Short hop

A short hop, or low jump in Super Smash Bros. 4, is the act of inputting a jump command and letting go of the appropriate button or control stick during a character's jump squat. This will result in a jump height that is lower than that of a normal jump. This technique can be performed in all  games.

Mechanics
A short hop can be performed using any controller and configured control scheme, including button-jump and control-stick-jump methods, although exactly how it functions depends on the game. In the original Super Smash Bros., characters have a different full jump height depending on the input type; a jump using the C buttons has a different height from a jump using the control stick. A short hop in Smash 64 refers to an input from lightly tapping the C button to jump. Every character in Smash 64 has a 3 frame window to perform a short hop, regardless of the length of their jumpsquat. If the jump button is still held after the third frame of a character's jumpsquat, they will perform a full hop. The height of a short hop in Smash 64 also depends to the horizontal position of the control stick. If the player is holding the stick fully forwards or backwards for example, they will perform a lower short hop than if they do not hold the control stick at all.

Starting from Super Smash Bros Melee, the window to perform a short hop is now based on the length of a character's jumpsquat, with longer jumpsquats leading to more lenient timing to perform a short hop. In addition to this, the jump buttons and the control stick have the exact same effect on jumping, so it is now possible to perform a short hop with the control stick. In Super Smash Bros. Melee, the window to perform a short hop is one frame shorter than the length of the character's jumpsquat. for example has a 3 frame jumpsquat, so the player must release the jump button before the 3rd frame of jumpsquat to achieve a short hop, giving the player a 2 frame window to jumpsquat. on the other hand has an 8 frame jumpsquat, so the player has a 7 frame window to short hop with Bowser. The horizontal position of the control stick also no longer affects the height of the short hop, with a short hop granting the player a consistent amount of height in all situations.

In Super Smash Bros. Brawl, the window to short hop is still based on the length of a character's jumpsquat but the window is now active until the character is airborne, rather than until the last frame of the character's jumpsquat, making short hopping easier to perform overall. Bowser for example still has an 8 frame jumpsquat but the player now has an 8 frame window to short hop with Bowser rather than a 7 frame window due to this change. It is also now possible to buffer a jump starting from Brawl and when a jump is buffered, a short hop will occur as long as the player lets go of jump before the character becomes airborne from the jump. This naturally gives the player up to 10 frames more leniency to perform a short hop in some situations, making a buffered short hop very lenient.

Additionally, in Brawl's Subspace Emissary mode, every character's jumpsquat is 2 frames shorter, which naturally makes performing a short hop more difficult.

Short hop functionality remained identical in Super Smash Bros. 4 but in Super Smash Bros. Ultimate, the standardized 3-frame jumpsquat makes it more difficult to perform short hops with any character (with the exception of who has a 7 frame jumpsquat, making it much easier to short hop with him than any other character). To compensate, players now have the ability to input both a jump and attack button at the same time to perform a short hop aerial (officially known as a "short hop attack" in English and small jump attack in Japanese). Short hop aerials have a 0.85× damage modifier applied to them, which, in turn, also makes them deal slightly less knockback. Additionally, update 2.0.0 notably added the ability to perform a regular short hop without attacking by pressing two jump buttons simultaneously, further compensating for the 3-frame jumpsquat.

In competitive play
The short hop technique is an essential move in competitive play, allowing the user to perform aerial attacks close to the ground and connect with grounded opponents. This can allow for a wider variety of options from a grounded neutral position.

In Super Smash Bros., short hops can be used in conjunction with Z-cancels and double jump cancels to cause perfect shield pressure, shield breaks, or grab confirms.

In Melee, short hops are used as part of the SHFFL technique to aid in aerial approaches and pressure. Melee also features the ability to combine short hops with double jump cancels, but it is not nearly as powerful as it is in Super Smash Bros. Short hopping is also used during wavedashing.

In Brawl, Super Smash Bros. 4 and Super Smash Bros. Ultimate, short hops can be combined with a reverse aerial rush for characters to approach with back aerials close to the ground. Short hops can also be combined with b-reverses and wavebounces for tricky and unusual momentum changes.

Outside of its applications in competitive play, short hopping can also be used for bat dropping in the Home-Run Contest.

Super Smash Bros.
Smash 64 doesn't have short hops in the same sense as later games. Jump heights are controller in part by the control stick's vertical position (v), being a range from 53 to 80 (53 being the minimum amount required to register a jump). Jumps also depend on jump multiplier (m) and the jump base (b). Unlike later games, a character's gravity (g) is also applied on the same frame as a grounded jump. The resulting jump force formula is. The listed heights use a vertical stick posistion of 53&mdash;the closest analogue to later games in the series.