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WoL Mechanics of Spirits: What the Numbers Mean and How to Efficiently Hurt Others

snjwffl

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tl;dr A hundred attack points boost damage by 4%, while 100 defense points resist 6% more damage; type advantages give a 30% boost to damage dealt and 15% reduction in damage taken; stacking abilities isn't very efficient.


Super Smash Bros. Ultimate introduced a new mechanic called spirits, which can have a drastic effect on how a battle plays out. A team of spirits comes with numbers that are supposed to indicate how good it is. However, besides "bigger number good", not much has been known for what exactly those numbers do. This post aims to rectify that lack of knowledge.

So first off, what are spirits? Spirits are items(?) in the form of characters from other games that you can equip to improve your character. They come in two varieties, called primary and support. Let's look at them separately.
Primary Spirits

These come with a rarity, series, level, numbers for attack, defense and power, a number of slots, a type, and sometimes abilities of their own.
  • Rarity is displayed as between 1 and 4 stars, with 1 star being the most common and 4 being the rarest. Roughly speaking, rarer spirits are better than more common ones.
  • Series is the game franchise from which they come
  • The level is a number from 1 to 99. The only effect this has is on increasing the attack and defense.
  • Attack and defense are what they sound like: higher attack means you dish out more damage, and higher defense means you take less.
  • Power is the sum of attack and defense. It's supposed to be a measure of how strong the spirit is. (It's not)
  • Slots, of which there are between 0 and 3, determine how many support spirits you can use.
  • A primary can be one of four types: Shield (blue), Attack (red), Grab (green), and neutral (gray).
    • These are then used in something akin to elemental rock-paper-scissors: Shield is strong against Attack, which is strong against Grab, which is strong against Shield. This forms a cycle where each is strong or weak against the other two. The last type, neutral, is not weak against any of the others, but neither is it strong against others.
    • Even though they're named things like attack/grab/shield, they don't actually affect those things.
  • Abilities, which not all primaries have, are additional enhancements that the spirit can grant. These are similar to the abilities that support spirits have, only there is less of a variety.
If the fighter and primary are of the same series, then both the attack and defense stats are increased by 10%. This is factored into the displayed numbers.
Support Spirits

Support spirits can be equipped to the primary spirit to add additional abilities They come with a rarity, cost, and ability. These do not have a series associated with them that will affect anything.
  • Rarity is the same as for primary spirits.
  • Cost is how many slots of the primary it takes up. You can't equip support spirits with a total cost more than the number of slots the primary has.
  • Abilities are the main feature of support spirits. A far-from-exhaustive list of the kinds of abilities is
    • increase damage dealt or damaged received in various situations
    • starting a battle with an item
    • changing your speed or jump height
    • reducing landing lag or smash charge time.

How do They Affect Damage?

The damage for an attack by you is given by
Code:
[Damage] = [Base_Damage] × (1 + 0.0004×[Attack]) / (1 + 0.0006×[Defense]) × [Type_Multiplier] × [Ability_Attack_Multiplier] × [Ability_Defense_Multiplier]
where
  • [Base_Damage] is how much the move would do if no spirits were involved
  • [Attack] is your attack; if you don't have a spirit equipped then this is 0
  • [Defense] is their defense; if they don't have a spirit equipped then this is 0
  • [Type_Multiplier] is:
    • 1.3 if you have a type advantage (e.g. Shield against Attack)
    • 0.85 if you have type disadvantage (e.g. Attack against Shield)
    • 1 otherwise
  • [Ability_Attack_Multiplier] and [Ability_Defense_Multiplier] are a bit more complicated, and will be discussed below.

In other words:
  • every 100 points of attack increases damage done by 4%
  • every 100 points of defense increase damage resistance by 6%
  • each point in defense takes 1.5 points in attack to cancel out
  • a type advantage deals 30% more damage, while a disadvantage reduces damage done by 15%

Ability Multipliers

This one is a bit more complicated. In general, these stack multiplicatively, so if two different abilities would increase damage by 10% each, then the multiplier would be 1.1×1.1=1.21. However, when multiple copies of the same ability and all come from support spirits, then the multiplier is given by something else. Some of the multipliers are:
  • Attack Multipliers:
    • Slightly increaces the power of _____
      • 1 copy: 1.1
      • 2 copies: 1.18
      • 3 copies: 1.26
    • Increases damage dealt to _____ (in particular, Metal Killers)
      • 1 copy: 1.4
      • 2 copies: 1.45
      • 3 copies: 1.5
  • Defense Multipliers:
    • Slightly decreases the damage taken from _____
      • 1 copy: 0.6
    • Reduces the damage taken from _____
      • 1 copy: 0.6

Example

Say we are using Shulk's Neutral A (a punch) with the following spirit team:
  • Primary: Giga Mac, lvl 45
    • Attack: 3193
    • Defense: 2041
    • Ability: Fist Attack ↑ ("Slightly increases the power of punches and elbow strikes.")
  • Support #1: Ricky
    • Ability: Fist Attack ↑ ("Slightly increases the power of punches and elbow strikes.")
  • Support #2: Fei Long
    • Ability: Fist Attack ↑ ("Slightly increases the power of punches and elbow strikes.")
  • Support #3: Rock Mario
    • Ability: Physical Attack ↑ ("Slightly increases the power of punches, kicks, and bites.")
And we're attacking a Pichu with no spirits.

We have [Base_Damage]=2.4, [Attack]=3193, [Defense]=0, and [Type_Multiplier]=1. Since the defender has no spirits, [Ability_Defense_Multiplier]=1. Finally, for [Ability_Attack_Multiplier]:
  • There is one relevant ability on the primary, so we get a ×1.1
  • There are two copies of the same ability on supports, giving a ×1.18
  • There is another single copy of a relevant ability on a support, giving another ×1.1.
Overall, we get [Ability_Attack_Multiplier] = 1.1 × 1.18 × 1.1 = 1.4278
Putting this all together, the damage is
[Damage] = 2.4 × (1 + 0.0004 × 3193) / (1 + 0.0006 × 0) × 1 × 1.4278 × 1 = 7.8...
It's more than tripled!

What if Pichu had only a primary spirit
  • Primary: Welt, lvl 99
    • Attack: 2736
    • Defense: 2964
    • Ability: None
Then the only change is that [Defense]=2964, giving
[Damage] = 2.4 × (1 + 0.0004 × 3193) / (1 + 0.0006 × 2964) × 1 × 1.4278 × 1 = 2.8..
Well, it's bigger than 2.4, but not by much. What's going on here? Going back to the formula, for each point in defense, the attacker would need 1.5 points in attack just to break even! Without all of the abilities (but same attack power), the damage in this situation would only be 2.0.

How to Efficiently Hurt Others

What will dish out the most damage?
  • Ability-wise, you want your supports to have as many differently-named abilities that affect the same attack. It doesn't matter if the primary has the same ability since it's still factored in separately.
    • If you're trying to choose between a primary (call it 'A') with an ability that boosts damage by 10%, or another primary (call it 'B') without that ability, then you would deal more damage with B as long as it's attack is more than 0.1/0.0004=250 of A's. [Not quite right. It depends on what your attack stat already is. More work to be done.]
  • As for types, you get a +30% with the advantage. Not taking the type advantage is only worth it if the other has 0.3/0.0004=750 more attack.
  • Specifically for Metal Killers: you don't do much more by stacking them. It's best to use one Metal Killer, and other damage-boosting abilities.

I hope this helps with choosing how to get the most out of this new mechanic!

PS: sorry for the uh... research-paper-style this is written in. Old habits die hard, but I at least managed to stop myself from adding in an abstract, a literature review, and a methodology section.

[Edit 12/13] I did a massive re-write and added more information about stacking abilities, spirits in general, and added a couple sample calculations.
 
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Justin Allen Goldschmidt

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What about the differences between spirits that cover just "fist" or "foot" vs ones that say "physical"? Based on description it seems like physical completely invalidates the other two.
 

snjwffl

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What about the differences between spirits that cover just "fist" or "foot" vs ones that say "physical"? Based on description it seems like physical completely invalidates the other two.
Thanks for asking. I have no idea, so I've added it to my to-do list.

Are there other aspects of spirits that affect damage? My to-do list right now is
  • Same-franchise boost (looks like 10% added to str/def, but more testing to be done)
  • Other enhancements besides "slighty improves ___"
  • Interactions of different types of enhancements.

As an aside: does anyone have any recommendations for characters that have punches that do consistent damage with button mashing (so I can just sit back and mash A/B or whatever)? Or at least ones where the damage doesn't depend on distance and doesn't have too much knockback? I like to take the total damage after 10 consecutive attacks so I can get the hundredths digit of the damage done, but of the ones I've tried so far (Shulk and Little Mac) it's a pain to get 10 attacks in consistently. Yoshi is super punchable by Shulk

I did a massive re-write of the first post that now includes a comprehensive formula (and sample calculations) for damage done due to spirit stats and abilities.
 
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Luigifan18

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Is this topic stickied yet? It seriously needs to be. Also, get to SmashWiki pronto!
 

snjwffl

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Thanks for the comments. I'm new to smashboards (actually, the smash community altogether) and don't know the etiquette. Should I message a mod about stickying or wait till one notices this?

As for SmashWiki, what should I do there? I didn't see any pages even talking about spirits. If it involves making brand new pages, honestly I'm not up for all the work lol
 

Muhznit

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Good read, but how do dojos factor in? I left a Wolf Link and Midna spirit at the Land-style dojo for 2 hours, and noticed a HUGE increase in Ganondorf's movement speed.
 

Circlesho

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Some of the traits are a little vague. I got a few questions about which traits apply to what attacks..

Shooting Attack- Does this apply to just weapons that shoot projectiles like fox's gun, or does it also apply to throwing projectiles in general, like with king k rool?
Physical Attack- Does this apply to every attack on every character that is made through use of the body, or just with kicks/punches?
Fist Attack- I'm assuming this just applies to all attacks made through the hand?
 

NMcCoy

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Additional stacking/stat/misc info:
"Weight ↓" primary skill decreases weight by 20%, while "Lightweight" decreases it by 10%. "Weight ↑", on the other hand, increases weight by 10%. These appear to stack linearly. This was tested using the Mushroom Kingdom scales and character weight numbers. I have not yet tested weight-modifying styles.

Impact Run stacks linearly, dealing 5% damage per instance when traveling at maximum momentum (early impacts deal less damage). This is not affected by attack stat modifiers.

Critical-Health Healing heals for 50%. Combining the support and primary versions causes it to heal for a total of 75% instead. Equipment Style does not affect this healing.

Isabelle's down-smash is not a water attack as far as spirits are concerned.

Multiple instances of giant/metal extend duration.

Richter's Holy Water does get boosted by Aura Attack ↑.

Transformation Duration ↑ affects invincibility gained from other skills. I have yet to test if it boosts temporary stat buffs.

Critical Hit skills proc independently.

Killing Edge appears to be neither a "Sword" nor a "Weapon".
 
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JiggyNinja

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Killing Edge appears to be neither a "Sword" nor a "Weapon".
Does Beam Sword count? If not then it's probably just referring to the weapons characters naturally carry. IIRC the Weapon Attack Up description refers to whips, and there are no whip items.

Killing Edge and Beam Sword are probably considered Battering weapons.

I think one question that needs an answer is why the hell is Olimar such a goddamned monster when he's buffed by a spirit.

Dojo effects! I haven't tested all of them, but here's some of the more important figures.

Offense, defense, and power effects I just tested their damage. Changing damage also changes knockback, but I'm less sure how to calculate that.

All damage was calculated using Lucina's Shield Breaker comparing two Lv 99 Lyn spirits, one with a Dojo style and one without.

Jump height was eyeballed from the Training stage grid.

Running speed was measured on the Training stage, setting the Ryu CPU to do Side Smashes and measuring how far I could run in between the "Heeyah!"

Demon Style
Greatly increase: Offense (+20%)
Greatly reduce: Defense (-20%)

Offense I am assuming to refer to the damage all your attacks deal, and defense the damage you receive from all attacks. However because Defense appears to be in the denominator of the damage calculation, 80% defense actually reflects a 25% increase in the damage you receive. This style is a double-edged sword just like it looks, but it buffs your opponent slightly more than it buffs you.

Land Style
Increase: Ground Power (20%), Move Speed (20%)
Decrease: Air Power (-70%), Jump (-13.3%)

Air Style
Increase: Air Power (+20%), Jump (+13.3%)
Decrease: Ground Power (-70%), Move Speed (-20%)

These two styles are basically perfect mirrors of each other. The boost is about the same as Demon style, but the reduction they provide to the other power is ridiculously huge. I think these styles would only be appropriate for characters with a much higher than normal emphasis on an air or ground game, like Jigglypuff or Little Mac.

Just so you don't think I'm kidding about the -70%, Lucina's grounded Shield Breaker does 34.5 damage normally, 41.4% with Land Style, and 10.3% with Air Style.

Brick Wall Style
Greatly increase: Defense (+40%)
Greatly reduce: Offense (-57%)

This is not the mirror of Demon Style. It's a bit worse.

Boulder Style
Increase: Defense (+10%), Move Speed (+20%)
Decrease: Offense (-30%), Jump (-13.3%)

Around here I stopped really investigating the dojos. They don't seem very useful because what they strengthen is usually massively outweighed by what they weaken. Demon Style is probably the most balanced, but it's still tilted slightly against you.

ETA: Oops, forgot to check about double posting.
 
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Team Orchid

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I'd just like to mention that the downsides of Tank Style can be negated with a jump up and a speed up, so spirits with one of those things and at least one slot open can enjoy boosted stats. Obviously it works best on three slot spirits.
 

CyberMario

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There are crazy combinations of spirit combos. It sucks that stacking support spirit traits diminish the return, but there could be ways around it. Good info.

Here is a challenging question:
What spirit combo will best break shields? That's not easily measurable and several traits overlap in what they do.

Traits that could be used:
Guard Breaker
Trade-Off Attack
Weapon Attack Up
Hyper Attacks
Special Attack Up
 

JiggyNinja

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There are crazy combinations of spirit combos. It sucks that stacking support spirit traits diminish the return, but there could be ways around it. Good info.

Here is a challenging question:
What spirit combo will best break shields? That's not easily measurable and several traits overlap in what they do.

Traits that could be used:
Guard Breaker
Trade-Off Attack
Weapon Attack Up
Hyper Attacks
Special Attack Up
It's very easily measurable. Create all your different combinations as Spirit Teams, then go into training mode and use frame-by-frame mode to screenshot the size of the shield just after attacking it.

I tested quite a few things, culminating in these two screenshots of a Master Core attacking a Protoman with Ganondorf's Warlock Punch. In the first, I buffed 3 different properties of the attack (Neutral Special, Fist, and Fire). In this second, I equipped 3 Shield Damage Ups. Triple Shield wins.

I tested on the sandbag in the Spirit Team test mode, and the neutral special (along with the other directional special buffs), Fist, Physical, Fire/Explosion, and Undamaged attack buffs all do the same damage to the Sandbag, 117.1% using Fierce Deity Link as the Primary. (106.5% with just FDL and no Secondary). The more general Special Attack Up (Mew and Shine Sprite) is weaker, doing 111.8% so I didn't even bother testing that against the shields.

Trade-Off attacks is more powerful than the other attack buffs (does 125.6% to Sandbag), but it does less shield damage than a Shield Damage buff. 1 TO Attacks + 2 Shield Damages might be more optimal, but I think it would be borderline and the starting 30% damage is a very significant penalty.

I didn't specifically test Giant since it's a temporary transformation, but being large does increase your damage which will do more damage to shields. I know I break a lot of shields when I'm using Medusa, Mother Brain, or Petey Piranha, even on Legendary fights. Of course, that's a charged Up Smash from a giant Ganondorf they're trying to block so I guess that will wreck anyone's day.

So for maximum shield breaking power for characters that aren't a mass of evil raw power, load up on Shield Damage buffs. They've got the best value for that.
 

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Saikyoshi

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I beat World of Light eight times (via speedrunning; I'll post the route if anyone's interested) so I could have a Galeem or Darkhon spirit for every dojo style, to equip to CPU opponents.

I was hoping for an equal matchup, but neutral style vs. neutral style is still affected due to the defense stat being more powerful. So it's not quite what I hoped for.

Are there any spirits that truly have equal attack and defense? Like... if two opponents equipped the same one, it'll be like they had no spirits equipped at all?
 
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JiggyNinja

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I beat World of Light eight times (via speedrunning; I'll post the route if anyone's interested) so I could have a Galeem or Darkhon spirit for every dojo style, to equip to CPU opponents.

I was hoping for an equal matchup, but neutral style vs. neutral style is still affected due to the defense stat being more powerful. So it's not quite what I hoped for.

Are there any spirits that truly have equal attack and defense? Like... if two opponents equipped the same one, it'll be like they had no spirits equipped at all?
Easy math.

Basically, you're looking for this part of the equation to equal 1: (1 + 0.0004×[Attack]) / (1 + 0.0006×[Defense]). Solve it and you find that the ideal Att/Def ratio is 1.5 (Attack is 50% higher than Def). There are 3 spirits that have this ratio at Lv 99 (accurate to 7 decimal places) and no special effect: Bonkers, Titania, and Eevee. There are 11 more Spirits that are slightly outside of this range, but still within 0.005 of the ideal ratio:

  • Poppi Bros. Jr.
  • Zoroark
  • Musashi
  • Zygarde (50% Forme)
  • Dee-Jay
  • Hades (not enhanced)
  • Teddy
  • Glory of Heracles Hero
  • Octoling
  • Akuma
  • Ninja King

I tested this with the Ganon spirit (perfect ratio, but has Weight Up effect so it's no good for you) and it made sure it didn't change the power of Lucina's Shield Breaker. 27.6% with, 27.6% without.

Source for the Spirit stats: SmashWiki
 
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Saikyoshi

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Easy math.

Basically, you're looking for this part of the equation to equal 1: (1 + 0.0004×[Attack]) / (1 + 0.0006×[Defense]). Solve it and you find that the ideal Att/Def ratio is 1.5 (Attack is 50% higher than Def). There are 3 spirits that have this ratio at Lv 99 (accurate to 7 decimal places) and no special effect: Bonkers, Titania, and Eevee. There are 11 more Spirits that are slightly outside of this range, but still within 0.005 of the ideal ratio:

  • Poppi Bros. Jr.
  • Zoroark
  • Musashi
  • Zygarde (50% Forme)
  • Dee-Jay
  • Hades (not enhanced)
  • Teddy
  • Glory of Heracles Hero
  • Octoling
  • Akuma
  • Ninja King

I tested this with the Ganon spirit (perfect ratio, but has Weight Up effect so it's no good for you) and it made sure it didn't change the power of Lucina's Shield Breaker. 27.6% with, 27.6% without.

Source for the Spirit stats: SmashWiki
Wow. Fitting that Eevee's one of 'em.
Also, huh. It worked. I just tested it. Mario's fully-charged Fsmash did the exact same amount of damage when both players have a lone Lv. 99 Titania spirit equipped as it did when neither had any spirit. This is good to know.
 

JiggyNinja

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It doesn't matter if the primary has the same ability since it's still factored in separately.
I don't know if this is something that patches have changed or if it's always been like this, but me testing just now shows that this is NOT true. The abilities of a primary spirit absolutely do count for the diminishing returns.

I have tested this with several different effects.

As a first example, Giant Killer (with Soma Cruz) or Metal Killer (from Big Boss) will count against any X Killer secondaries, so you can't stack two layers of them for a double 40% buff (which would be insane). You can stack Giant Killer and Metal Killer together if the enemy is both (like Omega Ridley), but that's pretty rare.

Second example, Ganondorf's power is counted as a Fire/Explosion attack. With Warlock Punch, both Fire/Explosion Up and Fist Attack Up increase damage by 10%, and both together boost it by 21% (1.1 x 1.1 = 1.21). Using the Dark Daroach primary (who has a Fire/Explosion buff), Warlock Punch does more damage with a Fist Attack secondary (119.9%) than a Fire/Explosion secondary (117.0%).

Third example, one level of Trade-Off Attacks gives a 23% boost, and a second Trade-Off Attacks gives an additional 7.4%. Using a Trade-Off Attacks secondary with the enhanced Hades spirit gives a 7.3% boost, exactly the same as going from 1 level to 2.

Primary effects are not applied independently of the secondaries.
 
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