Regarding the stun time equation

[Jihnsius]

I've searched all the archives and statistics lists many times over and have been unable to find any attempts at figuring the equation for stun time. I would imagine it shouldn't be much more difficult to figure than the knockback equation if you know what to look out for, I'm just not too sure where to start.

I once believed that stun was actually either a function of knockback or vice versa but in doing some character specific testing I came to the conclusion that the stun formula must be completely independent from the knockback formula. My main reasoning being specific attacks from characters that, when compared, would make no sense if knockback determined stun time. For example, Roy's aerial sweetspotted attacks having slightly less stun time than Sheik's tilts, though the difference in knockback is huge. When hit by Jigglypuff's rest (at least in my opinion) it seems that the stun should end much sooner than it does, giving Jiggly's rest a high killing capacity even though it's knockback values aren't all that high compared to other KO attacks. That coupled with character specific stun modifiers (Luigi being lowest and Roy being highest) points in the direction that stun is a unique formula.

Along the same lines as how the knockback formula was figured using the end-game stats I thought maybe a way could be devised to calculate stun time. I tried experimenting with the (the exact name escapes me at the moment) flight time values, as those are different from air and grounded times. The instant stun begins all physics are bypassed until the instant stun ends and you enter a tumble state, letting drag take over from there, the entire time adding only to the flight time counter. If this is only done once per match (only one stun inflicting blow given to a character,) then we could compare and contrast the outcome of each test to another and derive a formula. The only problem with this approach that I (think) I found is that the value doesn't increase linearly as one would expect, instead it adds arbitrary values for states such as hitting the ground during stun, the initial bounce after hitting the ground during stun, sliding from having character models overlap, etc.
Now if it were only these obvious states that added some sort of value to the flight time we could easily calculate and subtract where needed from the total value and figure from there. After realizing the above states adding to the counter I attempted to bypass them all by testing attacks that send the opponent straight off the edge so there is no interference whatsoever. This is about when I lost my job and apartment and since then haven't been able to play Melee to do any more tests, and hence why I'm posting here. What do you think? The reason I want to figure this out, mainly, is for reference for a project me and Buzz are working on. That and it's one last thing we haven't quite figured and documented about this game.

 

[Fortress | Sveet]

each move has its own knockback and hitstun formula. most include weight and percent in the equation but some dont (fox's shine has set knockback, but is effected differently by each characters weight; sheik's dthrow is almost uneffected by weight, but progresses by percent). as far as hitstun weight usually decreases hitstun, for example heavier characters can't get fox uthrow->uaired (mario, d.mario, samus, ect)

 

[Jihnsius]

There's a few parts in your post I don't quite understand. I know the knockback formula has two separate values for attacks, one for the kinetic energy and one for the potential of any given attack, are you saying the stun equation probably has the same variables for each attack? And when you say weight in regards to Fox's shine and Sheik's down-throw do you mean actual weight or character fallspeed? I thought friction was the only contributor to Fox's shine, aside from Impossible SDI hitbox windows that determine whether a character falls or slides. As for Sheik's down-throw being unaffected by weight I haven't really noticed, weight is usually a fairly small change in knockback and I would assume the same if it were applied to stun. Regardless, the only reason it seems negligible is that her down-throw is a mostly vertical move and weight is only noticeable in the pitch of knockback horizontally since fallspeed has a much more dramatic effect vertically.

As for the Fox up-throw up-air argument I see it exactly opposite of how you've proposed it - Mario and Dr. Mario are midweight. What Mario, Dr. Mario, and Samus have in common is that they have very low fallspeed. When thrown up by Fox they will travel a greater distance vertically than any non-floaty because of how little gravity has an effect on them and that the stun time is roughly the same for a fast-faller that would stay in the up-air range in the same time frame.

 

[Fortress | Sveet]

each character has a weight constant. fall speed doesn't directly effect the equation, but rather effects your character AFTER the hit happens. if you throw a baseball you don't say you threw the ball forward and down. you throw the ball forward, and gravity pulls down. sheik's dthrow throws everyone to basically the same height, but after reaching the height they fall at different speeds. thats why pichu gets chaingrabbed but fox doesnt. marth can jump out because he is light and slow falling.

in short, fall speed and weight are very different.

edit: and no, characters fall down from fox's shine because of their weight. marth is the lightest character that doesnt fall from the shine. the distance they move is dependent on their traction.

and marth is as floaty as samus and mario, but he is much lighter than them. they only get out because their weight gives them slightly less stun and allows a jump/nair/whatever before fox can jump and uair.

 

[Jihnsius]

I understand the difference between character gravity and character weight.

What I'm understanding from you is that the stun equation probably takes into account weight. The first reason you supplied is because Sheik's down-throw sends all characters the same distance vertically. The second reason is because some 'heavier' characters can avoid Fox's up-throw up-air combo by the stun wearing off before the up-air can connect.

After watching a couple videos I can't see what you're saying about Sheik's down-throw. It doesn't seem to do anything differently than any other attack. It has normal knockback and normal stun, during which the enemy's fall speed acceleration determines how quickly they decelerate going up and accelerate going down. From the looks of it it doesn't ignore or take anything extra into account whatsoever, it's just a normal throw with normal properties.

As for Fox's up-throw up-air combo being avoided by heavier characters; your examples are Mario, Dr. Mario, and Samus. Samus is ranked 3rd heaviest, Yoshi 5th, Mario and Doc 10/11. Yoshi cannot escape the combo before stun wears off. Nor can Falcon at 6th heaviest. The characters you used in your example happen to be very low-gravity and have the added benefit of decelerating vertically slower, so their stun time carries them a lot higher than higher gravity characters, high enough to be outside of Fox's speed:range to make the followup hit connect during stun. And that's not taking into account the character specific stun modifier ratings, which I couldn't find anywhere in the statistics thread. Luigi is about in the middle of the weight roster as far as heavyweights go, and on the opposite end Roy is in the middle of the lightweights. Luigi undoubtedly has the fastest stun recovery in the game and Roy the worst. If what you were implying were true wouldn't those titles go to heaviest and lightest respectively?

I personally believe the hit stun equation looks something like this:

T = (k)S + (p)S * D * C

T = total stun time in arbitrary units
S = unique stun settings per attack (k = kinetic, what the base stun time is, p = potential, how the stun time increases as damage goes up.)
D = percent damage
C = character stuntime modifier, somewhere between 0.85 for Luigi and 1.15 for Roy.

Overall it's very similar to the knockback equation.

I'll go ahead and agree with you on Fox's shine knockdown being dependent on weight, but even still the knockdown effect has nothing to do with stun time. Whether they are knocked down or not would be a function of gravity and platforms. Fox's shine has a kinetic stuntime of a certain amount and no potential stuntime. We know this because his shine does not increase stuntime as damage goes up. That means that if it were applied to my equation,

T = (k)P + (0 * D * C)

It's apparent that damage and character stun mods have no effect on the situation because it's nullified altogether by the lack of potential stun. The same goes for Yoshi's down-tilt. All that is taken into account during the equation for these attacks is the kinetic, default stun time.

 

[Fortress | Sveet]

i only used those as examples to show how which variables are taken into account. fall speed is NOT taken into account. only percent and weight, and each attack's formula looks similar to

Kt = (P*Kv + Kc ) * W

Kt = Knockback Total
P = Damage Percent
Kv = Knockback Variance (how much percent effects the knockback)
Kc = Knockback Constant (base knockback, how much knockback there is at 0%)
W = Weight Constant

sheik's dthrow has a high Kc and a lower Kb, which allows her to chaingrab for ~80%

fall speed effects knockback, but in a secondary way. after the knockback hits you (its a vector, having direction and force) there is a constant pull downwards by gravity (just like in real life, you can throw a baseball straight up at 20m/s and in 2s it will peak and come down because gravity pulls at 10m/s^2)

my fox uthrow uair comment was an example. there are many factors involved, i was just showing you how weight comes into play.

 

[Jihnsius]

I don't think we're on the same page. You're trying to explain the knockback formula when what I'm looking for is the hitstun formula. There's plenty of documentation and research on knockback but none on hitstun. In other words we already know how to calculate how fast a character is sent flying, but what is the formula for determining how long they stay in that flying state?

 

[RockCrock]

I've seen it posted before in one of the brawl+ threads, by leafgreen386. Can't find his post though.


Found it:

Almas is almost correct. Hitstun is calculated by the formula:

h = m*l / d

H is hitstun in frames. M is the hitstun multiplier constant (the brawl default is .4, and we're using .484 right now). L is the launch speed of the move (you can see max launch speed in the end game results screen). D is a character specific division constant, which can be any of the whole numbers 32, 33, 34, 35, or 36 (faster fallers have higher values and therefore suffer less hitstun).

As you can see, hitstun is linear. However, knockback is nonlinear. You start off going a distance equal to your launch speed, and then travel a progressively smaller value each frame. The rate of decay is believed to be a constant value (this is currently unverified), so moves with only slightly higher launch speeds will cause a drastically larger knockback at higher values. In regular brawl, most moves KOed players off the top of the screen when they reached a launch speed of 6200 to 6300.

This is why it's harder to combo at higher percentages. It's not that they're going too far away. It's that they're going too far away with a stun time that is proportionally smaller to that of when they stayed close.

 

[Jihnsius]

Bad4ass, thank you. A couple questions, though, perhaps someone can answer them. First off, how does Brawl's modifier constant being 0.4 make sense considering Brawl has no hitstun whatsoever? Or is hitstun redefined in Brawl to just be a period of time in which you are flying at the knockback pitch while you can still perform any action, unlike being completely stunned in Melee? Also, how close does this formula resemble Melee's? Would Melee just be an increased constant modifier and otherwise the same?

Doing some quick comparisons it looks like Brawl's knockback formula is incomparable to Melee's. While Brawl requires a KB pitch of around 6,000 to KO, Melee requires roughly between 150 to 200 KB pitch. A quick scale could probably make the stun formula convert from Brawl to Melee nicely.

 

[Fortress | Sveet]

oh my bad, i did misunderstand.

 

[Jihnsius]

Thanks, though, I appreciate the effort.

 

[Figgz]

each move has its own knockback and hitstun formula. most include weight and percent in the equation but some dont (fox's shine has set knockback, but is effected differently by each characters weight; sheik's dthrow is almost uneffected by weight, but progresses by percent). as far as hitstun weight usually decreases hitstun, for example heavier characters can't get fox uthrow->uaired (mario, d.mario, samus, ect)

True, so very true