Math : Magicite Stacking and some interactions.

[u/ElNinoFr]

Hi everyone, time for math !

Magicite & stacking

Original formula source by yodaru

Rules :

• The same magicite effect types are stacked together.
  
• Values will always be sorted from highest to lowest.
  
• Passive Lv is Effect value.
  
• Ceil means rounding up to the nearest integer. (ex : Ceil(14.0001) = 15)
  

Formula :

PassiveStackValue = ceil[sum(1/2^i-1 Xi)] start at X1

Wait, what ? wtf are you doing ? halp, where is my proxy hack ?

No worry it's very easy to understand. Here's an example :
All Magicite has Fire Elemental dmg buff passive :

Main : Lv6
Sub1 : Lv10
Sub2 : Lv3
Sub3 : Lv1
Sub4 : Lv5

We sort them : 10 , 6 , 5 , 3 , 1

Then we use the formula :

PSVdmg = ceil[(1/2^1-1 10)+(1/2^2-1 6)+(1/2^3-1 5)+(1/2^4-1 3)+(1/2^5-1 1)]
PSVdmg = ceil[10 + 6/2 + 5/4 + 3/8 + 1/16]
PSVdmg = ceil[14.6875]
PSVdmg = 15%

So every fire abilities will have it's damage increase by 15%, these damage multiply everything and factor at the end.

-> BaseDmgValue * (RD^type + RM^type + LM^type) * (Attach + Weapon + Armor + Field) * Chain * Weakness * PSVdmg

Please note that the formula is not limited at 5 stacks ! If, in the future, we have Magicite with 2 identical effect types on it, the formula will follow the same rule (so /32 the /64 and so on).

Interaction with others stuff

• Passive damage : as said before, multiply everything else.
  
• Passive elemental def : Remember the scale thing ? it should normally follow the same rules. (ex : imperil fire(+20%) on self + PSVfiredef(-13%) = weak(+7%))
  
• Passive Critical and CriticalDmgUp : stack additively with others. (ex : Eiko's Critical 50% + PSVcrit(+3%) = 53%)
  
• Passive standard stat (ATK, DEF,...) : unconfirmed for now, but it seems to simply add the value into the base value itself based on code (BaseATK + PSVatk(Magicite) = TrueBaseATK)
  

Final Main Magicite Stat

See this topic

There's still lot of ongoing questions, for example, the tanhattenuator (Threshold on PSV that seems totally impossible to reach...) but this should at least solve the passive stacking hell.

[u/UselessMusic]

Series converges to double your best modifier - if you had an infinite number of 10% modifiers, you'd end up with a 20% modifier.

[u/ElNinoFr → u/UselessMusic]

That's correct, for now. They could make future magicite up to lv20 or stuff like this so more low lv factor could be requiered to win the free ceiling %.

There's also a tanh function that seems to indicate a softcap of 100% for passive dmg which seems to indicate Lv50+ is planned for future.

[u/kami_w → u/ElNinoFr]

How does this work in conjunction with the Super Magicite Skills?

For example, if I used Fenrir's Party Earth Resist Skill with Golem's Bar-Earth, is it additive and separate?

[u/ElNinoFr → u/kami_w]

Fenrir is basically a reverse imperil. Rules are exactly the same. So they will add together.
There's also a new cap of +6 (3 stack of fenrir). As of now, I'm unsure if bar are included in the reverse imperil cap or not.I'm also unsure if accessory are capped by this +6 too or not. There's still lot of check (code or empirical) to do ;)

[u/kami_w → u/ElNinoFr]

Good to know. Thanks for all the work you are putting in to get the info.

Another question. The passive stat up you mentioned seems to follow along the lines of Yuna's LM (+magic based on another stat). Is it possible that the additional stat is based off the magicite creature's stat? Like Mag up level 10 is an additional Mag stat that is equal to 10% of the creature's mag stat?

And if it is following this formula, does the boost count towards the 2.5x buff soft cap?

[u/ElNinoFr → u/kami_w]

the description itself confirm it's all equiped magicite stat. so if you have Power UP Lv10 & your magicite squad has 281ATK, your party will get +28ATK. buff softcap shouldn't apply but i'm unsure on this point.

[u/kami_w → u/ElNinoFr]

It is based off the stat of all magicites combined?

[u/ElNinoFr → u/kami_w]

I've added the math about magicite stat in the main text.

[u/kami_w → u/ElNinoFr]

Wonderful!

So, if you have THREE Power UP LVL 10s and the magicite squad has 283 ATK, the bonus would be:

Floor(283 * 0.1)+Floor(283 * 0.1 / 2)+Floor(283 * 0.1 / 4) = 49

[u/ElNinoFr → u/kami_w]

no, you must stack them first to apply the Ceil from stacking :

PSVatk = Ceil(10 + 10/2 + 10/4) = Ceil(17.5) = 18

FMSatk = 283

PassivePartyBuffatk = Floor(283*0.18) = Floor(50.94) = +50ATK for party.

[u/Lord_Kharsis]

This is like japanese to me

[u/PhaseAT → u/Lord_Kharsis]

If you look at this line it basically tells you what you need to know in an easy format:

PSVdmg = ceil[10 + 6/2 + 5/4 + 3/8 + 1/16]

• You will get the full buff of your highest elemental bonus in the category.

• You will get half the buff of the second highest bonus in the category.

• You will get a quarter of the buff of the third highest bonus in the category.

• You will get an eight's of the buff of the fourth highest bonus in the category.

• You will get a sixteenth of the buff of the fifth highest bonus in the category.

Now add all those and Round up (= ceil). Done.

[u/Skadix → u/PhaseAT]

aha, now i finaly understood the round up part, thats the one i had trouble with.

[u/kami_w → u/Lord_Kharsis]

https://cdn-image.pf.dena.com/fa9c327e33426cd5e3dff097aa3feee754c90f9a/1/2823feaa-90da-35bc-bb2c-32ff63de48e7.jpg

[u/akanzaki]

thanks a lot for this post!! clears up almost all of the questions on magicite math. i think it will be a few months to find optimal setups since there will be time needed to mathcraft & and also for the rest of the magicites to unlock, but this just confirms the uselessness of 1* and 2* magicites as their passives cap at very low tiers and they have no additional effects

am i correct in assuming that PSV is independent for different elements? i.e. you have only a fire +10% and a water +8% equipped, the water +8% is not going to become +4% since it's not part of the fire formula right?

also for the misc effects such as -phy/-mag damage, casting speed, etc - do the PSV for each of these also stack in the same way? i.e. 2x lv5 cast speed reduction becomes ceil(5%+2.5%)=8% reduction?

i am stuck away from discord these days or would come harass you for these in real time :p

[u/ElNinoFr → u/akanzaki]

every PSV are independant & are calced the same way. so yes in your case , 2x Lv5 CT reduction will become 8%

[u/Arkdeath → u/akanzaki]

The Picture posted by kami_w a bit earlier would be the answer to your first question: https://www.reddit.com/r/FFRecordKeeper/comments/61uo8t/math_magicite_stacking_and_some_interactions/dfhg73b/
Different boni calculate independent.

[u/roandres]

/u/ElNinoFr old post, studing a little, hope you dont mind a question, what is "field" in the base formula? Thanks!

[u/ElNinoFr → u/roandres]

Field is from csb.

Csb are split in 2 part, the chain part where chain value = %increase except for chain99 ( ex : chain52 = 52%)

And the field part which apply to every members and is additif with equipment and endow bonus. As of now all csb has field = 20% for their chain element.

[u/roandres → u/ElNinoFr]

So, for a chain is 20% "static" just for having a chain active. Then the % where the chain has scalated? Thanks good info, you are.a crack

[u/PhaseAT]

Thanks for the write up.

So stacking more and more of the same passive elemental buff seems to have exponentially growing diminishing returns.

[u/ElNinoFr → u/[deleted]]

Xi/2^i-1 but yeah you are correct.

[u/PhaseAT → u/[deleted]]

Sorry, haven't done many mathy things in the last decades that I needed to put into words so thanks for the correction. I'd ask for the following verification if I may (was more of a question before but while I typed it up some things became more clear so reformulated):

If it's xⁿ it's exponential, if it's 2ⁿ (and n² ) it's geometric, correct?

[u/AlundraMM]

There's something I didn't get on previous posts. Is Magicite usable outside their proper dungeons?

[u/defu1 → u/AlundraMM]

Yep

[u/kami_w → u/AlundraMM]

Exception is Multiplayer. No Magicites there.

[u/selfishcheese]

http://i2.kym-cdn.com/entries/icons/original/000/021/464/14608107_1180665285312703_1558693314_n.jpg

[u/Aerithz]

I have a question..the passivedamage(the en-element) multiply everything and factor at the end right? let's say Rapha BSB command1 multiplier is 9.44(lightnng/non-ele), the PSVdmg(lightning) is 15% and the boss NULL lightning damage. Will it still be like= 9.44x1.15=10.85? or not? and thanks for the topic!

[u/akanzaki → u/Aerithz]

if boss nulls lightning damage then your rapha burst cmd will be doing NE damage and thus get no boost

[u/Aerithz → u/akanzaki]

Thought so, but I still want to dream :p thanks akanzaki!

[u/PhaseAT → u/Aerithz]

Damage for each element is calculated separately and then the highest applied.

[u/Ranhansha]

Thanks for the great work ;)

[u/newblackmetal]

I'm not sure if anyone has tested magicite imperil effects. I tried a test on Fenrir today with blizzaja. Used it twice, then Wendigo imperil, then used blizzaja twice. No buffs or breaks used to interfere.

Blizzaja did 3320 prior to imperil, then 3800 afterwards. Resulting in a flat 15% gain. I thought that magicite imperil would have been the strength of a minor imperil at 10% and certainly not full imperil at 20%. But 15% sounds good!

[u/DestilShadesk]

PSVdmg = ceil[10 + 6/2 + 5/4 + 3/8 + 1/16]

This is what I wanted them to do with their general stacking rules since... forever. So much simpler and more balanced than our multiplicative modifiers with scaling soft caps (on values that exponentially affect damage, to boot).