Knockback is the measure of how far an attack sends its target. For most attacks, knockback increases as damage on a character increases. An example of an attack with high knockback is Bowser's forward smash; it launches opponents very far, so far that at high damages it's more powerful than a Home-Run Bat's smash attack. Pikachu's neutral attack, on the other hand, has very low knockback - it hardly sends opponents anywhere, even at ludicrous damages. Attacks with relatively low knockback tend to be good for combos.
The knockback of almost every attack works in tandem with the target's damage - it increases as the target's damage gets higher. It is also affected by the target's weight, gravity, and a few other conditions (such as type effectiveness). While not the primary factor, the damage dealt by an attack is a significant factor in how much knockback it deals - this is the reason stale moves have less knockback than fresh ones, and the reason smash attacks deal significantly more knockback when fully charged.
Each hitbox of a move has two knockback values: a base knockback and a knockback scaling (also known as knockback growth). Base knockback is the minimum amount of knockback the attack can deliver under normal circumstances, and knockback scaling is a factor that controls how much the knockback increases as damage increases.
Moves with high base knockback can deal high knockback (such as performing a forward smash with the Home-Run Bat), even against fighters who haven't taken much damage, and tend to be more effective at KOing when fighters can easily be sent flying at low damage percentages (such as against lighter fighters, when near the edge of the stage, or when a fighter is handicapped to sustain more knockback). Tiny-sized fighters are usually the most vulnerable to getting KO'd by high base knockback attacks, due to having reduced weight, and an increased knockback taken multiplier.
On the other hand, moves with high knockback scaling can reach KO potential more quickly (such as Luigi's forward smash), especially if they have a high damage output, and tend to be more effective at KOing when fighters need to take greater knockback than what a high base knockback attack can deliver on its own (such as against heavier fighters, when far away from a stage's blast line, or when a fighter is handicapped to sustain less knockback). Advanced techniques to extend survival, such as DI and momentum canceling, are also less effective the stronger a move's knockback scaling is.
In Melee, the highest knockback delivered and received by each character is given in a match's results screen, labeled as "Fastest Pitch" and "Top Speed" respectively, though the numbers lack meaning. In Brawl, the velocity applied (in units per 1000 frames) is provided instead of the knockback value (though it's simply knockback divided by 0.03). The unit is given as "mph"; while this would presumably mean "miles per hour", this is obviously not the case, as a 1,000 mph hit would barely send characters anywhere. In Super Smash Bros. for Nintendo 3DS, knockback units are again shown without a meaning, while in Super Smash Bros. for Wii U, they are measured in "mph" as in Brawl, though in a lower scale. Strangely enough, knockback for a same move between the two games is actually shown in different scales: Ganondorf's Warlock Punch, for instance, scores 102 units of knockback against Mario at 0% damage (without other modifiers) in Smash 3DS, while scoring 53 mph under the same conditions in Smash U. Despite these differences among games, they all internally use the same knockback measurement units in accordance to the knockback formula, as evidenced by moves with unchanged damage and knockback values throughout them (such as Jigglypuff's back throw from Melee to Smash 4) keeping their knockback identical.
The following table gives an idea of various knockback strengths:
To determine how far a character is launched away, the numerical amount of knockback caused is multiplied by 0.03 to calculate launch speed, and the initial value then decays by 0.051 every frame, so that the character eventually loses all momentum from the knockback. During this time, character-specific attributes such as air friction are disabled; however, falling speed still takes effect when the character is close to stopping, giving fast fallers slightly better endurance against vertical knockback than others of their weight.
In Super Smash Bros. Ultimate, when hitstun exceeds 32 frames, the process of the character getting launched is sped up for a duration proportional to the hitstun inflicted. This is especially noticeable near KO percentages, where characters fly away very quickly, then come to a stop almost immediately, effectively causing the launch to execute much faster. The effect is also more noticeable for moves which have high hitstun modifiers, such as Isabelle's neutral attack, which can even trigger the effect before the knockback is strong enough to cause tumbling. Because of this change, the hitstun they experience scales much more slowly at higher knockback values. According to director Masahiro Sakurai, this change was implemented to increase the overall speed of the game, by reducing the time during which launched characters are incapacitated. The visual and mechanical differences this effect causes on knockback are notorious enough that it is often dubbed "balloon knockback" by the community, as it has similar physics to hitting a balloon in real life. Moves with set knockback retain traditional knockback physics.
Appearing in all games to date, visual effects known as angle indicators show when a hitbox collides with an opponent; as its name suggests, the angle indicator shows the angle of said hitboxes. In Brawl, angle indicators show different colors depending on who or what they hit. For player one, the angle indicator is red, with the second player's indicator being blue, and so forth. Computer-controlled opponents and objects like Sandbag have white angle indicators. Angle indicators appear in Super Smash Bros. as small "bubbles" appearing in the direction of the angle. In Smash 4, angle indicators appear as colorful, stylized "debris" flying off of an impact.
Smoke trails also indicate the angle at which a character is knocked away, but only appear when a character has taken a lot of damage, and are thus much less useful. In Smash 4, said smoke trails at higher knockback values are accompanied by thick light trails, colored depending on the player that dealt the knockback.
Starting in Brawl, a second formula is also used to alter knockback based on the target's gravity:
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 smashes on fast fallers.
In Ultimate, characters' falling speeds and gravity are homogenized for moves that launch at angles between 70° and 110°, making the effect negligible.
The total amount of knockback dealt can also be subtracted by the target's knockback resistance, which is applied after all the other calculations have been made. However, hitboxes that have the bury effect can ignore the knockback resistance.
If the move has a fixed knockback value set, then d is set to that value, and p is always 10. As a result, the knockback dealt is independent of current damage, damage dealt, and ignores stale-move negation's knockback modifiers. However, it still remains dependent on other factors.
Other physics of knockback
Set knockback, also referred to as fixed knockback, is a property of some attacks where the amount of knockback dealt by the attack is always the same regardless of the opponent's percentage, stale-move negation, or how much damage the attack does. Moves with this property can be thought of as those having a knockback scaling factor of 0, though this is actually not the case. Usually, set knockback is used for the first hits of a natural combo or multi-hit move, while the last hit deals normal knockback (sometimes called "scaling knockback" to contrast), to make it easier for the entire attack to hit regardless of the opponent's damage. While damage is not a factor for set knockback, the character's weight still is, so the term weight-dependent set knockback is sometimes used. In Smash 4, the effect of launch rates on fixed knockback was drastically reduced, to the point of barely having an effect at all, while Shulk's Smash Monado Art is ignored entirely. However, other knockback modifiers, such as rage, crouch cancelling, or charging bonus, are still calculated normally. In Ultimate, the effect of knockback modifiers on set knockback was removed altogether.
List of set knockback moves
With the exception of Captain Falcon, all characters in Super Smash Bros. have at least one move with set knockback.
From Melee onward, there are certain attacks that deal zero knockback, causing damage as usual but not flinching, meaning that the hit character can still perform any actions while being attacked. Most attacks with no knockback can rack up damage quickly, as they can hit foes repeatedly without launching them away from their range; other attacks that do cause knockback have hitboxes with no knockback in the middle of them for a similar purpose, an example being Roy's Blazer in Melee. These moves can also be used to "steal" KOs from opponents in free for all battles, as while they do not cause knockback, they will take ownership of the KO on an already fatally struck opponent. Fox's Blaster is the most well known example of an attack with no knockback. Due to the fact that it does not deal knockback, it will not interrupt an opponent's moves or force them out of a punishable state such as being asleep or being stuck in the ending lag of a missed Rest. Idle characters in Brawl will also turn around if they are repeatedly struck with moves that deal no knockback, which is noticeable with Fox's Blaster.
In Melee, phantom hits damage foes, but without any knockback. It is also possible for any character to receive no knockback from attacks by certain factors, such as by being giant and metal simultaneously on a low launch rate battle, and as mentioned above, armor will prevent characters from taking knockback while active.
List of moves with no knockback
Introduced in version 1.1.0 of SSB4, certain moves are coded to ignore the target's weight when inflicting knockback, instead using a set value of the default 100. As a result, they are much more consistent across the cast when used as set-up hits and similar.
A few moves not only treat the opponent's weight as 100, but also temporarily set their gravity to 0.085 and falling speed to 1.5, making their knockback even less character-dependant. However, since the gravity and falling speed alterations are temporary, the knockback is still heavily affected by them, and so the vertical KO power of such moves is heavily skewed towards fast-falling characters surviving much longer than heavy ones.
In addition, all throws in Melee treat the opponent's weight as 100.
Knockback stacking is the means by which the game applies knockback to a character who has already been sent flying. The new knockback will sometimes replace the old knockback entirely, sometimes have no effect at all, and sometimes a merge will be performed between the two velocities. This has a large effect on combos, as the character being comboed will often have already been struck when another hit lands.
In Melee, the method of knockback stacking used varies based on how many frames separate the first and second hit in addition to the relative angle between the two knockback directions. When the two hits are separated by fewer than 10 frames, the second hit's knockback always replaces the first's. This prevents attacks that hit repeatedly from accelerating the character that they hit with each strike, which would be the case were they added. This can also lead to some interesting scenarios that allow strong hits to be canceled into weaker ones, although this is mostly prevalent in team battles and with certain items. If the two hits are separated by 10 or more frames, the knockback is either set to the stronger value or the two are merged. The relative angle between the two hits' launch angles comes into play here: if the angle is large enough (meaning the hits are in opposite directions), then the two hits are merged via vector addition. However, if the relative angle is small (meaning the hits are in the same direction) the stronger hit is used and entirely replaces the weaker one. Since merging occurs when the hits are in opposite directions, merged knockbacks may be in a direction distinct from either of the previous two. For example, if a character is struck up and right by a strong hit and then up and left by an equally strong hit more than ten frames later, the character will be sent straight up (as the horizontal values cancel out and the vertical ones stack). This often leads to there being residual knockback from a previous hit in a combo which must be taken into account when trying to follow up.
In addition, hitstun duration is always refreshed by the second hit regardless of the time and angle between them, and the amount of hitstun applied is the amount that would be applied if the opponent had not already been hit. For example, the additional knockback put on the opponent from any merging does not factor in to the equation used to calculate the amount of hitstun that should be put on the opponent.
In Brawl and all future games, knockback stacking returns, but behaves rather differently to how it did in Melee. Knockback stacking occurs if the knockback of the second hit is of similar or lower strength to the first. When this happens, then game will stack the knockback. In the event that the knockback of the second attack is significantly stronger than the first, it will completely replace the knockback of the first move. Likewise if the angles of the two moves are almost completely opposite of each other (e.g. the first hit launching at 90° straight up, and the second hit at 270° straight down), knockback stacking will not occur, and instead either the second hit's knockback will be ignored, or if it is of similar or greater strength than the first, it will completely replace the knockback of the first hit. Unlike in Melee, the launch speeds of the two knockback sources will not be added. Instead, the game calculates what the resulting launch angle would be if the velocity vectors of the 2 knockback sources were added, and then uses this launch angle instead of the original angle. As a result, if the second source of knockback is much weaker than the first, it will appear as though the knockback didn't stack at all.
The following is a chart demonstrating how much knockback each character sustains in Brawl. While weight is the primary attribute for determining how much knockback a character sustains, there are other attributes that factor in, such as a character's gravity. This results in some characters sustaining more knockback than lighter characters.
The knockback value shown is how much knockback a character sustains when hit with Marth's Critical Hit at 0%, arranged from least knockback sustained to most knockback sustained.