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Nate
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"Damage Scaling (fighting game question)" , posted Sat 20 Oct 08:19post reply

So, in most fighting games released within the last seven or so years, damage scaling is present as a mechanism to balance characters somewhat. Slower, stronger characters who rely more on hard hits tend to have more life while faster, weaker characters dependent on more consecutive hits tend to have less. Depending on the game, however, the system works differently.

In Capcom games and most others that I've observed, each character has a set amount of life and takes the same amount of damage from attacks. Characters with more life can take more damage.

In Arc System Works/Sammy games (Guilty Gear and I think Rumblefish), characters all have the same amount of life but each has a different damage multiplier that applies to the damage they take from an attack. A character with a lower multiplier takes less damage per attack. In the case of Guilty Gear, another special factor applies (called "Guts", I believe) that further modifies damage taken when the character is low on life. I'm going to ignore this for my question as I'm not completely sure how it works, but it does factor in a bit.

My question is, are both these systems fundamentally the same? Let's assume the default amount of life in both games is 10000. Does a character with 8000 life take the same damage as a character with a x1.20 modifier in all cases? Is one more "fair" than the other? Why? Please let me know what you think. I'm curious.





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Red Falcon
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"Re(1):Damage Scaling (fighting game question)" , posted Sat 20 Oct 09:19post reply

quote:
t.

My question is, are both these systems fundamentally the same? Let's assume the default amount of life in both games is 10000. Does a character with 8000 life take the same damage as a character with a x1.20 modifier in all cases? Is one more "fair" than the other? Why? Please let me know what you think. I'm curious.


I think you're worrying about it too much, ha ha ha. I'm not going to sit here and do math, but in the end, they really are pretty much the same. Neither system is really more "fair" than the other, it's just how different developers decided to do things (perhaps just to make their game seem a little "different" in some cases.)





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Nate
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"Re(2):Damage Scaling (fighting game question)" , posted Sat 20 Oct 09:47post reply

quote:

I think you're worrying about it too much, ha ha ha. I'm not going to sit here and do math, but in the end, they really are pretty much the same. Neither system is really more "fair" than the other, it's just how different developers decided to do things (perhaps just to make their game seem a little "different" in some cases.)



Okay, I did some math.

Character A: 8000 health, regular damage (x1)
Character B: 10000 health, x1.2 damage modifier

Both take the first hit that does 1000 damage. Character A takes 1000 damage and has 7000 health left. Character B takes 1200 damage thanks to the modifier and has 8800 health left.

The next hit does 300 damage. Character A takes 300 and has 6700 health left. Character B takes 360 and has 8440 health left.

The final hit does 4000 damage total. Character A takes 4000 and has 2700 left. Character B takes 4800 and has 3600 left.

In the end, though they took roughly the same damage, Character B ends up with almost 1000 more health. The only thing I worry about is that the damage multiplier on B didn't quite match A's amount of health.

I tried this again with characters who take "less" damage.

Character A: 12500 health, normal damage (x1)
Character B: 10000 health, x.75 multiplier

The first hit is 600 damage. A takes 600 damage and now has 11900 health. B takes 450 damage and has 9650 health.

The second does 3000 damage. A takes 3000 and has 8900 health left. B takes 2250 damage and has 7400 health.

The third does 1500 damage. A takes 1500 and has 7400 left. B takes 1125 and has 6275 left. Again there's a difference of over 1000 health, but this time in A's favor. Again I'm not sure if 12500 health and a x.75 multiplier match up exactly.

Anyway, judging from this, the Capcom method favors characters able to take more damage while the ASW method favors characters able to take less. Interesting.





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"Re(1):Damage Scaling (fighting game question)" , posted Sat 20 Oct 10:11post reply

quote:
My question is, are both these systems fundamentally the same? Let's assume the default amount of life in both games is 10000. Does a character with 8000 life take the same damage as a character with a x1.20 modifier in all cases? Is one more "fair" than the other? Why? Please let me know what you think. I'm curious.


They are exactly equivalent. Let me show why: The way of measuring the damage is through the health bar. That acts as a measurement of how much % of damage the character has received, and when said % reaches 0, it is a KO.

The damage to the health bar is the following:

Health removed from the bar = P (from percentage)
Base damage = D
Damage modifier = M
Health amount = H

P = (H - D*M)/H = 1 - (D*M/H) = 1 - M*(D/H)

So, M, the damage modifier is an external constant that actually affects both H and D.
Capcom opts to apply the modifier to H, resulting in the following formula:

P = 1 - D/H'; H' = H/M being the modified health after applying the constant.

In Guilty Gear, the constant is applied to the damage received, so the formula would be:

P = 1 - D'/H ; D' = D*M being the modified damage after applying the constant.

Of course, since a constant lower than 1 reduces the damage D, applied to H increases the health, since it's dividing it, and the effect is exactly the same as long as the same constant is used.


Also, regarding the "guts" rating: It is a characteristic that reduces the damage the lower the health bar is. In GG games this depends on the character, but Capcom games have this measure implemented too (the lower the health, the lower the damage of each hit will be), although it's the same for all characters.

A third damage reducing measure that I'm sure you know is the one applied to combos. The algorithm varies from game to game, but usually reduces the damage of the hits in a combo depending on the number of previous hits, as well as the nature (specials, normals, super) of them and sometimes their power.





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Nate
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"Re(2):Damage Scaling (fighting game question)" , posted Sat 20 Oct 12:02post reply

quote:

They are exactly equivalent. Let me show why: The way of measuring the damage is through the health bar. That acts as a measurement of how much % of damage the character has received, and when said % reaches 0, it is a KO.

The damage to the health bar is the following:

Health removed from the bar = P (from percentage)
Base damage = D
Damage modifier = M
Health amount = H

P = (H - D*M)/H = 1 - (D*M/H) = 1 - M*(D/H)

So, M, the damage modifier is an external constant that actually affects both H and D.
Capcom opts to apply the modifier to H, resulting in the following formula:

P = 1 - D/H'; H' = H/M being the modified health after applying the constant.

In Guilty Gear, the constant is applied to the damage received, so the formula would be:

P = 1 - D'/H ; D' = D*M being the modified damage after applying the constant.

Of course, since a constant lower than 1 reduces the damage D, applied to H increases the health, since it's dividing it, and the effect is exactly the same as long as the same constant is used.


Also, regarding the "guts" rating: It is a characteristic that reduces the damage the lower the health bar is. In GG games this depends on the character, but Capcom games have this measure implemented too (the lower the health, the lower the damage of each hit will be), although it's the same for all characters.

A third damage reducing measure that I'm sure you know is the one applied to combos. The algorithm varies from game to game, but usually reduces the damage of the hits in a combo depending on the number of previous hits, as well as the nature (specials, normals, super) of them and sometimes their power.



Very interesting. I knew about the low health/combo scaling, yeah, but I wasn't sure exactly how it was done.

So basically, the Capcom method doesn't change the actual AMOUNT of life so much as apply a multiplier to it? That would make things basically even as opposed to the questionable math I did in my previous post.





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"Re(3):Damage Scaling (fighting game question)" , posted Sat 20 Oct 13:02:post reply

quote:
That would make things basically even as opposed to the questionable math I did in my previous post.



It kind of dazzles me to see such a subjective, specific and wide question; while the answer you are seeking is fairly straight and simple.

For example another factor that affects this; is the damage output that you deal for each hit; for example imagine a game that had a very big bonus to your damage; so, let's say you use a strong attack and the bonus for counter is something in the line of counter damage = 150% normal damge (wich isn't odd in fighting games); in said case, a character that takes great damage, faced against such bonus will receive incredible high amount of damage.

And in some cases, the game itselfs provide other modificators for damage, such as the distance, or how cleanly the hit lands.

A fairly easy example, is Samurai Spirits games, when against certain characters, on certain conditions, you can virtualy, or even literally one hit KO your enemy, and in some others, the same attack can take something like 25% of the enemy life in almost equal conditions; where as damage varation isn't as rough in games where your stamina is a number; if the stamina is low, everything kills you quickly, where as, if the multipliers are weird, something more specific will kill you quickly.

Other issues to add to the pondering, are how much do companies want to show off the stamina diferences between characters; for example, in my experience, many KoF games have a "different stamina number" for some group of characters; street fighter does the same; but said issue is fairly more notorious in late street fighters games, as in KoF this went on for many years almost unnoticed to the intrained eye.

This question is like asking something like "wich Final Fantasy main character takes the least damage", knowing that many games allow you to partially modify your stats each time you lvl up.

It's latte and I'm on scotch, so this better makes some sense





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[this message was edited by Toxico on Sat 20 Oct 13:10]

Nate
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"Re(4):Damage Scaling (fighting game question)" , posted Sat 20 Oct 13:58post reply

quote:

It kind of dazzles me to see such a subjective, specific and wide question; while the answer you are seeking is fairly straight and simple.

For example another factor that affects this; is the damage output that you deal for each hit; for example imagine a game that had a very big bonus to your damage; so, let's say you use a strong attack and the bonus for counter is something in the line of counter damage = 150% normal damge (wich isn't odd in fighting games); in said case, a character that takes great damage, faced against such bonus will receive incredible high amount of damage.

And in some cases, the game itselfs provide other modificators for damage, such as the distance, or how cleanly the hit lands.

A fairly easy example, is Samurai Spirits games, when against certain characters, on certain conditions, you can virtualy, or even literally one hit KO your enemy, and in some others, the same attack can take something like 25% of the enemy life in almost equal conditions; where as damage varation isn't as rough in games where your stamina is a number; if the stamina is low, everything kills you quickly, where as, if the multipliers are weird, something more specific will kill you quickly.

Other issues to add to the pondering, are how much do companies want to show off the stamina diferences between characters; for example, in my experience, many KoF games have a "different stamina number" for some group of characters; street fighter does the same; but said issue is fairly more notorious in late street fighters games, as in KoF this went on for many years almost unnoticed to the intrained eye.

This question is like asking something like "wich Final Fantasy main character takes the least damage", knowing that many games allow you to partially modify your stats each time you lvl up.

It's latte and I'm on scotch, so this better makes some sense



No, this definitely also helped. The main reason I asked this was because I was thinking of a character who's a female wrestler for an idea I had. She's small (hence many of her takedowns are based more on leverage than brute strength) but obviously knows how to take a hit, so I was wondering which system would work best to reflect that.





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"Re(5):Damage Scaling (fighting game question)" , posted Sat 20 Oct 15:33:post reply

quote:

No, this definitely also helped. The main reason I asked this was because I was thinking of a character who's a female wrestler for an idea I had. She's small (hence many of her takedowns are based more on leverage than brute strength) but obviously knows how to take a hit, so I was wondering which system would work best to reflect that.



Defense multiplier vs. reduced total quantity of health are equivalent given the correct values.

But really, that's the simplest part of the stamina equation; raw measure of health. By itself, all it lets you know is how many standard individual hits it takes to kill somebody (given the damage of that hit). Even in SF2, by itself it's only a rough view of how durable someone is. And as fighting games have shown over the years, there's a lot more to balancing how durable somebody is than just the sheer number of individual hits they take (though that is important).

How combo damage scales is important. Proration on attacks is common in fighting games nowadays. Some games like guilty gear have not only damage modifiers, but variable stun modifiers (e.g. most moves do X amount of stun on a hit, and Y on a counter hit, while others deal double or triple their normal value on a counter hit, in addition to scaling of stun in the combo), guts... even gravity! For instance, Yun and Urien in 3S: Yun has naturally low health, Urien has above average health. Q can do a combo of roundhouse command grab, strong over dash punch, strong dash punch on Yun. Against Urien, without any super meter, Q CANNOT do a double dash punch combo outside of the corner; Urien doesn't get launched high enough. Against many others, Q can only do roundhouse command grab, JAB overhead dash punch, JAB dash punch. The lower health of Yun is magnified not only by the fact that he has less to begin with (or has a lower defense value, whatever you wish), but by the fact that he can be hit by more powerful moves in a given combo. Urien's natural durability is similarly magnified by the fact that a good third of the combo can't actually hit him!

Another example:
In the 4-player fighting game Gundam Seed Destiny, there's this thing that looks like a giant crab (bear with me here). In Gundam Seed, durability is measured by the health number; high-cost units have 500-600 health, lower cost ones have maybe 400 health. The big crab has over 600 health and is very high cost. However, it's durability is in fact not so far above average, situationally. On one hand, it can make a shield that completely protects its forward area from gunfire. On the other hand, the way the knockdown system applies to it makes it EXTREMELY vulnerable to melee damage. In Gundam, after some amount of consecutive hits, you eventually get put into a knockdown state where you cannot be hit by ANYTHING, and while getting up you also cannot be hit. It doesn't matter how big the explosion or the sword is; it'll just go through you. The crab simply doesn't get knocked down easily. So if it can't burst out of the combo, it will get hit over and over again for damage that is far out of proportion with the increased amount of health it has.

Long story short:
- you can always add special code to make your character tougher, and that code can be more than just it's HP or Armor value.





[this message was edited by Spoon on Sat 20 Oct 15:35]

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"Re(3):Damage Scaling (fighting game question)" , posted Sat 20 Oct 20:58post reply

quote:

So basically, the Capcom method doesn't change the actual AMOUNT of life so much as apply a multiplier to it? That would make things basically even as opposed to the questionable math I did in my previous post.



Well, not exactly: Changing the AMOUNT of life is exactly the same as applying a multiplier to it. Let me show you with an example:

Chipp in GGXX has a multiplier for damage received of 1.3. That means that, for an attack that would do 100 damage on Anji (who has a 1 multiplier) Chipp takes 130 damage. Since all GGXX characters have exactly 420 hit points, so that attack would remove exactly 31% of his health bar.

Now, let's imagine that Capcom did the game, and wanted exactly the same durability for Chipp. According to Capcom, the 100 damage attack would do the same amount to all the characters, but Chipp would only have 420/1.3 = 323 hit points, compared to the 420 hit points Anji would have. So, with a 100 damage attack and 323 hit points, the attack would do... 31% damage, also.

So, whether you make the health different or the damage received different, it doesn't matter, both give the exact same results given the same premises (I.E. I want this character to take hits like a girl, etc.).

I hope I've made this clear.


Ah, also: As said above, there are many other methods to balance the durability of a character. Apart from different gravity, counter hit damage, combo scaling, etc. that has been already mentioned, there's the factor of the mobility you give to your character. While it doesn't directly affect the damage, if you make a character with Chipp-like defenses but make him as slow and big as Potemkin, it will be much, much less durable than the standard Chipp. Yeah, this is obvious, but it's also something to take into account.





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"Re(4):Damage Scaling (fighting game question)" , posted Sat 20 Oct 22:55post reply

Nate and posters: I love this thread! It's mathematically completely out of my leaguge, but this is awesome anyway. It's like all the good parts of Shoryuken.com but with all the bad parts replaced with the Cafe's civility.





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"Re(5):Damage Scaling (fighting game question)" , posted Sun 21 Oct 03:07:post reply

Here's something else to think about.

I'm going to draw an example from everyone's favourite social cesspool, dota.

In dota, of the three character statistics Agility, Strength, and Intelligence, for any character ONE of those is their "primary attribute". A character's base attack damage is directly proportional to their primary attribute.

In dota, there are two fundamental measures of durability: HP and Armor.
Armor reduces the damage of normal attacks in proportion with the Armor value.
HP is HP.

Furthermore, the Agility statistic directly increases Armor value, while the Strength statistic directly increases HP value.

Here's where differences show:
With only some exception, spell damage is NOT reduced by armor (it is reduced by magic resistance, but that is not something based on Armor, HP, Agi, or Str; you typically need to have special abilities or items to get more magic resistance).

Another key point:
Agility directly increases attack speed.

So the summation of all this:
STR-based characters increase their durability and damage dealing by increasing their STR. AGI-based characters likewise with AGI. In fact, AGI characters increase their damage dealing capacity at a faster rate per point than STR-based characters, since their rate of attack increases with each point of AGI in addition to their attack damage. However, an AGI character that does not increase their HP in some fashion will be extremely vulnerable to nukes and spell combos, because all that Armor doesn't count for anything against spells; only HP does. STR characters tend to be resistant to nuking because increasing their STR increases their raw HP count. However, in a straight up slugging match, all else being equal, they'd probably lose to an AGI character because even though they're roughly equal in normal attack durability, the AGI character hits faster.

Long story short:
- there can be multiple types of durability that don't require coding exceptions.





[this message was edited by Spoon on Sun 21 Oct 03:08]

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"Re(4):Damage Scaling (fighting game question)" , posted Sun 21 Oct 03:54post reply

quote:
Well, not exactly: Changing the AMOUNT of life is exactly the same as applying a multiplier to it. Let me show you with an example:



Your example is clear, but it still does take into account that the base damage, thinkinh that it isn't subjected to changes; you didn't consider that the enemy can inflict "increased" or "decreased" damage per swing.

Each game itself can add bonus to normal damage, such a "counter attack damage increased" or "with full gauge, your power is increased".

And, hence, those bonus also have effects on the damage the character receives; and mostly, damage bonuses are dealt with multipliers rather than fixed numbers; and that's my experience while playing games instead of a source code checking.

Think of like these circunstances; if your health is number, then; you'll have that:

Damage * percentage bonus applies vs a variable number
Else we got that:
Damage * percentage bonus applies over percentage, then it's applied to fixed number

In the long run, it's up to how the game handles bonuses and modifiers how different a character will manage to resist this.





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"Re(5):Damage Scaling (fighting game question)" , posted Sun 21 Oct 05:26post reply

quote:
And, hence, those bonus also have effects on the damage the character receives; and mostly, damage bonuses are dealt with multipliers rather than fixed numbers; and that's my experience while playing games instead of a source code checking.


Exactly. And that's why it doesn't matter if I do not take into account additional effects: Since those additional effects are multipliers, and since, remember, multiplication obeys the commutative rule, we can establish an equivalence between scaling the base damage and scaling the base number of hit points without having to consider other effects. Those can be added later to the final damage formula regardless if the approach is the HP variable one or the damage variable one.

What I mean is: having "critical hit", "random damage hits", and other kind of additional effects do not affect the initial discussion as long as they are multipliers, since we can alter the order of the operations as we please to consider them last.





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