Low Hero's ACA does not apply its damage boost correctly

*Deciding to post this as a bug report because it runs counter to the description provided in Nise's Damage Computation post. I also write to open a discussion on the necessity of utilizing a "Defense Adjusted Average Range" measure for dpm calculations.

Heroes and Paladins are two classes with effectively the same clean ranges due to wearing the exact same armor and weapons. Both even come with a skill multiplier to their damage (ACA orbs and Elemental Charges, found in the "Modifiers" step of Nise's damage calculation). Additionally, balance changes to panic were implemented with the intent of aligning hero single target output with that of element neutral paladin. Whether or not that is the correct balance point isnt the topic at hand today, but rather, I demonstrate that hero and paladin are not affected by monster defense in the same way (and as usual its not to hero's benefit ).

Paladin:
Paladin damage appears to be calculated as outlined, by applying the elemental skill's boost first (such as 175% for fire and 185% for holy charges) and then applying defense reduction. Additionally, if the mob is weak to that particular element, it is additionally multiplied by the 1.5x before the defense reduction. This is demonstrated with the image below, where for the given range and mob defense (freezer is fire weak), the damage values seen follow the Element boost (175%) -> Super Effective Boost (150%) -> Defense Reduction. If the mob is neutral to the element, simply remove the 1.5x step from the pipeline.



Hero:
Hero also gets a 1.9x damage multiplier when all 10 orbs are active. However, this multiplier is NOT applied before the defense reduction step. Instead, the multiplier waits until after the range has been reduced by defense before multiplying. This is demonstrated in the image below, where the damage is lower than possible if ACA applied before defense.



What does this mean?
This means that for these two classes, which have supposedly been balanced to where hero outputs similar single target damage to element neutral paladin, due to the more favorable order of operations, hero suffers from weapon defense far more than paladin, let alone on element weak mobs. If a hero and paladin are wearing the exact same gear, their "Defense Adjusted Average Ranges" are not the same on realistic targets. This disparity gets amplified for higher defense targets.

If my calculations below are correct, against a monster with a very reasonable 1700 w.def (one of which is Pink Bean), the hero is 430 average range lower than their equivalently geared paladin counterpart. There's no official documentation on it and I'm not going to stop an entire pb run to collect the data, but I believe in pb's specific case, special resistance applies when paladin element bonus would (i.e. before defense reductions). This means we can simulate it by just lowering the starting range min and max values, which has no effect on the Defense Adjusted Average Range calculation.


*Note: Defense Adjusted Average Range can be thought of as the range that the user would have against a 0 defense target, for the purposes of calculating dpm. Apply damage calculation steps as normal otherwise.

This means that the hero is actually 430 range behind the paladin on holy-neutral 1700 def targets (think pb and ht). I'll leave it as an exercise for the reader to determine how much attack it would take to cover this gap. This value is higher on high defense targets such as toad (like a 1k range difference there). Not to mention against element weak targets.

Not included in this analysis:
I do not include the effects of SE as that becomes more involved than I care for with panic. Additionally, I do not include dk in this for two reasons. First, I do not have a dk atm, although I am pretty sure zerk multiplies last (after crits) to get higher crit values. Second, they do not aim to have the exact same damage range as hero/paladin due to wearing a different weapon.

Tl;dr Bug: Hero does not apply its multiplier boost at the listed step before defense. This implies that the equally geared hero will not have the same dpm as a paladin against a non-zero defense, holy neutral target, even after the panic buffs attempted to align them.

 

Step 8 implies that ACA should multiply after crits (step 5), similar to zerk

Edit: These may not be compatible as listed, but I've got no dk to play with and zerk isn't even listed in any step on the formula sheet.

 

Pardon the dust as I wasn't planning to share the spreadsheet. I've converted it to a google sheet and applied some touch-ups to hopefully make it a bit easier to follow.

The minimum and maximum range as well as mob defense are inputs (in gray), and the observable attack outputs for scenarios are shown beneath it. In addition, the Defense Adjusted Average Range represents a character's range which would have the same dummy dpm as the above character against a 0 defense target (what dummy dpm testers compare against). For both classes, this is calculated by applying their multipliers and defense in the previously determined order, and then dividing the multipliers back out.

Of course, these ranges are utilized with different values of buff/skill multipliers between the two classes, but the original post aimed to challenge claims that hero single target output (post panic changes) closely matched that of paladin's holy neutral single target output outside of anything other than 0 defense targets.

https://docs.google.com/spreadsheets/d/1cFi0aqHV0tcxyTsyyjBad4l-YzZQ5UfJCcouqXg1Qb4/edit?usp=sharing

 

I've got my share of issues with the charging damage, but those are mainly because I dont believe the system has the flexibility needed to be capable of the balancing it needs.

You kinda lose me on the analysis with amp, though that may be because of how the skill % is being read. From the formulas on Nise's formula sheet, these tables show the damage multiplier at each orb level, as well as the total damage multiplier for using each skill at each orb count. The Finisher Damage% table specifically includes the ACA multiplier, panic/coma specific multiplier, and both lines of brandish to outline the effective skill % of a single cast of that skill against a 0 defense target (no se). Special shoutouts to Coma being fairly close to no se brandish if it didnt even consume orbs or orb multiplier wasnt an issue (the attack speed would make it slightly better than brandish; the extra line on se would make it worse than brandish).

Weapon defense cuts the range in window by essentially a flat amount. The strength of lines plays no role in how impacted you are by defense, but characters/classes with lower ranges are impacted more by defense than those with larger ranges. Thus follows that the same window range paladin has an effectively larger range than its equivalent hero due to charges+weaknesses multiplying its range before defense reductions.

And this isnt even what makes paladin the better cleaver in any non-cwk situation...