Knockback is a measure of how far an attack sends its target. For example, Bowser's forward smash is an attack of high knockback; 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.
The knockback of most attacks increases as the target's damage increases. Knockback is also affected by the target's weight, gravity, and a few other conditions (such as type effectiveness). The damage dealt by an attack is a significant factor in how much knockback it deals, but it is not the primary factor - this is the reason stale moves have less knockback than fresh ones, and why many chargable special moves deal less knockback when fully charged (the knockback values of the fully-charged move are altered to compensate for the higher damage, whereas the same is often not true when not 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 (in normal circumstances), and knockback scaling is a factor that controls how much the knockback increases as damage increases. Moves with high base knockback deal high knockback under any circumstances, such as the swing of a Home-Run Bat. They additionally tend to be more effective at KOing when less knockback is needed to KO (such as against lighter characters, when near the edge of the stage, or when an opponent is handicapped to sustain more knockback). On the other hand, moves with high knockback scaling take less damage to reach KO potential, such as Luigi's forward smash. They additionally tend to be more effective at KOing when the opponent requires more knockback to be KO'd (such as against heavier characters, when far away from a stage's blast line, or when an opponent is handicapped to sustain less knockback). Advanced techniques to extend survival such as DI and momentum cancelling 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 match results, though the number lacks 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 barely sends characters anywhere. The following table gives an idea of various knockback strengths:
Brawl uses a second formula to alter knockback based on the target's gravity:
The result of this formula is added to the vertical component of the knockback. As a result, characters with higher gravity take more knockback then those with lower gravity, depending on how vertical the angle is.
If the move has a weight-based knockback value set (so the move deals set knockback), then d is set to that value, and p is always 10.
Other physics of knockback
Set knockback, sometimes referred to fixed knockback, is a property of some attacks where the knockback dealt by the attack does not depend on the opponent's percentage or how much damage the attack does. This results in it dealing the same amount of knockback regardless of stale-move negation.
List of set knockback moves
In Super Smash Bros. Melee and Super Smash Bros. Brawl, there are attacks with zero knockback as well. They normally make damage to the foe, but without any flinching, so that they can still make any actions while they are being attacked. Other than this, however, some of this attacks can also be used for racking up damage quickly, as they hit foes easier since they don't make them flinch. When a player is about to KO another character, these attacks can also be used to mockingly steal his/her KO, as the enemy will get KO'd as usual, but due to KO priority, it will belong to the character that dealt the attack with no knockback.
Fox's Blaster is an infamous example of this, as it can quickly deal great amounts of damage to non-skilled players, as well as mostly being used to steal KOs in three or four-player battles. Other attacks that deal no knockback are: Togepi's Leech Seed, the middle hits of Roy's Blazer and Charizard's forward air, Fox's shots in his throws (except forward throw), thrown Grenades, Olimar's antennae, and in the Subspace Emissary, Amaranthine gas and some consecutive-hitting attacks used by bosses (such as Rayquaza's, Thunder). Mario's and Dr. Mario's Capes also have similar properties, except that they use the Reverse effect. Fox's Blaster in Brawl can also turn idle foes around it they are shot repeatedly.
In Melee, phantom hits damage foes, but without any knockback. It is possible for any character to receive no knockback from attacks by certain factors, such as by being giant and metal simultaneously on a low damage ratio battle, or during the actions of certain attacks in Brawl, such as Charizard during the first frames of Fly. This is known as launch resistance. Additionally, if Master Hand or Crazy Hand is used on a battle by glitches or hacks in Melee, when he grabs a foe and then crushes it, other foes near him will still take damage, but with no knockback.
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.