbilityMultiplier) the sets do. Also a 6 dot CD triangle mod is used.
With +0% CD bonus
As can be seen from the data and graph, the more initial Offense you have, the more Damage you get. CD Set is always better in this case.
With +100% CD
Partial data showing where the CD set gets higher than Offense Set (+100% CD):
As the data shows, Off set does more damage below the threshold of equal damage while CD set does more Damage above the threshold.
So for 1.085 Offense (the lowest we can get) the CD will be 2.17. If we substract the 1.5 (base) and 0.42 (triangle), then we need +25% extra CD to reach the threshold were both sets do same damage.
On the example and graph above with +100%CD, the Offense needed will be (1.5+0.42+1)/2 = 1.46
Conclusions:
If Total CD is lower than 217%, CD set will always do more critical damage
If Total CD is equal or higher than 217% then three possibilities are given:
* If Offense (before sets) is below the threshold, Offense set will do more damage.
* If Offense (before sets) is on the threshold, both sets will do same damage.
* If Offense (before sets) is above the threshold, CD set will do more damage.
Relics don’t affect these, as they modify base damage, which doesn’t affect sets relationship. The up to +13.5% CD of relics doesn’t affect the conclusions either.
There will be a moment, as +CD_Bonus gets higher, when the required Offense to get to the threshold or past the threshold will not be feasible and CD set cannot get to the damage done by Off set.
(All this post assumes no partial gear pieces as it break the premises of the equations used)
Against stupidity the gods themselves contend in vain
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I didn't check your formuli, but it looks like you're on the right track.
I guess so. I haven't said anything about CC at all.
Anyways, CC is irrelevant on the case of same critical damage or Off set doing more damage.
If both sets do same critical damage:
Off set line in chart will be above CD set from 0%CC until 99.99999% CC and then both will do same damage at 100%
If Off set does more critical damage:
Off set line in chart will be above CD set from 0%CC to 100%CC
If CD set does more damage:
Then a similar chart as the ones you provided will be needed for each CD bonus and initial offense.
It may seem that no one has understood that you can have bigger crit damage with an offense set if CD bonuses are high enough.
Let’s take an example:
Night sister acolyte can have +200CD when using her special attack (5 ni in team and 5 debuffed enemies -> 20*10= 200% ) and she’s g13r7 with 9395 special damage base.
Let’s suppose we put square, cross and arrow with offense primaries and triangle with CD. Using 6* mods that’s 8.5*4= 34 and we have no other offense secondaries.
Let’s see damage done on crit if they are a set of Critical damage:
[(Base*AbilityMultiplier)*(1+Off_Mods)]*(1+Off_Bonus)*(1.5+CD_Mods+CD_Bonus))
[(9395*1.420)*(1+0.34)]*(1+0)*(1.5+.42+.30+2)= 75440.12132
Let’s see damage done if they are a set of Offense:
[(Base*AbilityMultiplier)*(1+Off_Mods)]*(1+Off_Bonus)*(1.5+CD_Mods+CD_Bonus))
[(9395*1.420)*(1+0.34+0.15)]*(1+0)*(1.5+.42+2)= 77921.52872
So, Offense set does more damage when crit and when not crit. Making CC irrelevant in order to choose the best set as Offense Set is doing more damage regardless of CC if CD bonus is high enough.
That's pretty cool
I'm trying to follow your logic here, but the bit I've highlighted is confusing me. This part of your formula adds in Crit Damage multipliers, which assumes that you have actually scored a critical hit. The reality is that you don't always get a critical hit, which is why you must include critical chance in your calculations. Seems your formula is only valid when you crit.
If you don't get a crit hit then you don't get to add in the highlighted bit, which reduces your output by quite a lot, nearly a factor of 4 in your example.
The calculations are done for the damage when doing a critical, yes.
If you don't score a critical, Offense set is always better. So if the Offense set can do more damage on a critical, then it is a win-win and regardless of the CC Offense set will do more damage than CD set. That's why I am only considering damage on a critical hit.
In general:
CD UP buffs or attacks with internally increased CD increase value of offense mods and decreases value of CD mods.
Offense UP buffs or attacks with internally increased Offense doing the opposite (unless such offense increase is multiplicative).
And debuffs reverse behavior above.
But it's very useful for long fights in the controlled environment (hello raids).
Yeah, this is a good heuristic. The case given by the OP is a limited example of this in which the CC break point is either less than 0% or greater than 100%. But the above comment applies broadly speaking as the CC break point between the sets can be shifted by CD and Offense modifiers.
Things get more complicated when you include secondaries on the mod sets you are using as well as in battle mechanics. I prefer to try and do ADPH calculations for each specific mod set with likely in battle modifiers to offense, CD and CC included when deciding between CD and Offense mods.
Got it now. Interesting bit of math there.
Also, to show the +Offense% from leadership, Uniques and Buffs not affecting the CDset/Offset Ratio for critican damage:
There is really only 4 variables that can sway the overall damage increase to favoring 1 set over the other:
1. Offense secondaries
2. Crit damage bonuses from leaders, abilities, and buffs
3. Crit chance % after leader, abilities, mods, and buffs are accounted for.
4. Incomplete gear tiers.
You are absolutely correct that without equal secondaries there's no point comparing, the one with better secondaries is always better.
cc=breakpoint where cd set surpasses offense set
o= offense including mods but not the set bonus
u= unmodded offense value.
cd= crit damage from mods abilities buffs and leaders.
The more offense secondaries and primaries you have, the lower the value of the offense set. Other offense increases don't affect its relative value since they are basically all multiplicative (qgj lead being the only exception I can think of since it adds an amount of offense unaffected by your current offense). The more crit damage increases you have from anywhere, the lower the value of the crit damage set because it is always only additive (the amount of crit damage that gets added is never affected by your current crit damage).