Hitstun is a period of time after being hit by an attack that a character is unable to act outside of directional influence or teching. It is directly dependent on knockback, so at a same damage percentage, an attack like Falcon Punch will have more hitstun than one like Thunder Jolt. Each Smash game has a programmed value that is multiplied by the amount of knockback received to determine the amount of frames a character is locked in hitstun after being hit; for example, Melee has a hitstun multiplier of 0.4 frames per unit of knockback, so a hit that deals 100 units of knockback will leave the target in hitstun for 40 frames.
Hitstun is an essential component of combos, as the basis of a combo is to have enemies trapped in hitstun while constantly being attacked. As a result, games that have more hitstun for equivalent knockback open up more potential combos.
The amount of hitstun in the original SSB is much higher than in the subsequent Super Smash Bros. games, being a x0.533 multiplier. The multiplier is so high that long, highly damaging combos are commonplace, with competitive matches being heavily centralised around them. Zero-death combos are not uncommon in SSB, as every character in the game except Samus is capable of pulling a zero-death using their normal moves. The commonness of zero-deaths in this game is one of the primary reasons why competitive matches are played with 5 stock, more than Melee, despite the game not being as fast-paced as Melee.
The amount of hitstun in Melee is a significantly lower x0.4 multiplier, making Melee a less combo-oriented game, and zero-death combos a rarity. However, with the increased falling speeds, and generally faster and more varied movement, combos remain frequent, though generally more difficult to pull off consistently.
Brawl has the same hitstun multiplier Melee has. However, when hit by an attack that causes tumbling (or reeling), characters can now air dodge after 13 frames and use an aerial attack after 25 frames out of hitstun, regardless of the actual amount of hitstun they sustained. This new mechanic, known as hitstun canceling, drastically reduces the amount of actual hitstun characters have to sustain upon being hit, especially at higher knockback. For example, while a character sustaining 100 units of knockback in Melee will be in hitstun for 40 frames, that character will be in actual hitstun for only 13 frames in Brawl if they air dodge or 25 frames if they attack, and if that knockback value is doubled, the Melee character would sustain an inescapable 80 frames of hitstun, while the Brawl character will still only sustain 13 or 25 frames of hitstun.
This change drastically reduces the amount of true combos, and means the only attacks that can truly combo are those that deal low enough knockback to not cause tumbling while having low enough ending/landing lag to followup (such as chain throws and Sheik's forward tilt), and at tumble percentages, very few attacks, if any, are fast enough to followup within 13 frames before the opponent can air dodge, such as Meta Knight's up aerial. Any attack that deals even slightly more knockback or has slightly more ending lag will require the player to read the opponent's action to successfully followup. This new mechanic also allows launched characters to act before their knockback wears off, which allows characters to perform certain actions during knockback to reduce their aerial momentum, allowing them to survive blows that would have otherwise KO'd.
The much slower falling speeds, loss of L-canceling with most aerials not having their landing lag fully compensated, and generally slower movement also reduces the amount of possible combos, though the effect of these is minuscule compared to the ability to act so early out of hitstun.
This new mechanic is one of the most controversial additions to Brawl, with detractors criticising it for making true combos rare and making it impossible to truly combo with moves that deal anything beyond very low knockback. This eliminates the comboing ability of characters that relied on higher knockback moves with faster mobility to combo (Captain Falcon being the most prominent example, with Jigglypuff also suffering severely), allows characters to survive longer than intended through momentum canceling and significantly increases the chance of getting punished for landing a hit (Ganondorf's Dark Dive is a notable example of this, as its extremely weak knockback means that many characters can hit Ganondorf with a quick attack as soon as the move completes).
While some players argue in support of the mechanic, such as by stating that players should have to successfully read their opponent's actions to get successful followups and that opponents should have means of escaping combos, the majority of competitive players, even those who prefer Brawl over Melee, see the mechanic as a negative addition to the game, due to severely slowing down the pace of matches. As such, those who mod the game usually remove the mechanic unless they intend to keep the vBrawl engine intact (as in Balanced Brawl), and all major mods except the aforementioned have removed the mechanic completely.
In Smash 4, hitstun has a very slightly altered formula: by default, the result is decreased by one frame compared to Melee and Brawl, but if the character is sent tumbling (not reeling) or launched by an electric attack, one more hitstun frame is added, with both factors being able to stack. For example, if a character that sustains 100 units of knockback is sent reeling, they will be in hitstun for 39 frames, but if they are sent tumbling by an electric attack, they will be in hitstun for 41 frames. On top of this, the ability to act out of hitstun is still present, but it is much less pronounced; characters are able to act out of hitstun after 40 frames with an air dodge, or 45 frames with an aerial; provided the current launch speed is below 2.5 and 2 respectively, meaning that these numbers also increase proportionally to the amount of knockback taken (beginning to increase after sustaining roughly 56 frames of hitstun to cancel with an aerial or roughly 59 frames of hitstun to cancel with an air dodge), and become irrelevant at extreme knockback values. Additionally, unlike with normal hitstun, the hitstun cancel window does consider extra launch speed from the gravity penalty, and as such fighters with low gravity will have a slightly stronger hitstun cancel.
Compared to Brawl, the window for canceling hitstun occurs significantly later, which coupled with the generally increased gravity and falling speeds makes true combos past low percentages possible again. Also due to this, momentum canceling is effectively impossible, allowing moves to KO earlier. Furthermore, air dodging to cancel hitstun actually marginally worsens horizontal endurance, as similarly to Brawl, a fighter is not able to begin opposing their momentum with directional inputs until all of the knockback momentum is gone (despite hitstun actually ending a little earlier than this).
Because of the changes to hitstun, characters such as Sheik and Captain Falcon are indirectly buffed, as their comboing abilities from previous games have been restored, while Brawl newcomers such as Meta Knight and Zero Suit Samus also benefit significantly by gaining a similar or even greater combo potential. However, with the retained ability to air dodge or attack out of hitstun at higher percentages, gravity increasing knockback as in Brawl and falling speeds still being slower than in Melee, true combos at higher percentages are exclusive to a few characters (and even then, they must not be at high percentages themselves), making them less prevalent than in Melee and especially the original SSB.
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