Damage Calculation

To simplify, damage = (1/1)^1,35
Then you add the buffs and subtract the ailments.
+48%Atk = 1,48Atk // (1,48/1)^1,35 = ~1,70 damage, so damage + 70%
-44%Def = 0,56Def // (1/0,56)^1,35 = ~2,19 damage; damage + 119%
Both active // (1,48/0,56)^1,35 = ~3,71 damage; damage + 271%

Edit: Isarnia is so brutal :smiley:

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Gracias friend :smiley:

I’m impressed with your math, very good. If in my defense Kiril 30% defense, as I add the defense calculation, how much damage can my defense absorb?

With Kiril’s defense buff your heroes will take (1/1.3)^1.35 = 0.7 of the actual damage, that is 30% less damage compared to without his buff. :slight_smile:

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Gracias friend :smiley::smiley:

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This is correct, but misleading.

Damage is non linear.

+30% just happens to fall in the balance point of the curve.

+63 defense is
( 1 / 1.63 )^ 1.35= 0.51 or 49% less

+10% defense is
( 1 / 1.1 )^ 1.35= 0.87 or 13% less

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Yes, I know. I was also just wondering that If I only told 30% decrease it would have been misleading, that’s why I showed the calculations just in case. But yeah, it’s a coincidence that both are 30% in this case. :slight_smile:

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I spent 20 minutes convinced you were wrong. But you were correct.

Math is weird.

And that is not even getting into the INCREASED damage if the increase in defense stat results in a reduction of the nerf from the attack stat soft cap. This is one of the reasons it is important how the attack stat soft cap is calculated.

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True. In fact, after helping with numerous posts on damage calculations, I was pleasantly surprised how much difference even a simple attack buff or defense debuff totally plays a big part. In fact, the basic fundamental principle here at play is that:

  1. Ratio greater than 1, increases more when raised to positive power greater than one.

  2. Ratio less than 1, decreases more when raised to same power.

Once players can grasp this, the damage output can be increased even without doing much calculations.

Typical example being reversing the Wilbur shared damage with a pulverizer, and then attacking the least defense hero with snipers so that max damage is shared. Simple, but wonderful things. :slight_smile:

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I’m playing math, I think I missed something, check it out

Richard + 30% atk by Kiril
Thorne -44% def

(1/1) ^ 1,35

Richard. 813x415% = 3373
Thorne Def 935x120% = 1122

+30 ATK -44% Def

(1,3/0,56)^1,35 = 3,11 dano + 211%

(100x(3373/1122)^1,35)+211% = 1374

damage real 761

I believe I lost something lol

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Yeah, the math is fine. Using the given formula it would yield a variation ( θ) of about 0,55 and that seem unlikely. There’s probably an attack soft cap in effect so the actual damage is much lower.

Edit: I tried adding the modifiers directly to the base stat and it would result in 900, which can be fine if we assume θ can be around 0,84.

Atk 813* 4,45 = 3617
Def 935* 0,76 = 710
100(3617/710)^1,35 = 900
761/900 = θ = 0,84

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Y’all need to quit pretending you know what that formula means… I’ve read it 5 times now and I still don’t know what damage is. If I have a hero and it says he does 240% damage… 240% of what?? A bunch of y’all saying thanks knowing you’re as lost, if not even more now, on what that % is… Now, if someone could put it where your average everyday working shlub could understand it that’s different…

240% of the attack stat.

Yes, it could be stated a whole lot more clearly – this “damage” is not the actual health loss the target suffers. Just using a different word might have spared many of us a whole lot of confusion.

But that’s the word SGG used … nothing we can do about it.

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Most MMOs I have played list the damage.

The players just have to figure out the formula behind the damage for making decisions like emblem paths, troops, costumes, etc.

But Empires hoards info like gold.

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I don’t believe this is accurate. The number crunching I’ve been doing implies that they do actually mean “Damage.”

Consider the scenario presented by markpessan just above, and consider three formulae

  1. The attack/defense modifiers being a coefficient on the base calculation, as markpessan ran them. This results in a significant overestimation of expected damage (80% higher than actual), with a fairly high extreme Theta (0.55).
  2. The attack/defense modifiers being added together and applied directly to the stats in question, as Liliac ran them. This results in a smaller exaggeration, but still off: 18% high, with a Theta of 0.88.
  3. The numbers being exactly what the text says they are (other than the hidden 20% boost to the AI’s defense). Those numbers would be as follows:

Richard: A = 813+234 = 1047 Attack
Thorne: D = 935-412 = 523 Defense
AI Defense Boost: D = 523 * 1.2 = 627
Special: S = 415% Damage

100 * (A/D) ^1.35 * S
100 * (θ * 1047/627)^1.35 * 415%
100 * (θ * 1.668)^1.35 * 415%
100 * θ^1.35 * 199.8 * 415% = 829

That’s an estimation of 8.96% higher than actual, for a Theta of 0.94.

So, on top of being a much smaller error, and a much smaller Theta (which we would expect to be more likely from a Gaussian distribution), this formula also trusts that what they’re telling us is accurate.

SGG is generally very precise in their descriptions, so why would they have some specials that say “attack” when they mean “attack” but others that say “damage” when they mean “attack”?

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Can you explain the damage done in this video? :slight_smile:

From the formula given in this thread, I calculated it as follows:

Damage = 100×(1.153×869×3.65÷(982×1.2))^1.35 = 461 (random parameter = 1.153)

I am curious to know if what you stated might be able to arrive at a similar solution.

PS: For the Richard - Thorne case I just assumed it was one of the outlier cases in the Gaussian distribution with random parameter = 0.65 (which is still within the bounds of 0.606 and 1.649)

Damage = 100×(0.65×1047×4.15÷628)^1.35 = 761

With Special As Damage Multiplier it would be
100 × 415% × (1.612 × 869 / (982×1.2))^1.35 = 461 (random parameter = 1.612).

That, admittedly, is more of an outlier than the “special modifies attack” calculation, but it is still within the e^±0.5 range

NB: I made a typo in the Richard/Thorne case, and propagated that error through; the attack bonus is 243 rather than 234, for a total of 1056 attack, and a Theta of 0.64. Not that that’s a huge difference, and still within the expected bounds, but I wanted to correct my error.

So for either of the formulas, one of these two cases is becoming an outlier. So we can’t be sure which one is the correct one, unless we do a few more. I will try it when I have some free time. Will probably look into 10 different cases and try to come up with the damage calculation using the corresponding formulas and we can tally the results here after a few days I guess. :slight_smile:

That’s been on my backburner for a while, now, because I’ve been talking about this with Bloodfenraptor on the subreddit for the game. So far, I have 39 data points logged in my spreadsheet, including the Leo/Kun-chan and Richard/Thorne above. Most are attacks from Kageburado, Gravemaker, Rana, Seshat, or Joon, because those are who I raid with.

…I really should do more with Joon, given that he has the highest special modifier of my heroes, and should therefore display the difference most clearly.

The following is a histogram of results of the Ln(θ), where Blue is “Special Modifies Damage” and Red is “Special Modifies Attack.” You will note that while neither (yet) makes a smooth bell curve, the Red series (“Modifies Attack”) has a strong skew towards low θs, while the Blue series (“Modifies Damage”) is much more balanced.

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This looks like a very interesting project. Cool, let me know if you want me to supply data points too. We really need a large number of data to find any kind of statistical significance. :slight_smile: