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Introduction
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So most genshin players probably experienced the endless artifact grind for a perfect set, but honestly, do you need to actually go for the right set bonuses when you have a ton of good substats on random artifacts sitting around? I’m here to give some math to answer this question.
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Notes on my methodology
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Basically, the question I’m asking is how many extra crit rolls on your offset artifacts do you need for them to better than specific set bonuses. I’m only going to count crit rolls since along with elemental dmg%, they are the rarest source of buffs compared to atk% or em. In practice, in terms of individual power atk% rolls are just as valuable as crit rolls since they stack multiplicatively, but since in a team there are 4 members and there’s so many possible atk buffs, atk% becomes less valuable compared to crit.
Also a quick note on how I count rolls. I count the total number of rolls into crit, including the initial values when you get the artifact. For example, an artifact that starts with both cr,cd already has 2 rolls into crit. An artifact that started with only cr and rolled into it twice from upgrading has 3 rolls into crit. From this, the maximum number of rolls an artifact can have into crit is 7 (2 initial rolls + 5 rolls from upgrading).
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Calculations
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So the core of my calculations will be percent increase in damage. How much damage increase do you get from the +15% elemental damage bonus from 2 set CW, TF vs extra crit substats for example, and here are the formulas:
Dmg increase from elemental damage %: (new percent damage – old percent damage)/(1+old percent damage)
Dmg increase from Crit: (New cd * new cr – old cd * old cr)/(1+ old cd * old cr)
So lets take the 2pc elemental dmg bonus pcs (2pc CW, TF, BS) for example. Let’s assume the most damage increase they can get from the 2pc, so they only have a elemental dmg% cup, and let’s assume 50/100 crit ratio.
Increase in dmg from set bonus: 0.15/(1+0.466) = 10.2%
Let’s match this increase in dmg to our crit formula.
0.102 = (New cd * new cr – old cd * old cr)/(1+ old cd * old cr) = (New cd* new cr – 0.5)/1.5
new cd* new cr = 0.653
If their crit rate stays the same at 0.5, new cd = 0.653/0.5 = 1.306. cd
That means to match the increase in damage from the 15% 2 set bonus, we need 30% extra crit damage, which is around 45 crit rolls. I’ve done calculations for distributing cd and cr equally across the rolls and the change was not significant enough to impact the number of rolls.
One interesting about this is that the number of rolls does not change if you have higher crit investment. That’s why crit scales so good in late game. Let’s take the same scenario as above but with 80/160 crit.
Increase in dmg from set bonus: 0.15/(1+0.466) = 10.2%
Let’s match this increase in dmg to our crit formula.
0.102 = (New cd * new cr – old cd * old cr)/(1+ old cd * old cr) = (New cd* new cr – 1.28)/2.28
new cd* new cr = 1.51
If their crit rate stays the same at 0.8, new cd = 1.51/0.8 = 1.89 cd
To match the increase in damage, you need 1.891.6 = 0.29 = 29% cd, so the number of rolls doesn’t change. However, keep in mind that this is extra rolls on cd/cr, so if your 2 TF had combined 4 rolls into crit, you will need your 2 off pieces to have 89 rolls combined into crit to match that.
I will include the values I got at the end for the other common set bonuses, feel free to double check my math.
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Conclusion – TLDR
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Note on how to interpret the values: 2pc TF – 45 extra crit rolls > If your 2pc from TF had 3 combined crit rolls (ex. plume w/ 3.0% cr and flower w/ 14% cd), you will need 2 off pieces with a combined 78 crit rolls to match the damage (ex. plume w/ 20% cd, flower w/ 6.0% cr and 14% cd)
So here are the values for how much crit rolls each set bonuses are worth:

2pc 15% elemental dmg (2pc CW,BS etc) – At most 45 extra crit rolls across 2 pieces, can be less if you have extra bonus dmg sources (stringless, serpent spine, ascension stat etc)

2pc nobless – at most 6 crit rolls across 2 pieces, can be less if you have extra bonus dmg sources

2pc gladiator – 4 extra crit rolls across 2 pieces, less if you have bennet etc.

~35% dmg bonus (4pc TS, LW, bolide) – At most 910 crit rolls across 4 pieces, can be less if you have extra bonus dmg sources.

4 pc glad – add last 2 together – 1314 crit rolls across 4 pieces, note that this can change by a lot since it has so many components.

Xiao (TL 6 ult, anemo cup), 2pc vv – at most 3 extra crit rolls across 2 pieces. I just wanted to calculate this since Xiao is such a special case. Farming VV for Xiao is really not that good since maiden is pretty useless.
So from my calculations above, we can see that set bonuses are not really worth that much compared to extra crit substats. If your set bonus pieces are not that good (12 crit rolls), it is very easy to find off pieces that can surpass the set bonus in damage. Also, off pieces can be literally any off piece, so if you have been farming artifacts for some time, it is actually much easier to maximize your dps damage by using those off pieces by rather than farming the same domain over and over again. Also, since you will have more options, optimizing 1:2 crit ratio is also easier with off pieces. So next time, don’t go and feed your good sub maidens or lava walkers. If you can get that godly 67 rolls into crit in that one off piece, literally no set bonuses will compare to it.