KHUx Formula
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Kingdom Hearts Union ₓ [Cross] - Damage Formula v1.0
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PART 1 - TERMS
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STRStrengthCombined with DEFENSE, this is the primary stat wich is used to determine BASE DAMAGE.
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STR1000Trait: STR +1000Trait that adds 1000 STRENGTH to a medal.
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CHIPSChip MedalsChip Medals are medals that can be used to increase STRENGTH on other medals, up to 1000 STRENGTH.
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BOOSTBoosted MedalsSome medals can be pulled with boosted stats that have 1000 more STRENGTH or STRENGTH & DEFENSE.
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SLOTKeyblade SlotEach keyblade has slots you place medals into that have multipliers for STRENGTH. Two multipliers are usually available, one for matching type (Physical, Speed, or Magical) and one for matching type AND side (Upright or Reverse)
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GARGeneral Attack RatingAlso known as "Raises Strength." Increases total STRENGTH by a certain percentage based on the GAR level.
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DEFDefenseCombined with STRENGTH, this is the primary stat which is used to determine BASE DAMAGE.
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GDRGeneral Defense RatingAlso Known as "Lowers Defense". Decreases total DEFENSE by an amount based on GDR level.
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A.DEF-60%Trait: Aerial Enemy DEF -60%Trait that decreases DEFENSE of aerial enemies by 60%
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G.DEF-60%Trait: Ground Enemy DEF -60%Trait that decreases DEFENSE of ground enemies by 60%
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PSMARPhysical, Speed, Magic Attack RatingAlso known as "Raises X-based Strength" or "Raises PSM STR". Part of a multiplier used on BASE DAMAGE.
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PSMDRPhysical, SPeed, Magic Defense RatingAlso known as "Lowers X-based Defense" or "Lowers PSM DEF". Part of a multiplier used on BASE DAMAGE.
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TYPE (PvE)Attribute Type (Player vs Enemy)There are 3 attributes in the game and they work in a paper-rock-scissors method. Each medal has a attribute and each enemy has an attribute. Depending on the attribute, more or less damage is delt. Some medals have no attributes or ignore attirbutes.
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SKILLSkillMedals can have various skills added to them, some of these skills can increase damage. Part of a multiplier used on BASE DAMAGE
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RANDRandom Damage ElementThe game assigns a random value to damage between 97% and 103%. Part of a Multiplier used on BASE DAMAGE
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SPA TYPESpecial Attack TypeThis is a custom function for the formula that is used to identify whether or not the formula is fixed damage ("=") or a multiplier ("x"). Fixed damage skips a lot of the calculation.
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SPASpecial Attack DamageThis is the damage amount found in the special attack section in the medal information. It is either a fixed value, or a multiplier(s). Part of a Multiplier used on BASE DAMAGE
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GUILTGuiltThis is a medals guilt value. Part of a multipler used on BASE DAMAGE
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TapOrSwipeTap or SwipeWhen using a normal attack, a medal can be tapped or swipped. A tap does more damage, but a swipe will hit all targets. Part of a multiplier used on BASE DAMAGE
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CRITICALCriticalWhen using a normal attack, a critical will sometimes occur. A critical looks like a normal attack, but deals 1.5x more damage. Part of a multiplier used on BASE DAMAGE
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R.DMG+40%Trait: Damage in Raids +40%Trait that deals 40% more damage in raids. Part of a multiplier used on BASE DAMAGE.
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ExATKTrait: Extra Attack: 40% PowerTrait that allows an extra attack at 40% Damage.
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ABx / ABxMSkill: Attack Boost / Attack Boost MaxSkill that increases damage.
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SC / SC2Skill: Second Chance / Second Chance 2Skill that allows your character to recover from KO once per fight.
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Skill PerkSkill PerkSome outfits have the bonus "Skill Perk" attached to them. This further increases the chance that skills will trigger.
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Proc ChanceProc ChanceProc chance is synonymous with trigger chance, chance to occur, etc.
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PART 2 - Formula Overview
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Below are the topics I will cover on the rebuilt damage formula:

I. A History of the Damage Formula.
II. What Goes into Developing a Damage Formula?
III. What is the Current Well Known Damage Formulas?
IV. Why a New Damage Formula?
V. A Brief Overview of the Rebuilt Damage Formula.
VI. The Strength Formula.
VII: The Defense Formula.
VIII: The Buffs1 Formula.
IX: The Buffs2 Formula.
X. The Extra Attack Formula.
XI: The Entire Rebuilt Damage Formula.
XII: Lookup Tables.
XIII: Summary/Closing.
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I. A History of the Damage Formula
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It should be noted that prior to the release of the NA version of KHUx on 7 April 2016, the JP version had been out since 3 September 2015.
Some of the mechanics of the game may have been known prior to the NA release, but may not have been readily available or left otherwise untranslated.
Since I do not know how to read Japanese, I cannot provide a history beyond this point.
Also, at this time there were several communities that centered around the Kingdom Hearts brand that may or may not exist today.
Information discovered in these communities may no longer be available.
Some of the people mentioned in this section may or may not still be part of the KHUx community as a whole.
Please keep this in mind if you wish to contact these individuals, as they may no longer play KHUx or keep up with it's updates.
There is a high chance that the initial version of this history only covers Reddit, but that is a oversight by the author (me) and will gladly take any information at other community sites.
If a post has a link to a resource, it is possible that the resource may disappear at any time.
I hope to cover what that resource cointains or may have contained and I might even make copies of those resources with the permission of the authors.
Ultimately, I decide what gets put into this history (for now), so don't be upset if you message me and your post isn't implemented. It probably means it wasn't worth mentioning.
On the other hand, if you believe you contributed to the community and I have not covered it and would like for me to add it, I would be delighted to work with you so you receive your deserved recognition.
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II. What Goes into Developing a Damage Formula?
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III. What is the Current Well Known Damage Formulas?
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IV. Why a New Damage Formula?
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To put it simply, the damage formulas that were being developed were limited in scope and were not meant to be all inclusive.
This makes it easy to do quick testing on a few medals, but leaves some unanswered questions regarding special casse scenarios.
For example: we know how medals with fixed damage work, but since the calculation is easy AND most don't scale very well for heavy damage, it turns out to be not very interesting and generally left out.
This is fine for most cases, but what if a new medal is released that has better stats? or what if maybe someone just wants to know for any unforseeable reason?
The current damage formulas leave information like this out and it's only revealed to those who do some hard searching, testing or asking around.

On the other side, new things have been added to the game since the introduction of the original Damage Formula.
Things like guilt has been added, but stuff like traits has been left out
New areas with higher difficulty or different enemies has been introduced.
The game has also been completely rebranded, while this doesn't seem to have changed the Damage Formulas, no one has really gone back and done extensive testing to make sure.

Finally, there has been things that has always existed in the game that were never fully figured out or even looked at.
Defense, critical rate, and the randomness of damage come to mind.

It is my expectation that this Rebuilt Damage Formula is all inclusive as possible.
This will make the Damage Formula more complicated than previously, but the idea is that you should be able to take any medal in the game and be able to determine how much damage it can do against a specified target.
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V. A Brief Overview of the Rebuilt Damage Formula.
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Here is what you've been waiting for:
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DMG = ROUND( STR - DEF ) x BUFFS1 x BUFFS2
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Not very impressive, I know.
But it's fundamental that I present this brief overview of the damage formula so that I can discuss it's individual parts instead of the entire thing.
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VI. The Strength Formula.
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STR = (A x ( STR + STR1000 + STR1000 + CHIPS + BOOST ) + B x ( STR + STR1000 + STR1000 + CHIPS + BOOST ) ^ 2 ) x SLOT x GAR
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Now this is a formula! As you can see, the Rebuilt Damage Formula is much longer than the older Damage Formulas.
Do not fret though, this is pretty much identical to all the damage formulas you've known in the past!
This one accounts for traits, boosts, and chips - which most people were doing already. This just lays it out in the clear.

One notable difference between this formula and the old Damage Formula is the A+B vs the A-B format.
If you recall the discussion on linear regression, then you'll realize how important it is in ensuring your variables are correct so that you can develop an A&B that will be effective for a wide range of medals.
A-B was useful in displaying the format to the end-user, but *working* with an A-B system to develop a model is a headache.
It's much easier to make it A+B and let the variables themselves hold the negative values if they require it.
You'll notice that A-B with a positve B is the same as A+B with a negative B.
The formula is basically the same, but I just want to let everyone know the small detail change.

The Slot multiplier remains unchanged from the original Damage Formulas.

I've renamed General Attack Up (GAU) to General Attack Rating (GAR). Since enemies can inflict Attack Down, it didn't make sense to label this as GAU. I will just simply call this GAR (GAR+1, GAR-2, etc.)
The GAR multiplier is still under development, but from my current testing it is not a simple formula or step value.
I am using a lookup table to determine the values for GAR. This is not the first time I will do this, and I will explain the reasons later.

If the special attack is fixed damage, then this part of the formula is skipped.
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VII: The Defense Formula.
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DEF = UNK
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Surprise!
Well, unfortunately the defense formula is still unknown.
I have done some initial testing around this and it does not look good, but more data is needed.
What we do know is that this value is made up of the enemies base defense, General Defense Rating (Not General Defense Down), Aerial Defense -60% and Ground Defense -60%.
I've not seen any testing regarding the last two, and I've conducted a few very short and quick tests.
However, I am optimistic that the two traits may give us a glimpse into how defense may be influenced.

If the special attack is fixed damage, then this part of the formula is skipped.
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VIII: The Buffs1 Formula.
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BUFFS1 = (PSMAR + PSMDR - 100%) x SKILL x TYPE x RAND
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Buffs1 looks similar to parts of the other Damage Formula. So lets break it down real quick.

Just like GAR and GDR, I will not be calling these variables PSMAU and PSMDD, as enemies can also inflict PSM-Attack Down, or have PSM-Defense Up.
If you look back at the PSMAR and PSMDR history, you will see that this part remains unchanged.
What has changed is that PSMAR and PSMDR are now lookup tables.
The old formulas used were fairly accurate at the lower tiers, but as you moved onto the higher ones they were off by a bit.

SKILL remains unchanged.

TYPE remains unchanged.

RAND is a random number between 97% and 103%.

If the special attack is fixed damage, then this part of the formula is skipped.
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IX: The Buffs2 Formula.
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BUFFS2 = SPA x ( 100% + Guilt ) x (R.DMG+40% + R.DMG+40%)
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BUFFS2 = TapOrSwipe x Critical x (R.DMG+40% + R.DMG+40%)
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Now to main the reason I broke the formula up. If you've noticed the last sentence after each formula, then you'll see that fixed damage skips a huge chunk.
The above applies to normal and regular special attacks, but for fixed damage attacks, only the top BUFFS2 is used for the entire formula.
This should still look pretty familar however.

SPA remains unchanged.

GUILT remains unchanged.

Unlike some references seen online, R.DMG+40% is SUMMED before being used as a multiplier.
The difference? Only 16% (196% to 180%) damage.
Not very noticable in the grand scheme of things, but a quick test with some fixed damage units made this a simple find.

TapOrSwipe remains unchanged.

Critical remains unchanged. I would like to note however, that I have not seen critical hit rate testing.
I've done my own and recorded the observations in the KHUx tab.
It is my opinion that the CHR is 6%. It is the value I am using in the Tables Tab.
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X. The Extra Attack Formula.
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ExATK1 = ExATK(DMG)
ExATK2 = ExATK(DMG)
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This was omitted from the base formula, but it needs to be included.
Extra attacks are special in that they perform the same attack at 40% power.
Originally I assumed this meant 40% DMG, but as I encountered tougher enemies my first attack would do normal damage and my second attack would do 1.
The only situation where I can see this occuring is when an enemy has high defense and your strength is lowered.
This becomes a problem however, since fixed damage medals are unaffected by this and expereince 40% DMG as expected.
So how can a medal's DMG be affected by both what appears to be STR/DEF issues, yet still be affected when a medal has fixed damage and doesn't rely on STR/DEF at all?
I need to experiment more to determine the exact cause of this issue.

On the reverse side, I have also seen instances where an enemy has either very strong defense, you are debuffed or has buffs that prevents damage.
In this case, you will see the exact oposite happen. The medal will do 1 damage on the initial attack, and do more (but not normal) damage on the follow-up attack.
This is pretty interesting to see, but it points to a very obvious fact that we should all know by now - medals that have buff or debuff effects are *usually* reapplied.
In this case, it's not just a matter of using the "same damage at 40% power". The medal will recalculate damage based on the new buffs and debuffs.
This is important when comparing medals with different stats, as an extra buff or debuff plus the extra damage gained from the medal itself and any other medals combined may be better than a comparable high damage medal.

Finally, you'll notice that there is not one, but two Extra Attacks. This is not in error. If you use special attacks, you will only be able to use one Extra Attack.
However, if you use normal attacks, you can use two Extra Attacks, for a total of 3 attacks from 1 medal. Assuming all the attacks are the same TapOrSwipe, this gives a 180% boost to a regular attack.
Unfortunately I can't think of a situation where this would actually be useful. And no, you can't start with a normal attack and follow-up with two special attacks.
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X: The Entire Rebuilt Damage Formula.
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NORMAL SPA DMG = ROUND( (A x ( STR + STR1000 + STR1000 + CHIPS + BOOST ) + B x ( STR + STR1000 + STR1000 + CHIPS + BOOST ) ^ 2 ) x SLOT x GAR - DEF ) ) x (PSMAR + PSMDR - 100%) x SKILL x TYPE x RAND x SPA x ( 100% + Guilt ) x (R.DMG+40% + R.DMG+40%) + ExATK(DMG)
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FIXED SPA DMG = SPA x ( 100% + Guilt ) x (R.DMG+40% + R.DMG+40%) + ExATK(DMG)
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NORMAL ATK DMG = ROUND( (A x ( STR + STR1000 + STR1000 + CHIPS + BOOST ) + B x ( STR + STR1000 + STR1000 + CHIPS + BOOST ) ^ 2 ) x SLOT x GAR - DEF ) ) x TapOrSwipe x Critical x (R.DMG+40% + R.DMG+40%) + ExATK(DMG) + ExATK(DMG)
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This is the entire Rebuilt Damage Formula. Ok so it's 3 formulas, whatever.
For developers, it's just a simple matter of determining if the medal is performing a normal attack, or if your special attack is fixed damge.
I broke them apart here just for the sake of ease, but if you really want to see the entire formula in action, I encourage you to look at the way I've used it in the Damage Calculator Tab.
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XII: Lookup Tables
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So why the lookup tables? It's pretty simple - I was unable to find formulas that would easily describe the numbers I was seeing.
It's not unpratical either, the game surely houses it's own data tables somewhere within it's files for things like base medal stats, quest details, base enemy stats, and the like.
Until such a time the data I've collected can be explained via a formula, it's best to have it within a table.
You can see all the detalis I think is relevant under the Tables Tab.

As always, this information is still under testing and is subject to change.
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XIII: Summary/Closing.
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PART 3 - BEST PRACTICES
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STRENGTH & DEFENSEIn regards to all other stats, in order to do damage, your STRENGTH must overcome the DEFENSE stat. STRENGTH and DEFENSE is what determines your BASE DAMAGE. Most of your other buffs depend on a high BASE DAMAGE value to do even greater damage, and if your base damage is low, then you will do very little damage overall no matter how much buffs you have.

Consider for example: You have a medal that has 1000 STR. You also have 150% GUILT, 150% TYPE (PvE), 180% AB4M, and 400% SPA for a total of 880% BASE DAMGE multiplier. But the enemy your fighting also has 1000 DEFENSE. Your BASE DAMAGE is 0. 0 * 880% = 0 DAMAGE. But the game rounds up to 1 since you can't do 0 damage. Don't you feel lucky?

This is why anything that increases STRENGTH and decreases DEFENSE is one of the most important stats in the game.
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SLOTKeyblade slot is a multiplier toward STRENGTH. As previously discussed above, this is very important. If your medal has slot preferences in the special attack section, it is usually always better to ignore it if you can fufil the keyblade slot conditions.
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STRENGTH & DEFENSE MULTIPLIERSGAR, GDR, Traits, etc. Notice that these come in two flavors - One to increase STRENGTH and one to decrease DEFENSE. Also note that STRENGTH and DEFENSE work against each other, so lowering DEFENSE is akin to raising STRENGTH. Unfortunately we don't know the exact formulas for DEFENSE, but don't forget that if your capped on STRENGH that lowering DEFENSE has a similar effect.
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BASE DAMAGE MULTIPLIERSSomething you'll notice with BASE DAMAGE multipliers is that their numbers can be much higher than the multiplers you will see for STRENGTH & DEFENSE. This is intentional, because as you get high enough BASE DAMAGE, the trade off between GAR & GDR and something like PSMAR & PSMDR becomes more attractive. I would like to do an analysis someday to find when a good turning point would be and I'm sure it's quite simple to figure out. But basically, the more BASE DAMGE your doing, the better BASE DAMAGE multipliers become.
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PSMAR & PSMDRPSMAR & PSMDR is a special multiplier. Unlike other multipliers, they work together to form one multiplier together. They both have the same table - IE: PSMAR1 is the same as PSMDR1 and so on. The difference is that PSMAR is on your character and PSMDR is on the enimies themselves. Nevertheless, you can lump them together to form one giant PSM value (PSMAR+PSMDR), but once complete you remove 100% (since a base PSMAR0 + PSMAR0 would give you 200%). This gives you a range of 100% to 440%.
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TYPE (PvE)If you follow Paper>Rock>Scissors then the attribute system would be Physical>Speed>Magical. If it is weak, it will deal 66% damage. Neutral, 100% damage. Strong is 150% damage. What I did not cover was the "no attribute" and "ignores attributes".

If a medal has "with no attributes" description, then it will deal the same as neutral - 100% damage.
If a medal has "ignores targets' attributes" description, then it will deal the same as strong - 150% damage.
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SPA & GUILTWhen comparing medals (and all other stats being similar) consider both the SPA and the GUILT. The section of the formula for both is (SPA)*(100%+GUILT).

For example: A medal with an SPA of 4 and a GUILT of 100% has a multiplier of 800%. A medal with an SPA of 3.2 and a GUILT of 150% also has a multiplier of 800%. Here you can see that neither SPA nor GUILT is a good indicator that one is better than the other. Some tier 5 medals actually have lower SPA values than their tier 4 cousins, but since they can get higher GUILT it makes them both comparable with each other.
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ExATKExtra Attack reduces the total damage after all calculations by 40%, therefore a high DEFENSE enemy will still take damage (IE: it does not decrease STRENGTH).
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Skill PerkSkill Perk does not add points directly to the percentage chance for a skill to proc. The exact formula is (SKILL%)*(1+SKILLPERK/100)
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PART 4 - BEST TRAITS
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Rank 1:
Aerial Enemy DEF -60%
Ground Enemy DEF -60%
When pushing tiers, the biggest problem is running into enimies with strong defenses. Even boosted medals with maxed chips, STR +1000 traits and all the buffs and debuffs you can give, it will still be unable to pierce a particularly strong enemies defenses. On the other hand, a midly strong medal with a DEF -60% trait can easily hold it's own against the same enemy. Put the same trait on your best medal and you can push through the most difficult of tiers with ease. The reason? The defense knockdown is a percentage instead of a flat value. This makes it even stronger as the enemies defenses go up. Will stack with the other, but not itself. Try to get both for the best attack medal!
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Rank 2:
Extra Attack: 40% Power
This trait is mainly used for utility rather than for damage. Put this on your AP/HP/Buffing/Debuffing Medal and you'll be able to double it's effects. But watch out! It will cost double the SP. Stackable, but only for normal attacks.
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Rank 3:
Damage in Raids +40%
This is a special case. Combine this with your best all target medal with a ABxM & Lux+ skill and you'll rake in the lux. Perfect for those monthly raid events. Stackable.
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Rank 4:
STR +1000
Best all purpose trait - works under any condition. Not very strong but worth keeping if you can't get anything better. Stackable.
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Rank 5:
DEF +2000
Best defensive trait - works under any condition. Stackable.
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Rank 6:
Max Gages +2
Some high end keyblades have less SP, which may make this more desirable. There are other ways to reduce SP consumed or restore SP without sacrificing much damage. Stackable.
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Rank 7:
Poison Resist +20%
Paralyze Resist +20%
Sleep Resist +20%
Special case senarios. Not relly useful unless you can get 100%. Stackable.
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Rank 8:
HP + 800
Absolute worst trait. As enemies get stronger they hit much harder and HP doesn't mitigate the damage as much as DEFENSE would, so DEF + 2000 is better. It is fun to see your HP bar creep all the way across the screen though! Stackable. Medals that do damage based on HP percentage, so raising your Max HP will not have an effect. Stay at full health and you'll have your max multiplier.
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