KQM | Genshin Impact - royal-mechanics

Yuehai Ticketing SecretaryBOTJun 22, 2021 12:36 PM

@Bobrokrot | Don't invest in ₼BUG - royal-mechanics As an author, It is your responsibility to complete the ticket - Take advice constructively - NO disrespectful behavior - The ticket will be scrapped if: No activity > 1 week or open for > 1 mo. - When done, type $close

Theory/Finding/Bug: Title of your submission Evidence: Explanations with calculations and/or Youtube/Imgur proofs Significance: Conclusion

Bobrokrot | Don't invest in ₼BUGJun 22, 2021 12:53 PM

Things to test:

the most important things to verify

1) do major elemental reactions(i.e. overload, swirl, etc) add crit stacks?

2) does triggering multiple elemental reactions with one abilitiy (i.e. Sucrose double swirling a bunch of stuff for example) add multiple stacks?

3) how it calculates crit rate for AoE. if multple elemental reactions add stacks should be quite easy to do even without cryo set

First test: Sucrose with (lvl 90) R1 Royal catalyst swirls some cryo. https://youtu.be/mTEGm35iLmI Here we get 1 stack each non-crit then the stack count resets to 1 (instead of 0) when crit does happen.

Bobrokrot

Royal Swirl test

A confirmation for a relatively know fact: AoE abilities (in this case Sucrose's N1), when crit, sometimes reset to 0 stack and sometimes to 1. https://youtu.be/dev3qyr-AJI

Bobrokrot

Royal AoE 2 target test

Initial theory: crit is calculated one-by-one. Each time you either reset to 0 stack if it crits or gain a stack if the amount of stacks you got already is no more than one.

Here I tried a chain reaction of Swirl into Superconduct. No different from simple Swirl test. https://youtu.be/hWfeeU6b9tM

Bobrokrot

Royal Swirl SC chain reaction test

Bobrokrot | Don't invest in ₼BUGJun 22, 2021 1:23 PM

For the last 16 minutes I've been doing the following: gain full stacks on Royal weapon, exit combat. Then equip character so that his crit is above 100%. Then use an AoE ability (2 targets here) to see if one of them doesn't crit. https://youtu.be/cUd-kFqAOSU(edited)

With this setup the 2nd instance of damage should have 60,6% chance to crit (in the clip it's all tests after the first one). Both instances of damage so far were crit, so it seems like AoE abilities do snapshot crit.

Bobrokrot | Don't invest in ₼BUGJun 22, 2021 2:08 PM

One more series of tests. Result is the same. https://youtu.be/eJijOEJs4L0 Do note that in the last test I checked whether crit stacks have a cooldown. I performed a quick Sucrose's N1 + N2 at 0 stacks. Both attacks were non-crit, however, only 1 stack was gained.

Bobrokrot

Royal crit test 2

Theroy: AoE abilities do snapshot crit rate. However, Royal weapon's passive specifically works the following way: — Go through a list of damage instances that the ability outputted one by one. — If the current damage instance is a crit, remove all crit stacks. — If the current damage instance is not a crit, gain a stack and put this on a cooldown.

The cooldown thing can also by found in the datamines. https://discord.com/channels/763583452762734592/763610791839924224/856864191855460352

I am checking Electro-charged right now and it seems like it never adds any extra stacks. Might only work on reactions that can radiate.

https://youtu.be/PrXV4em0ssc

Bobrokrot

Royal Overload and Electo-charged test

It kinda makes sense I guess. When you trigger Swirl/Overload/Superconduct, you do damage simultaniously to multiple enemies. And you add all targets to a single list to determine Royal passive stacks. Electro-charged, however, is a status that deals damage to a target as long as it has both Electro and Hydro aura. So it kinda makes sense that it is treated separately by the game.

What else to test? I think the fact that Royal weapons gain stack off-field is a common knowledge at this point. As well as the fact that crit rate including Royal stacks is snapshoted by everything that can snapshot.

PoiyoJun 22, 2021 3:37 PM

royal weapon can get perma one stack at multiple enemies - but it is inconsistent and ping probably does affect it

https://www.youtube.com/watch?v=gplujHD-dvY

poiyo doraad

royal weapon perma stack

https://www.youtube.com/watch?v=L7o5mdapKMQ

poiyo doraad

royal weapon stack reset

and from my own testing, all transformative reactions do not give any stacks

from simulations, this is the average cr gained per refinement at one enemy

also multihit attacks like razor Q (AA+companion) also count as one stack and will reset if either damage crits - same as in aoe situations

Bobrokrot | Don't invest in ₼BUGJun 22, 2021 6:07 PM

Yeah I think your tests do line up with mine.

If my hypothesis is correct (that game goes over a list one by one for royal passive) then it is possible to calculate exactly how many crit stacks you can get (reset to 0 or 1) after an AoE hitting N enemies.

Bobrokrot | Don't invest in ₼BUGJun 22, 2021 6:41 PM

I also did my own calculations for effective crit rate. Instead of simulations I chose to calculate it theoretically using a formula for transition matrix for Markov chains. I don't think it is possible to get an answer analytically but I was able to calculate an exact probability distribution for all 6 possible states (0 stacks, 1 stack etc) after N = 100 million steps for all possible variations of base crit rate (b) and refinements of royal weapon (d — crit gain per stack). The result is literally the same as you can get from simulations, here is the table for it. https://docs.google.com/spreadsheets/d/1Gc_kr4hmc2-MPo65rZ-xqsIfu_5-mwLF9OavxChAK-Y/edit?usp=sharing

Royal weapon calcs

Royal Total crit chance,Effective crit rate of the weapon Royal weapon refinements,Royal weapon refinements Base crit rate,1,2,3,4,5,1,2,3,4,5 0,00%,18,94%,21,15%,23,00%,24,61%,26,03%,18,94%,21,15%,23,00%,24,61%,26,03% 0,10%,18,90%,21,10%,22,96%,24,56%,25,98%,18,80%,21,00%,22,86%,24,46%,25,88% 0...

The code for it. Basically the element of the matrix M[k,n] is the probability of going from the state k to the state n. Vector base = [1,0,0,0,0,0] represents the state of having 0 stacks (we are in state 0 with probability 1, in state 1 with probability 0, in state 2 with probability 0 and so on). By multiplying the transposed matrix by the vector N times we can calculation the probability distribution of being in a number of states. Having that, can calculation the average amount of crit rate we have after N steps.(edited)

The good part about this matrix is that it gives us and easy way to calculate our effective crit rate after N = 2 steps for example. I imagine the most optimal way to play using Royal weapons is to hit a few times to stack the passive then use AoE abilities or snapshoting abilities.

Bobrokrot | Don't invest in ₼BUGJun 22, 2021 6:48 PM

Bobrokrot | Don't invest in ₼BUGJun 22, 2021 7:12 PM

Anyway, this is not the point of the ticket though. Can save it for another time.

We know that the gaining stack is on cooldown. What we don't know is whether removing stacks is on a cooldown as well. It might be essential if ever want to calculate exact probability of having either 0 or 1 stacks after an AoE ability.

<@!409364174020280331> pinging you in case you didn't see the ticket.

HatsuharufagJun 22, 2021 7:56 PM

goin' purely by code, it works like this:

if no_crit then add crit_stack add crit_stack_CD if no_crit and crit_stack_CD=true then do nothing else remove crit_stack

(edited)

there're no parts that metion any kind of cooldown for removing stacks

HatsuharufagJun 22, 2021 8:05 PM

most important takeaway though from all of this is that abilities that hit multiple targets are calculated case by case, going through all targets that were hit in some order. this also explains why sacrificial series of weapons are almost guaranteed to proc when multiple targets are hit.

kind of understandable and semi-common knowledge, but good to have solid verification for the game mechanic behind it(edited)

Bobrokrot | Don't invest in ₼BUGJun 23, 2021 8:44 PM

Theory: AoE abilities do "snapshot" crit rate. Evidence: https://youtu.be/cUd-kFqAOSU and https://youtu.be/eJijOEJs4L0 The tests were conducted as follows: gain 5 stacks of a Royal weapon, exit combat and then raise crit rate up to >100%. Then use an AoE ability and counter the number of non-crits. If crit didn't "snapshot" and instead was calculated one by one, then after the first crit the crit rate would drop to ~60% due to losing 5 stacks of a R1 Royal weapon and the 2nd instanse of damage would have a reasonable chance to not crit. In the above tests, not a single event of non-crit has been observed which allows us with a reasonable amount of confidence claim that AoE abilities do "snapshot" crit rate. Significance: For Royal weapons it means that they can potentially have an increased efficiency given a right rotation. Although you can't gain multiple stacks with an AoE ability, what you can do is take advantage of the stacks you already gained through single target attacks. Damage dealt to all targets is guaranteed to have an increased constant crit rate, although it requires further analysis whether it actually yields better efficient crit rate or not for different rotations and combinations of base crit rate and Royal refinements. One particular charcter that could take advantage of this that comes to mind is Yanfei since her typical attack pattern consists of 2-3 single target attacks followed by an AoE attack (which coincidentally cares about critting).

Bobrokrot

Royal crit test 1

Bobrokrot

Royal crit test 2

Bobrokrot | Don't invest in ₼BUGJun 23, 2021 9:01 PM

Theory 2: Mechanics of Royal weapon stacks: — After gaining a stack you cannot gain another one for a small period of time (cooldown). — For an AoE ability, damage instances dealt by the ability, including damage dealt by reactions Overload, Swirl and Superconduct caused by the ability, are put in a list. Then the game applies the following logic to all elements of the list one by one: if no_crit then add crit_stack add crit_stack_CD if no_crit and crit_stack_CD=true then do nothing else remove crit_stack — Stacks can be gained when the character equipped with the Royal weapon is off-field. Evidence: 1) Sucrose's quick N1-N2 gaining 1 stack instead of 2. https://discord.com/channels/763583452762734592/856875279872032829/856892434205638717 plus multiple evidence of an AoE ability gaining no more than 1 stack when it non-crits multiple times. 2) After a single-target ability crits and causes a Swirl, the number of stacks is reset to 1 instead of 0 implying that damage from a Swirl is taken into account and is considered as non-crit. https://discord.com/channels/763583452762734592/856875279872032829/856876233522151475 3) Superconduct and Swirl chain reactions https://discord.com/channels/763583452762734592/856875279872032829/856879568320069682 4) Overload and Electro-charged https://discord.com/channels/763583452762734592/856875279872032829/856896851211321404 Significane: Royal weapons have an increased efficiency in situations when the holder triggers Overload, Swirl or Superconduct due to the fact that they can potentially always have at least 1 stack.

<@!409364174020280331> I'm closing this ticket. Anything to add?

HatsuharufagJun 24, 2021 2:32 AM

no. once again, really appreciate your help

Yuehai Ticketing SecretaryBOTJun 24, 2021 6:05 AM

Ticket Closed by @Bobrokrot | Don't invest in ₼BUG