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==Formula==
===''SSB''===
[[File:SSB64KnockbackFormula.svg|450px|class=invert]]
===''Melee'' onward===
[[File:SSBMKnockbackFormula.svg|500px|class=invert]]
[[File:gravity knockback.gif|thumb|A demonstration of the effect of gravity on knockback, the Shulk on the left uses the hyper Speed Monado Art, increasing his gravity, and as a result, the knockback he sustains.]]<br>


Starting in ''Brawl'', a second formula is also used to alter knockback based on the target's [[gravity]]:
[[File:SSBBKnockbackFormulaGravity.svg|125px|class=invert]]
The result of this formula increases vertical launch speed if the target enters tumble. As a result, characters with higher gravity get launched faster than those with lower gravity, depending on how vertical the angle is, resulting in fighters with higher gravity stats having worsened vertical survivability, seemingly as an attempt to normalize the effect of combos and multi-hit moves on characters of differing gravity. This formula is also applied to moves that launch opponents downwards, though since vertical launch speed is negative in this case, the result of the formula effectively decreases it slightly instead, reducing the effectiveness of [[meteor smash]]es on fast fallers.
In ''Ultimate'', moves that launch at angles between 70° and 110° now instead cause characters' falling speeds to be homogenized to a set value of 1.8 during hitstun. Furthermore, the additional launch speed from the gravity formula is no longer applied. As a result of these changes, falling speed no longer plays as much of a factor on determining a characters' vertical survivability, and moves that deal vertical knockback are generally easier to survive compared to ''Brawl'' and ''SSB4'', thus making vertical survivability among the cast much more consistent than in previous games. Note that weight-independent moves do not homogenize falling speeds or use the different gravity value, so gravity and fall speed (especially the latter) still have an impact on the vertical survivability against those moves.
<hr>
==Formula==
===''SSB''===
<big><math>\left ( \left ( \left ( \left ( \left ( {p \over 10} + {{p \times d} \over 20} \right ) \times w \times 1.4 \right ) + 18 \right ) \times s \right ) + b \right ) \times r</math></big>
===''Melee'' onward===
<big><math>\left ( \left ( \left ( \left ( \left ( {p \over 10} + {{p \times d} \over 20} \right ) \times { 200 \over { w + 100} } \times 1.4 \right ) + 18 \right ) \times s \right ) + b \right ) \times r</math></big>
[[File:gravity knockback.gif|thumb|A demonstration of the effect of gravity on knockback, the Shulk on the left uses the hyper Speed Monado Art, increasing his gravity, and as a result, the knockback he sustains.]]<br>
Starting in ''Brawl'', a second formula is also used to alter knockback based on the target's [[gravity]]:
<big><math>(g - 0.075) \times 5</math></big>
The result of this formula increases vertical launch speed if the target enters tumble. As a result, characters with higher gravity get launched faster than those with lower gravity, depending on how vertical the angle is, resulting in fighters with higher gravity stats having worsened vertical survivability, seemingly as an attempt to normalize the effect of combos and multi-hit moves on characters of differing gravity. This formula is also applied to moves that launch opponents downwards, though since vertical launch speed is negative in this case, the result of the formula effectively decreases it slightly instead, reducing the effectiveness of [[meteor smash]]es on fast fallers.
In ''Ultimate'', moves that launch at angles between 70° and 110° now instead cause characters' falling speeds to be homogenized to a set value of 1.8 during hitstun. Furthermore, the additional launch speed from the gravity formula is no longer applied. As a result of these changes, falling speed no longer plays as much of a factor on determining a characters' vertical survivability, and moves that deal vertical knockback are generally easier to survive compared to ''Brawl'' and ''SSB4'', thus making vertical survivability among the cast much more consistent than in previous games. Note that weight-independent moves do not homogenize falling speeds or use the different gravity value, so gravity and fall speed (especially the latter) still have an impact on the vertical survivability against those moves.
<hr>
==Power-ups==
[[File:stickerMenu.png|left|thumb|Stickers being placed on a trophy base.]]
On Friday, Jan 18th 2008, [[Smash Bros. DOJO!!]] announced that stickers can be used as power-ups. To do so, the stickers must be placed on the undersides of character trophies. Different stickers give different boosts, as well as some that are character-specific (most of them can be used by any character). Larger stickers give higher boosts, but take up more space on the trophy base. The statistical boost is only for The Subspace Emissary and does not apply to any other modes. Applied stickers can be moved around, but removing one discards it permanently (though they can be regained through playing).
[[File:Stick.jpg|thumb|A sticker as an in-game item, with {{SSBB|Yoshi}} about to grab it.]]
Stickers with the same effects do not stack; e.g. if an Arm +13 and an Arm +20 are placed on the base of a trophy, that character will only receive the larger +20 boost to arm attacks, not +33, although an Arm/Leg sticker will stack with individual Arm and Leg stickers - i.e., an Arm/Leg + 10, an Arm +10 and a Leg+10 sticker will all combine to boost Arm and Leg attacks by 20. It is also possible for a single attack to fall under several categories, like Captain Falcon's Falcon Punch, which deals Arm, Specials: Direct, and Fire damage.
The stickers page can be accessed in The Subspace Emissary by pressing the [[1 button|1]] or [[B button]] on the level map and selecting the "Stickers" option to the left of the "Save" option. Also, using a Continue in The Subspace Emissary deducts half of the stickers currently earned in the level.
{{clrl}}
===Power-Up Effects===
Each sticker has a single effect which may be any of the following. The number listed with the effect indicates how much the aspect is improved.
====Attack-based effects====
The largest category of stickers simply increases the damage dealt by the user's attacks.
The formula for the damage multiplier is:
[[File:StickerAttackFormula.svg|125px|class=invert]]
[Specials: Indirect] Attack is an exception and uses:
[[File:StickerIndirectAttackFormula.svg|125px|class=invert]]
Where '''v''' is the value given by the sticker description and '''r''' is the damage multiplier; '''r''' cannot be greater than 25.675, though this can't be reached without hacking. For example, a sticker with a value of 20 will deal 1.25× damage compared to base damage. Note, in the code the sticker's value is cut in half and rounded down, resulting in every odd number being the exact same as the even number before it (e.g. 3=2, 25=24, etc.).
{{clr}}
{|class="wikitable"
|-
!Icon!!Effect!!Description
|-
|{{TypeIcon|Hand}}||[Arm] Attack||Increases the damage done by [[Arm|punches, slaps, pokes, and elbows]].
|-
|{{TypeIcon|Foot}}||[Leg] Attack||Increases the damage done by [[Leg|kicks, knees, and stomps]].
|-
|{{TypeIcon|Hand}}{{TypeIcon|Foot}}||[Arm],[Leg] Attack||Increases damage done by the previous two categories as a single sticker.
|-
|{{TypeIcon|Head}}||[Head] Attack||Increases the damage done by [[head]]butts and the like.
|-
|{{TypeIcon|Body}}||[Body] Attack||Increases the damage done by [[Body|full-body attacks]] such as {{SSBB|King Dedede}}'s [[dash attack]] or {{SSBB|Yoshi}}'s [[Yoshi Bomb]]. Always paired with [Spin] attack boosts in a sticker.
|-
|{{TypeIcon|Spin}}||[Spin] Attack||Increases the damage done by attacks which involve [[spin]]ning. Always paired with [Body] attack boosts in a sticker.
|-
|{{TypeIcon|Tail}}||[Tail] Attack||Increases the damage done by [[tail]] attacks. Only Yoshi, {{SSBB|Pikachu}}, {{SSBB|Diddy Kong}}, {{SSBB|Pokémon Trainer}}, {{SSBB|Fox}}, {{SSBB|Falco}}, and {{SSBB|Wolf}} can apply stickers with this effect.
|-
|{{TypeIcon|Bite}}||[Bite] Attack||Increases the damage done by attacks which involves [[Bite|fangs or biting]]. Only Yoshi, {{SSBB|Wario}}, {{SSBB|Pokémon Trainer}}, and Wolf can apply stickers with this effect.
|-
|{{EffectIcon|Slash}}||[Slash] Attack||Increases the damage done by [[slash]] attacks.
|-
|{{TypeIcon|Weapon}}||[Weapon] Attack||Increases the damage done by any [[weapon]], including swords, hammers, bats, umbrellas, and so on.
|-
|{{TypeIcon|Throwing}}||[Throwing] Attack||Increases the [[Throwing|damage done by throws]].
|-
|{{EffectIcon|Flame}}||[Flame] Attack||Increases the damage done by [[flame|fire-based]] attacks.
|-
|{{EffectIcon|Electric}}||[Electric] Attack||Increases the damage done by [[electric]] attacks.
|-
|{{EffectIcon|Freezing}}||[Freezing] Attack||Increases the damage done by [[freezing|ice-based]] attacks.
|-
|{{EffectIcon|Water}}||[Water] Attack||Increases the damage done by [[water|water-based]] attacks. Only the Pokémon Trainer's {{SSBB|Squirtle}} can apply stickers with this effect.
|-
|{{EffectIcon|Grass}}||[Grass] Attack||Increases the damage done by [[grass (effect)|plant-based]] attacks. Only the Pokémon Trainer's {{SSBB|Ivysaur}} can apply stickers with this effect.
|-
|{{TypeIcon|Energy}}||[Energy] Attack||Increases the damage done by [[energy|energy-based]] attacks such as Fox's {{b|Blaster|Fox}}.
|-
|{{TypeIcon|Magic}}||[Magic] Attack||Increases the damage done by [[magic (type)|magical]] attacks. Only {{SSBB|Peach}} and {{SSBB|Zelda}} can apply stickers with this effect.
|-
|{{TypeIcon|PK}}||[PK] Attack||Increases the damage done by [[PK]]-based attacks. Only {{SSBB|Ness}} and {{SSBB|Lucas}} can apply stickers with this effect.
|-
|{{EffectIcon|Aura}}||[Aura] Attack||Increases the damage done by {{b|aura|effect}}-based attacks. Only {{SSBB|Lucario}} can apply stickers with this effect.
|-
|{{TypeIcon|Pikmin}}||[Pikmin] Attack||Increases the damage done by [[Pikmin]]-based attacks. Only {{SSBB|Olimar}} can apply stickers with this effect.
|-
|{{EffectIcon|Darkness}}||[Darkness] Attack||Increases the damage done by [[darkness|dark-based]] attacks. Only {{SSBB|Ganondorf}} can apply stickers with this effect.
|-
|{{TypeIcon|Explosive}}||[Explosives] Attack||Increases the damage done by [[explosive|explosion-based]] attacks.
|-
|[[File:SpecialsDirect.png|16px|link=Specials: Direct]]||[Specials: Direct] Attack||Increases the damage done by moves that are considered to be [[Specials: Direct|direct]]. The exact criteria are unknown.
|-
|[[File:SpecialsIndirect.png|16px|link=Specials: Indirect]]||{{NTSC}} [Specials: Indirect] Attack<br>{{PAL}} [Indirect] Attack||Increases the damage done by moves that are considered to be [[Specials: Indirect|indirect]]. This includes all projectiles and a few regular, distanced attacks.
|}
====Defense-based effects====
When used, these stickers reduce the damage taken by incoming attacks.
The formula for damage reduction is:
[[File:StickerResistanceFormula.svg|125px|class=invert]]
Where '''v''' is the value given by the sticker description and '''r''' is the damage multiplier. For example, a sticker with a reduction of 20 will cause attacks to be scaled to 0.75 of the original damage, or a damage reduction of 25%. Note, in the code the sticker's value is cut in half and rounded down, resulting in every odd number being the exact same as the even number before it (e.g. 3=2, 25=24, etc.).
To prevent the player from taking no damage, values of 80 or more set damage to 1%; this is not possible without hacking, as the highest value on a resistance sticker is 44. Values below 80 behave normally and can potentially reduce damage below 1%.
{|class="wikitable"
|-
!Icon||Effect!!Description
|-
|{{EffectIcon|Normal}}||[Battering] Resistance||Decreases damage taken from [[normal]] attacks.
|-
|{{EffectIcon|Slash}}||[Slash] Resistance||Decreases damage taken from slash attacks.
|-
|{{EffectIcon|Flame}}||[Flame] Resistance||Decreases damage taken from fire-based attacks.
|-
|{{EffectIcon|Electric}}||[Electric] Resistance||Decreases damage taken from electric attacks.
|}
<hr>
==Power-ups==
[[File:stickerMenu.png|left|thumb|Stickers being placed on a trophy base.]]
On Friday, Jan 18th 2008, [[Smash Bros. DOJO!!]] announced that stickers can be used as power-ups. To do so, the stickers must be placed on the undersides of character trophies. Different stickers give different boosts, as well as some that are character-specific (most of them can be used by any character). Larger stickers give higher boosts, but take up more space on the trophy base. The statistical boost is only for The Subspace Emissary and does not apply to any other modes. Applied stickers can be moved around, but removing one discards it permanently (though they can be regained through playing).
[[File:Stick.jpg|thumb|A sticker as an in-game item, with {{SSBB|Yoshi}} about to grab it.]]
Stickers with the same effects do not stack; e.g. if an Arm +13 and an Arm +20 are placed on the base of a trophy, that character will only receive the larger +20 boost to arm attacks, not +33, although an Arm/Leg sticker will stack with individual Arm and Leg stickers - i.e., an Arm/Leg + 10, an Arm +10 and a Leg+10 sticker will all combine to boost Arm and Leg attacks by 20. It is also possible for a single attack to fall under several categories, like Captain Falcon's Falcon Punch, which deals Arm, Specials: Direct, and Fire damage.
The stickers page can be accessed in The Subspace Emissary by pressing the [[1 button|1]] or [[B button]] on the level map and selecting the "Stickers" option to the left of the "Save" option. Also, using a Continue in The Subspace Emissary deducts half of the stickers currently earned in the level.
{{clrl}}
===Power-Up Effects===
Each sticker has a single effect which may be any of the following. The number listed with the effect indicates how much the aspect is improved.
====Attack-based effects====
The largest category of stickers simply increases the damage dealt by the user's attacks.
The formula for the damage multiplier is:
<big><big><math>r={v \over 80}+1</math></big></big>
[Specials: Indirect] Attack is an exception and uses:
<big><big><math>r={v \over 40}+1</math></big></big>
Where '''v''' is the value given by the sticker description and '''r''' is the damage multiplier; '''r''' cannot be greater than 25.675, though this can't be reached without hacking. For example, a sticker with a value of 20 will deal 1.25× damage compared to base damage. Note, in the code the sticker's value is cut in half and rounded down, resulting in every odd number being the exact same as the even number before it (e.g. 3=2, 25=24, etc.).
{{clr}}
{|class="wikitable"
|-
!Icon!!Effect!!Description
|-
|{{TypeIcon|Hand}}||[Arm] Attack||Increases the damage done by [[Arm|punches, slaps, pokes, and elbows]].
|-
|{{TypeIcon|Foot}}||[Leg] Attack||Increases the damage done by [[Leg|kicks, knees, and stomps]].
|-
|{{TypeIcon|Hand}}{{TypeIcon|Foot}}||[Arm],[Leg] Attack||Increases damage done by the previous two categories as a single sticker.
|-
|{{TypeIcon|Head}}||[Head] Attack||Increases the damage done by [[head]]butts and the like.
|-
|{{TypeIcon|Body}}||[Body] Attack||Increases the damage done by [[Body|full-body attacks]] such as {{SSBB|King Dedede}}'s [[dash attack]] or {{SSBB|Yoshi}}'s [[Yoshi Bomb]]. Always paired with [Spin] attack boosts in a sticker.
|-
|{{TypeIcon|Spin}}||[Spin] Attack||Increases the damage done by attacks which involve [[spin]]ning. Always paired with [Body] attack boosts in a sticker.
|-
|{{TypeIcon|Tail}}||[Tail] Attack||Increases the damage done by [[tail]] attacks. Only Yoshi, {{SSBB|Pikachu}}, {{SSBB|Diddy Kong}}, {{SSBB|Pokémon Trainer}}, {{SSBB|Fox}}, {{SSBB|Falco}}, and {{SSBB|Wolf}} can apply stickers with this effect.
|-
|{{TypeIcon|Bite}}||[Bite] Attack||Increases the damage done by attacks which involves [[Bite|fangs or biting]]. Only Yoshi, {{SSBB|Wario}}, {{SSBB|Pokémon Trainer}}, and Wolf can apply stickers with this effect.
|-
|{{EffectIcon|Slash}}||[Slash] Attack||Increases the damage done by [[slash]] attacks.
|-
|{{TypeIcon|Weapon}}||[Weapon] Attack||Increases the damage done by any [[weapon]], including swords, hammers, bats, umbrellas, and so on.
|-
|{{TypeIcon|Throwing}}||[Throwing] Attack||Increases the [[Throwing|damage done by throws]].
|-
|{{EffectIcon|Flame}}||[Flame] Attack||Increases the damage done by [[flame|fire-based]] attacks.
|-
|{{EffectIcon|Electric}}||[Electric] Attack||Increases the damage done by [[electric]] attacks.
|-
|{{EffectIcon|Freezing}}||[Freezing] Attack||Increases the damage done by [[freezing|ice-based]] attacks.
|-
|{{EffectIcon|Water}}||[Water] Attack||Increases the damage done by [[water|water-based]] attacks. Only the Pokémon Trainer's {{SSBB|Squirtle}} can apply stickers with this effect.
|-
|{{EffectIcon|Grass}}||[Grass] Attack||Increases the damage done by [[grass (effect)|plant-based]] attacks. Only the Pokémon Trainer's {{SSBB|Ivysaur}} can apply stickers with this effect.
|-
|{{TypeIcon|Energy}}||[Energy] Attack||Increases the damage done by [[energy|energy-based]] attacks such as Fox's {{b|Blaster|Fox}}.
|-
|{{TypeIcon|Magic}}||[Magic] Attack||Increases the damage done by [[magic (type)|magical]] attacks. Only {{SSBB|Peach}} and {{SSBB|Zelda}} can apply stickers with this effect.
|-
|{{TypeIcon|PK}}||[PK] Attack||Increases the damage done by [[PK]]-based attacks. Only {{SSBB|Ness}} and {{SSBB|Lucas}} can apply stickers with this effect.
|-
|{{EffectIcon|Aura}}||[Aura] Attack||Increases the damage done by {{b|aura|effect}}-based attacks. Only {{SSBB|Lucario}} can apply stickers with this effect.
|-
|{{TypeIcon|Pikmin}}||[Pikmin] Attack||Increases the damage done by [[Pikmin]]-based attacks. Only {{SSBB|Olimar}} can apply stickers with this effect.
|-
|{{EffectIcon|Darkness}}||[Darkness] Attack||Increases the damage done by [[darkness|dark-based]] attacks. Only {{SSBB|Ganondorf}} can apply stickers with this effect.
|-
|{{TypeIcon|Explosive}}||[Explosives] Attack||Increases the damage done by [[explosive|explosion-based]] attacks.
|-
|[[File:SpecialsDirect.png|16px|link=Specials: Direct]]||[Specials: Direct] Attack||Increases the damage done by moves that are considered to be [[Specials: Direct|direct]]. The exact criteria are unknown.
|-
|[[File:SpecialsIndirect.png|16px|link=Specials: Indirect]]||{{NTSC}} [Specials: Indirect] Attack<br>{{PAL}} [Indirect] Attack||Increases the damage done by moves that are considered to be [[Specials: Indirect|indirect]]. This includes all projectiles and a few regular, distanced attacks.
|}
====Defense-based effects====
When used, these stickers reduce the damage taken by incoming attacks.
The formula for damage reduction is:
<big><big><math>r=-{v \over 80}+1</math></big></big>
Where '''v''' is the value given by the sticker description and '''r''' is the damage multiplier. For example, a sticker with a reduction of 20 will cause attacks to be scaled to 0.75 of the original damage, or a damage reduction of 25%. Note, in the code the sticker's value is cut in half and rounded down, resulting in every odd number being the exact same as the even number before it (e.g. 3=2, 25=24, etc.).
To prevent the player from taking no damage, values of 80 or more set damage to 1%; this is not possible without hacking, as the highest value on a resistance sticker is 44. Values below 80 behave normally and can potentially reduce damage below 1%.
{|class="wikitable"
|-
!Icon||Effect!!Description
|-
|{{EffectIcon|Normal}}||[Battering] Resistance||Decreases damage taken from [[normal]] attacks.
|-
|{{EffectIcon|Slash}}||[Slash] Resistance||Decreases damage taken from slash attacks.
|-
|{{EffectIcon|Flame}}||[Flame] Resistance||Decreases damage taken from fire-based attacks.
|-
|{{EffectIcon|Electric}}||[Electric] Resistance||Decreases damage taken from electric attacks.
|}

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