Shield HP Depletion & Regeneration
 Shields at full health have 60 HP.
 Shield health is drained at a rate of 0.28 health per frame while shielding.
 Attacks deal only x0.7 their damage to shield health.
 While not shielding, shield health regenerates at a rate of 0.07 units per frame.
Analog Shield (Lightshield) Data
Several shield properties in Melee are altered if the LShoulderButton/RShoulderButton are not fully pressed. Put in simple terms, lighter shields are larger and take longer to deplete, but take more damage, and increase the defender's shieldstun and pushback, while reducing the attacker's pushback. As a result, they are safer to use preemptively and can prevent Shield Poking much more reliably, but are significantly less effective for subsequent retaliation.
In all formulas, s is an analog factor equal to n / 140
, where n is the /AnalogL/RValue with a range between 43 and 140 /AnalogL/RValue. As a result, s can be as low as 0.30714 with the lightest possible shield, and caps at 1 with a full shield. Shielding with the ZButton corresponds to s = 0.35
, or n = 49/140
.
Attribute  Formula  Analog variable (a)  Result with lightest possible shield 

Damage multiplier  a + 0.7 
0.2 * (1  (s  0.3) / 0.7) 
0.89796× 
Size multiplier  (HP * a / 60) * 0.85 + 0.15 
1  (0.5 * (s  0.3) / 0.7) 
(HP * 0.9949 / 60) * 0.85 + 0.15

Depletion per frame  (a + 0.1) * 0.14 
1.9 * (s  0.3) / 0.7 
0.0167132 (1.002792 per second) 
Shieldstun  (damage * (a + 0.3) * 1.5 + 2) * 200 / 201 
0.65 * (1  (s  0.3) / 0.7) 
(damage * 1.415055 + 2) * 200 / 201

Defender shield pushback  (damage * (a + 0.09) + 0.4) * shield 
0.195 * (1  (s  0.3) / 0.7) 
(damage * 0.283011 + 0.4) * shield

Attacker shield pushback  damage * a + 0.02 
(s  0.3) * 0.1 
damage * 0.000714 + 0.02

Hitbox ID Priority
If two or more hitboxes hit on the same frame, the hitbox with the lowest ID takes priority and its damage, angle, and knockback values are applied.
Values are listed in order of lowest ID to highest ID, and thus highest to lowest priority.
If sequential hitbox ids have identical data, their values are only listed once.
Knockback and the SSBM Knockback Formula
Knockback is the measure of how far an attack sends its target. For most attacks, knockback increases as damage on a character increases. There are many properties pertaining to the attack, the victim, and the general game settings that determine how far the victim is knocked back.
Latex Code:
Full knockback formula: $$\textrm{Knockback}(\textrm{regular}) =\left\{(.01 \times G) \times \left( \left[ 1.4 \times \{(.05 \times u \times \{ s + \lfloor v \rfloor\}]) + .1 \times (s+\lfloor v \rfloor)\} \times \left\{ 2.0  \left( \dfrac{2.0[.01 \times w]}{1 + [.01 \times w]} \right) \right\} \right] + 18 \right) + b \right\} \times d \times a \times r$$
LaTeX Code:
Simplified formula: $$\left \{ G \times \left (1.4 \left [ \frac{ (u+2) \left ( s + \left \lfloor p \right \rfloor \right )}{20} \right ] \left [ 2.0  \left ( \frac{2W} {1 + W} \right ) \right ] + 18 \right ) + b \right \} \times d\times a\times r $$
SSBM Full Knockback Formula Variables
u is the Unstaled Damage of the Attack.
s is the Staled Damage of the Attack.
G is the Knockback Growth (a.k.a. Knockback Scaling) of the Attack.
v is the Current Percent of the Victim after the Attack Damage is applied.
w is the Victim's Weight.
b is the Base Knockback of the Attack.
The Victim Defense Ratio (d), the Attacker Offense Ratio (a), and the Global Damage Ratio (r) are a series of ratios based on a number of factors, including:
 Difficulty
 Handicap (The Higher the Handicap on the victim, the more knockback taken)
 Singleplayer mode conditions (e.g. in Melee's Event 24: The Yoshi Herd, all Yoshis give x0.5 knockback while taking x3.7 knockback)
 Launch rate (between x0.5 and x2.0; Tournament Standard is x1.0)
 Crouching penalty/Crouch cancel factor (x0.666667 Melee)
 Smash charge interruption bonus(x1.2 in Melee, applied if the opponent was charging a smash attack when hit
 Frozen penalty factor (x0.25 in Melee). Characters in frozen state take reduced knockback.
 Size changes made by the Super Mushroom and Poison Mushroom (less knockback is dealt to giantsized fighters, while tiny fighters take more knockback than normal)
 It should be noted that in the Standard Tournament Ruleset, d, a, and r are all equal to 1.
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 stalemove negation's knockback modifiers. However, it still remains dependent on other factors.
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 of launch speed then decays by 0.051 every frame, so that the character eventually loses all momentum from the knockback. During this time, characterspecific attributes such as air friction are disabled; however, falling speed still takes effect, giving fast fallers better endurance against vertical knockback than others of their weight.
Knockback in SSBM is capped to a final value of 2500.
Knockback in SSBM can be visualized and dissected using I KneeData Calculator: Displays a visualization of theorycrafted physics situations and framedata using various criteria.
StaleMove Negation
StaleMove Negation refers to how moves cause less damage and knockback as they are used multiple times in a row. The strength of a move increases back to its regular power as other moves are used. Starting in Melee, being KO'd resets the staleness of all of that player's moves. Moves not yet affected by stalemove negation are referred to as "fresh."
Stalemove negation is calculated with a queue of the last nine moves a character has connected with. When a move is repeated in the queue, its damage is decreased an amount based on both how often the move is in the queue and how recently the move has been used. The following table lists how much a move becomes weakened for each position it appears in the queue.
Queue position  1  2  3  4  5  6  7  8  9  10 (Fresh)  Total of All Slots 

Reduction Factor (1.00 minus 0.xx)  0.09  0.08  0.07  0.06  0.05  0.04  0.03  0.02  0.01  (0.00)  0.45 
Recency  1st Most Recent                9th Most Recent  10th  Fresh!   
To determine the damage of a staled move, multiply the unstaled damage by the reduction factor corresponding to the place in queue that move is in. This number is how much the damage will be decreased. For example, Yoshi’s up smash does 14 damage unstaled. If he does it twice in a row, the second up smash will be staled by the first multiplier. This means that his damage will be decreased by 14 × 0.09 = 1.26. Therefore, his second up smash deals 14  1.26 = 12.74 damage. If the same move appears multiple times in the queue, the multipliers of each place are added together, and then that multiplier is applied. For example, if Yoshi hits 10 upsmashes in a row, the tenth upsmash will be staled by every multiplier. This means that its damage is decreased by 0.09+0.08+0.07+0.06+0.05+0.04+0.03+0.02+0.01=0.45x. From here, we use the same process as before. 14 × 0.45 = 6.3 damage reduction, so the fully staled upsmash deals 14  6.3 = 7.7 damage.
StaleMove Negation Special Properties
The calculation of knockback in Melee partly ignores a move's staleness for nonprojectiles. Since the knockback formula bases the knockback a player suffers on the postdamage of an attack, there is still a decrease in knockback as a move is staled, though it is extremely minimal. Typically a move will require around the same postdamage to KO regardless of its staleness value, so the additional damage needed to KO with a stale move will be around the damage dealt lost to stalemove negation (for example, a fullystaled Fox up smash will deal 9.9% damage, so it will require about 8.1% more damage than a fresh up smash to KO).
Hitting noncharacter targets, such as Shy Guys on Yoshi's Story, doesn't affect staleness.
A move will enter the queue if any of its hitboxes connect, and the stale move multiplier will affect any hitboxes of that move that happen later. For multihit moves, the first hit that connects will put the move into the queue, causing all of the later hitboxes of the move to be staled. A single usage of a move will only add that move to the queue once, even if it hits multiple times or against multiple opponents.
If a move shoots multiple projectiles, such as Fox's Blaster, each projectile fired will have its staleness set to the move's staleness at the time it is fired. If one projectile deals damage, the move will be added to the queue, but the rest of the projectiles that exist at the time will only "reupdate" their staleness if their hitbox changes. For example, if the first Blaster shot connects, the second Blaster shot will still deal fresh damage  until it changes from the clean hitbox to the late hitbox, which updates its staleness to the new value. In addition, if a move shoots multiple projectiles, only one projectile produced per animation can count in the queue. For example, Fox's Blaster will count every shot because he shoots one laser every time the animation loops, while Bowser shoots multiple chunks of Fire Breath per loop, so only a portion of them contribute to the queue.
The Ice Climbers share one staleness queue, which is affected by both climbers equally  for example, if both Popo and Nana hit their forward smash, the forward smash stales twice. As a result, their moves tend to stale faster and refresh faster. In addition, the queue resets when either of them is KO'd, meaning all Popo's moves are reset when Nana is lost, and vice versa.
Zelda and Sheik also share one staleness queue. The queue is not reset on Transform, so for example Zelda's up air is always as equally stale as Sheik's.
Reflected projectiles (whether by moves that reflect or by powershielding) contribute to the staleness queue, applying to the defender's queue based on the projectile's move type (e.g. reflecting a LeftStickBButtonNeutral Special Projectile will stale the defender's LeftStickBButtonNeutral Special move if it connects).