Spiral Knights - Reforming damage calculation

Reforming damage calculation

16 replies [Last post]

Sat, 06/11/2016 - 15:35

Amnimonus

Changing how damage is calculated which is currently assumed to be :
Damage dealt = A - D , A being the weapon's attack power and D being the matching defense

When attacking a monster with it weakness this leads to a constant of 60 points damage increase for weapon with attack power with twice the value of the targets defense leading to a higher damage out put for lower damage multi hit weapons (like blitz on fiend and beasts) than higher damage short combo weapons (Grandfaust alchemers and every other heavy weapon).

My suggestion a new equation for calculating damage

Damage dealt = A*[B/(1+ exp((-A+D)/40))+M]
Where A and D are the same as before B is a predetermined constant and M is the minimum damage ratio

So the part in the brackets is you damage "booster/ penalty" with a maximum damage boost of M + B and a minimum damage boost of M
This would work with damage of any size unlike the current system that has separate equations for low and high damage

Sun, 06/12/2016 - 13:42

Sir-Pandabear

I could plot that in a graph, or you could explain what it does, what the old formula does wrong, and what the new formula does better.

Sun, 06/12/2016 - 14:36

Nizada

Responding and stuff

A graph would be nice I don't understand any of this... O.O

Would I understand the graph though? ...

Sun, 06/12/2016 - 22:12

Amnimonus

It a logistic type function

@Sir-Pandabear and Nizada
And it look likes this , its a nice equation with two horizontal asymptotes representing minimum and maximum damage multiplier.

So the problem with current damage system is that attacking monster with there weakness awards you with extra 61 to 63 damage in tier 3 training room and this is seen through all weapon that deal enough damage (which about 80 damage). This extra damage is also not influenced by damage booster from armor , pet or drops it is constant.

This means that is has to be attack power minus defense and a monster's weak defense is 62 point lower than neutral defense. This scales horribly as weapon damage increases in other words falls short for heavy weapons.

The equation I have made multiplies damage by a certain number (ideally a maximum no greater than 1.5 aka your variables M and B added together)
What even better that it is a single equation for damage of all values the current system use two one for high-middle range damage and another for low damage because attack power minus defense would equal negative damage if attack power is less than defense. In my suggestion this would lead to a damage multiplier between 1 and zero)

In short this would allow scaling of damage when using the damage a monster is weak against (a percentage boost in a sense)

Does that make sense or should I go into more detail?

Also this is far from perfect and would require a and entire rework of the values of damage and defense in the game so far and damage and damage bonus would have to be chosen to ensure that weapons can reach certain bonuses this just the best i could thin up of that would work in both pve and pvp.

Mon, 06/13/2016 - 01:34

Nizada

Nope!

I give up! I understand numbers...., but when it becomes 2+(X-SEGA):(OOO < GH)*365=42 I don't understand a thing... O.O

Mon, 06/13/2016 - 02:28

Corporal-Shade

I'm a Wizard

How about a Before and After damage comparison. That will likely look more English.

Mon, 06/13/2016 - 03:44

Triplescrew

Why not just add slight

Why not just add slight resistance bypass for heavy weapons?

For example if you shoot Robo with Blitz, damage is halved.... But if you shoot Robo with Callahan, damage reduced only by 35%. Stuff like that.

Anyway its nearly same.

Mon, 06/13/2016 - 05:48

Dagunner

Sounds good, but we need data

This does sound like an interesting idea, to know if it really would be good I guess we'd have to see the stats from old and new from all weapon archetypes (fast, balanced, heavy, gun, bomb, sword, type advantage, etc.). As if we change the damage system the resulting system needs to still be fairly consistent with the old/current system, as it would feel weird if everything did different amounts of damage, so calibration and experimentation is necessary.

Mon, 06/13/2016 - 15:00

Sir-Pandabear

Alright, let's try making some data out of this. (This is homework you should be doing, by the way.) I'm assuming a max amplitude of 1 because the last thing this game needs is for more damage for Acheron. I'm also assuming a min amplitude of 0.15 because that closely mimics the current results.

Our formula then becomes:

dmg * (0.85 / (1 + exp((def - dmg) / 40)) + 0.15)

Let's see what happens when we put existing damage values into it, starting with weak, ending with strong.
All values depth 24, using my chart to get existing damage numbers and enemy defence.

Dark Retribution

Current values

vs weak:77
vs neutral:46

New values

vs weak:127
vs neutral:90

Okay, they're a lot higher than before, but that doesn't have to mean anything special. If all weapons end up a lot stronger after this it just means we need a universal reduction of damage or universal health buff. The difference between special and neutral damage is really small now, which I guess is your intended result.

Deadly Crystal Bomb (shards)

Current values

vs weak: 166
vs neutral: 95

New values

vs weak: 228
vs neutral: 216

Hey, a shard bomb buff! It didn't get nearly as buffed as Dark Retribution so over the board it seems like a Shard Bomb nerf. However, the difference between special and neutral damage is barely perceptible at this point.

Okay, what if we try doubling enemy defence?
New values

vs weak: 216
vs neutral: 97

That's uh, pretty hefty. Compare this to doubling enemy defence with the current damage formula:
Current values

vs weak: 94
vs neutral: 58

It stays really stable, but with your formula we get numbers that go all over the place. You might say that we need to tweak the damage numbers and defence numbers of all the monsters and all the weapons, but to that I say:

Show your work

Oh, and in case you're curious, the existing formula for when damage < defence * 2:
damage * (1 - (1/2 + 0.19 * LOG10((defence * 2 - damage)/15 + 1)))

I've taken a stab at making a formula that would work for any damage level but still giving similar results, it looks like this:
dmg * 0.5 ^ (2 * def / dmg)

Mon, 06/13/2016 - 18:13

Amnimonus

Okay breaking out a graph

@Sir-Pandabear How nice of you to test out the formula, although you used number i didn't expect, here is a hypothetical
graph done on matlab.
I tweaked the formula to Damage dealt = A*[B/(1+ exp((-A+D)/D))+M] and gave me better results.

In this scenario lets say we have a gremlin with it defenses reworked to have normal and piercing=150 elemental = 300 and shadow = 75
The formula in this case has B=1.4 and M = .1 so the maximum damage bonus is 1.5 damage giving us
Damage dealt = A*[1.4/(1+ exp((-A+D)/D))+.1]
then damage between 0 and 300 were recorded giving us the graph.

Now i know this is for any specific weapon but it can be used to see how each damage scales and it work until you reach high damage which would be hard to avoid with charge attacks. Although it is not shown on my graph the three lines eventually converge.

So how did this work? Well it is mainly controlled by the inside of the exponential function: (-A+D)/D) when this equal to 0 you deal 85% of the weapon attack power as damage, when it is equal to negative you get damage higher than 85% but that caps at 150% get a positive number you get a damage lower than 85% but caps at 10%.

The maximum damage is when the difference between attack power and defense is around 6 times greater than defense with the inverse holding true as well, this becomes a problem again at higher damage just like the current system but with to much damage being dealt instead with normal damage eventually getting the 150% damage as well. Thing that make this problem achieve able are damage booster on armor as well as the increase attack strength, with tweaking of damage and defense value this can be avoided but it starting to look like more trouble than its worth.

So here is plan B and it is something I've seen other mmos that involves completely changing defense rather than attack and defense.
Instead defense would encompass a percentage of damage reduction where zero defense you take the face value of a weapon damage

Defense would be a value between 1 and 0 although getting to a defense of 1 should be impossible
the new system would work like this
damage dealt = Attack(1-defense)
This is allot easier to work with because the the difference between weak, neutral, and resistant damage is a constant percentage.
Work great against monster but what about knights well this become more complicated with the leveling system and stars of armor as well as trinkets and pet perks and abilities because as mentioned before the defense should not reach a value of one or even close to it maybe capping at .9.

Mon, 06/13/2016 - 19:26

#10

Sir-Pandabear

Like you said the percentage thing would be difficult because it'd be hard to make defences meaningful in tier 1 and 2 while not giving way too much defence for 5*. .

And besides that, I think the current formula brings more depth and variety. Is it so horrible that Callahan's charge attack doesn't get that big of an edge over Iron Slug's charge attack? There aren't that many places where the current system fails. It adds decisions where you can choose to either get a normal weapon and pump its damage to overcome defences, or get a special damage weapons and get ASI to maximise the bonus you get from exploiting weaknesses. Of course, the damage formula was designed long before lock down trinkets and sprites perks and kat armours and triple uv tickets and all that jazz that makes max ASI + max damage obtainable to everyone easily. But I get the intention.

I also like how interesting it makes the current low-damage normal weapons like Dread Venom Striker. It appears weak, but you can use the weapon's own strong poison along with sprite abilities to make it absolutely lethal. With a percentage based defence no such hidden gems can exist; you would only need to find the weapon that has the most dps at any level of damage bonus and buff that one.

Mon, 06/13/2016 - 20:04

#11

Rhons

I Sorta Get What's Happening...

... But I'm mostly just lost.

Mon, 06/13/2016 - 22:39

#12

Amnimonus

@Sir-Pandabear These hidden

@Sir-Pandabear These hidden gems as you call them are example of how the game should work to benefit weapons, combining two attack for a greater benefit. Changes to the damage calculation would not affect it because they are to separate attacks.

Other example for the striker line is that they can cut threw gremlin mender shields because the shield is based on a number of hit rather than damage, they can also cut threw stone block faster than other weapons.
Graviton bombs complement heavy weapon like divine avenger and Callahan's charge attacks well by keeping enemies pack together

But what do these have in common well the exploit weapon mechanics rather than the actual damage. So these hidden gems can still exist.

One of the game selling points is the different type of damages, however it falls flat at higher damages as the difference becomes negligible.

Tue, 06/14/2016 - 01:36

#13

Sir-Pandabear

I'm talking specifically about how at no damage bonus, Leviathan blade has a higher dps than DVS, but as damage bonus increases, thus relationship changes. You seek to eliminate nuances like that.

Could you give me three examples of special damage weapons you don't feel are worth it because the normal variant is better?

Tue, 06/14/2016 - 16:53

#14

Amnimonus

And I'm talking about how

And I'm talking about how specifically about how weapon of the same damage type have drastically different damage bonuses in proportion to weapon strength.
Takethe basic attacks Blitz needle , riftlocker and Callahan, on the same depth blitz needle gets a much higher damage bonus than the other two and and damage bonus increases are much more effective on it as well.
Against neutral enemies the riftlocker and Callahan fair somewhat well when compare to blitz but put them against fiends or beasts and blitz quickly out shines them all.

As for normal damage weapons and special damage counter parts is another problem all together, While not as big problem with newer weapon like the shard bombs and the special blaster line as both special and normal deal the same damage against neutral monsters. The problem is that there isn't a situation or at least not many in which the aspect of normal damage is actually used. I f the was a area where you had every single type of enemy these normal damage weapon would actually do really good.

Actually before arsenal stations i still found my self using and preferring to carry at least one normal weapon while going through the clockworks that different monster families in each depth, you had to plan ahead because you could switch gear till the next terminal

Ideally from games that have several type of damage. you would have the damage working as such:
-using weapons with the effective special damage will result in increase in damage by a certain factor
-using weapons with the neutral special damage will result in the same or a little less damage than their neutral counter parts (something that is not done with 5* brandishes and the leviathan blade)
- and using ineffective damage resorting in a decrease of damage by a certain factor

But as said before this would be simple to do on enemies but not player themselves because they are hybrids of defenses

To summarize the current damage system make larges differences between normal and special at low damage for weapon such as shard bomb torto guns and certain low damage weapons may benefit from too well (blitz, DR, antigua lines) while heavier weapons benefit too little. To make it clear i don't want to create a bigger damage difference between normal and special damages just more constant heck a 20-30% would be optimal and giving a slight nerf to weapons like blitz and slight buff.
Yeah it might add a sense of decision making however it is mainly towards a small group of weapons in the large hit count area and there aren't really any for the rest.
And top of that you can max out all your stats.

Wed, 06/15/2016 - 00:01

#15

Sir-Pandabear

So your problem is that rift locker and and blitz are somewhat balanced against neutral enemies but blitz is overpowered against weak enemies.

It is no secret that blitz and brandishes are overpowered. I think the solution is to reduce their damage so that blitz will be less viable against neutral enemies compared to riftlocker while remaining somewhat stronger against weak enemies, not to redo the damage and defence of every piece of equipment in the game.

Wed, 06/15/2016 - 18:45

#16

Amnimonus

I thought the same too at one

I thought the same too at one point but that was before a I knew how damage worked in the is game and this is now one of the reasons and here another graph about how current damage works.

The tool note there are the sweet spots slightly bellow these damages (depth 19) you begin to get increasing returns for damage, the rate of change increase fast and fast the closer you get to it. Blitz, DR, antigua line and i would say tortoguns (except normal) and shard bomb (which mainly seem to fail from a mechanic stand point mainly) damage changes seem to be complicated at low damage especially when the charge attack and normal attack fall under the high end or low end of the spectrum of damage.

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Reforming damage calculation