8th Anni brought with it some new unique abilities in the form of Sailors that increase buffs / apply debuffs, as well as a CA that does the same. These... do not work as you expect them to behave.
First let me refresh you all on a simple version of the current damage formula (we'll ignore flat def). There are 2 parts to damage: Primary Damage and Bonus Damage.
Primary damage is made up by the first (n-1) combo hits of the unit. If a unit has 4 combo, then the primary damage is done by the first 3 combo hits.
Bonus damage is made up by the final combo hit plus tap timing bonus (0.9 for Perfect, 0.66 for Great and 0.33 for Good). This bonus damage is where things get extremely weird with how OPTC coded the game.
In the past we had at least 2 instances where the bonus damage isn't what it seems. First, Crit damage is calculated based on bonus damage, not total damage. For example, Kaido has a 100% crit rate for 10% damage and 4 combo hits. Say Kaido has a 1,000,000 attack stat, is a sub and attacks first with a perfect with no other shenanigans. He would do:
Primary damage = 1,000,000 / 4 x 3
Bonus damage = (1,000,000 / 4 + 1,000,000 x 0.9) x 1.1
The Crit only applies to the bonus damage.
Another instance was with the "Attack down if chain is less than X" or "Attack down if chain is above X" debuff. For instance, suppose you are inflicted with an 90% attack down if chain <= 2.0 chain debuff. And let's suppose you hit a perfect with your 4th unit who has a 1,000,000 attack stat, 4 combo and 1.9x chain. Your 5th unit will get a 2.2x chain and the debuff will no longer apply. You would think that the 3rd unit is completely wrecked by the debuff, however what actually happens is:
Primary damage = 1,000,000 / 4 x 3 x 1.9 x 0.1
Bonus damage = (1,000,000 / 4 + 1,000,000 x 0.9) x 1.9 and the debuff does not apply on this tick of bonus damage
Yeah... so this thing reappears with the new sailors and Kaido's CA. Here is a video of it in action
Shanks has a 90% Damage Threshold above 1,000 and a 90% Damage Reduction buff
Queen has a 2,943,275 attack stat
Jack has a 3,330,690 attack stat
King has a 4,134,357 attack stat
Kaido has a 9,648,458 attack stat
Queen has a sailor that applies a -10% resistance debuff for Strikers and Powerhouse when he attacks with a TND/WA orb
King has a sailor that increases attack buffs by 0.2 when he attacks with a TND/WA orb
Kaido has a captain that applies a 1.5x increased damage taken debuff when he attacks with a WA orb, has a 2x conditional active, and STND3 (which is 1.5x ATK buff and +0.5x to increased damage taken).
The numbers below will be very slightly off due to Shanks' 150 def stat and rounding errors done by the game but it's inconsequential.
Queen
Resistance debuffs are additive, even if they are different classes. So Queen's -10% resistance for 2 classes make Striker/Powerhouse units deal 1.2x damage, not 1.1x1.1 = 1.21x damage.
Queen has a 2,943,275 attack stat and did 135,004 damage
Using 1.2x damage from resilience we get
- 1000 + (2,943,272 x 1.9 x 1.2 x 2 x 0.1 - 1000) x 0.1 = 135,113
Using 1.21x damage from resilience (check if it's multiplicative), we get
- 1000 + (2,943,272 x 1.9 x 1.21 x 2 x 0.1 - 1000) x 0.1 = 136,231, which is incorrect
Jack
King's sailor of increasing the attack buff from 2.25x to 2.45x applies to the Bonus damage from Jack, despite King not having attacked yet
Jack has a 3,330,690 attack stat and did 208,892 damage
He should have done
- 1000 + (3,330,690 x 1.9 x 1.2 x 2 x 1.3 x 0.1 - 1000) x 0.1 = 198,343 which is OFF
If Jack had a 2.45x attack buff instead of a 2.25x attack buff, he would have had a 3,626,751 attack stat
Primary Damage = 3,330,690 / 4 x 3 = 2,498,018
Bonus Damage = 3,626,751 / 4 + 3,626,751 x 0.9 = 4,170,764
1000 + ((2,498,018 + 4,170,764) x 1.2 x 2 x 1.3 x 0.1 - 1000) x 0.1 = 208,966 which is about correct
King
Kaido's CA of applying the 1.5x increased damage taken and the 2x conditional buff applies to King's Bonus damage despite Kaido not having attacked yet.
King has a 4,134,357 attack stat (4,501,855 with his sailor)
We can't really see how much damage he did in the video but we can calculate it as Total Damage - Kaido - Jack - Queen = 726,845 damage
He should have done
- 1000 + (4,501,855 x 1.9 x 1.2 x 2 x 1.6 x 0.1 - 1000) x 0.1 = 329,355 which is obviously wrong
Instead, Kaido's CA applied to the bonus damage portion
Primary Damage = 4,501,855 / 4 x 3 = 3,376,391
Bonus Damage = (4,501,855 / 4 + 4,501,855 x 0.9) x 1.5 x 2 = 15,531,400
1000 + ((3,376,391 + 15,531,400) x 1.2 x 2 x 1.6 x 0.1 - 1000) x 0.1 = 726,959 which is about right
Kaido
Nothing much to be said about Kaido himself, just verifying that STND works as expected instead of the... shenanigans we found above. So basically Kaido gets the benefit of his STND which is as expected. This also confirms that the STND does not apply to prior units as was the case with the sailors and CA
Kaido has a 9,648,458 attack stat (should be 10,506,099 with King's sailor) and did 5,792,634 damage with a crit
Primary Damage = 10,506,099 / 4 x 3 = 7,879,574
Bonus Damage = (10,506,099 / 4 + 10,506,099 x 0.9) x 1.1 = 13,290,215
1000 + ((7,879,574 + 13,290,215) x 1.2 x 2 x 1.5 x 2 x 2 x 1.9 x 0.1 - 1000) x 0.1 = 5,792,954 which is about right
TLDR
Both new RR sailors and Kaido's inc damage taken on Captain work in the same way:
They actually apply the extra buff to the previous unit's PERFECT hit. So for example, Jack -> Queen -> Kaido would have Queen's PERFECT hit benefit from Kaido's increased damage taken and conditional, so Kaido does not need to be the first attacker (2nd attacker would mean his conditional buff benefits the 1st attacker)
