This is for quick reference and back-of-the-envelope calculations. This is mostly for estimation, and actual numbers may be different.
If you assume the enemy has 10% RES to physical and all elements:
Notes on Bennett's burst (Fantastic Voyage) ATK buff:
Suppose Bennett's Base ATK is a (for a well-invested Bennett, this can be within the range 600-900; for example a Level 90 Bennett with a Level 90 Skyward Blade will have around \( a\approx 800\) Base ATK; this can be increased further if one uses an Aquila Favonia instead).
If one has a C5 Bennett with level 12 Q, the buff gives
extra ATK to party members within Bennett's field. For a well-invested Bennett, it can usually give at least 1000 extra ATK to characters.
If a character has 2000 ATK initially, then Bennett's buff can increase it to 3000 ATK (increasing damage by 1.5 times).
Actual numbers may be more or less, but this is just to give a ballpark estimate for how much Bennett can increase damage. For some characters who gain other ATK boosts, Bennett's buff may not work as effectively or may hit diminishing returns.
For a level 90 Bennett with Aquila Favonia the base ATK is 191.16+674=865.16. The atk buff is then +1142.
An R5 Thrilling Tales (TTDS) will increase ATK by 48% (for the new character swapped in). This is additive with other sources of ATK%. Suppose one's DPS character has an ATK% sands (giving 46.6 ATK%) and no other sources of ATK% or flat ATK (none on artifact substats, character ascensions). Then TTDS will increase damage by \( 194.6/146.6\approx 1.33 \) times. If one has additional ATK% from other sources then this boost will be smaller.
The buff will last 10 seconds and can be procced once every 20 seconds.
If one combines TTDS with Bennett's buff, then Bennett's ATK boost is added after the TTDS buff is factored in. That is, for the calculation, let A be the target character's base ATK. Then the buffed attack is:
Example: for a character with say 2000 ATK and ATK% sands and a well-invested Bennett, combining TTDS with Bennett (use Bennett Q, swap to TTDS character, swap to DPS) can give around 3600 ATK (actual number in game may be more or less), increasing damage by around 1.8 times.
The total damage gain will be the damage gain from TTDS plus the damage gain of Bennett's ATK boost:
Suppose a character is level 90, and an enemy is level 100. Based on DEF, incoming damage is then multiplied by:
or is roughly halved.
Suppose that an attack ignores a portion x of DEF. Then the multiplier becomes:
The damage increase becomes
For example:
Usually x will be smaller than 1 so we can approximate further with a taylor expansion
So a very rough rule of thumb is that if a portion x of DEF is reduced or ignored, then damage will increase by at least x/2.
Note that actual values in game may be more or less, so do not take the value out of context.
Some characters like Xiao or Yoimiya will gain greater damage bonus over time through their passives. Some weapon or artifact sets also have this feature of "accelerated" damage over time. The impact of this on DPS can be approximated as follows. If they gain \(b\) more damage bonus every \(t\) seconds (rate \(r=b/t\)) for a max damage bonus of \(nb\) then the increase in damage is $$(b+2b+\ldots+nb)/(nt) = bn(n+1)/(2nt) = b(n+1)/(2t) = r(n+1)/2$$ This can be approximated as an integral too $$\frac{1}{T}\int_0^T rt \ dt = rT/2$$ The integral approximation becomes more accurate the more hits there are (such as for a rapid fire C6 Yoimiya).
Suppose a typical character has 10k base hp. The flower will give 4780 flat hp. Assuming no HP on substats, the character will have around 15k total hp. In practice and based on empirical observations, many characters can reach up to 20k (due to hp% and flat hp on substats).
Now suppose a character is built to scale with hp (i.e. Yelan). Such characters typically have higher base hp. To be conservative say they have 13k base hp. Suppose they use an HP sands which gives 46.6% HP (ATK sands also give 46.6% ATK). Then they can reach total hp of $$13000*1.466 + 4780 = 23838$$
If they have 14k base hp they can reach $$14000*1.466 + 4780 = 25304$$
Sometimes these characters can gain additional hp buffs. For example, the Staff of Homa can increase hp by 20%. In this case $$14000*1.666 + 4780 = 28104$$ Homa then converts .8% of hp to atk or around 225 more atk. When under 50% hp it converts 1.8% of hp to atk or around 506 more atk.
Yelan has a passive that increases hp by 30% when there are four different members in the team (e.g. dendro international). In this case $$14000*1.766 + 4780 = 29504$$ so she can reach 30k hp. In reality such characters can get more than 30k hp due to higher base hp or hp substats.
Suppose a typical character has around 300 atk (many may have lower). The feather gives 311 flat atk. An ATK sands gives 46.6% atk. Suppose a weapon gives around 600 base atk. In total $$(300+600)*1.466+311 = 1630.4$$
TTDS gives 48% more ATK $$(300+600)*1.946+311 = 2062.4$$ This is a 1.265 times increase in damage (comparable to vv buff).
If one uses Bennett this adds around 1142 more atk. $$(300+600)*1.466+311+1142 = 2772.4$$ The increase is 1.7 times.
If one combines Bennett and TTDS buff the ATK is $$(300+600)*1.946+311+1142 = 3204.4$$ This is a 1.156 times increase from using Bennett alone. So the vermillion set can give a 15% increase in damage (if using Bennett) and 26.5% increase (if not using Bennett). Other sources of atk include noblesse, pyro res, tom, weapon and talent passives, etc.
Suppose a typical character has around 700 base def. A def sands gives 58.3% def. This gives total def of $$700*1.583 = 1108.1$$ Certain things such as the husk set, weapons (like whiteblind), Gorou can increase def even further.
For example, Gorou with level 13 E gives 438.09 more def. Husk gives up to 24% more def. Itto has 959.16 base def at level 90 and can reach $$959.16*1.823 + 438.09 = 2186.6$$ total def. With whiteblind and def substats on artifacts this can be higher.