Damage Calculation

simsiyah · November 30, 2018, 1:36pm

Fantasik work !!! Congrats

PHATDIAMOND · December 12, 2018, 5:06am

Do we know how defensive buffs stack into this equation? Sure seems to be like “defense against special skills” either isn’t working or doesn’t work like it should.

I have an enemy Alasie attacking me with no attack buffs, hitting my Hansel with a 30% defense buff from Victor and his 75% against special skills self buff, and doing almost 700 damage. I feel like that 75% defense isn’t doing a damn thing. With the 30% defense buff active my defense score is 945. Alasie is attacking with 894. Spirit arrow does 462%. Naturally I assume the defense buffs aren’t multiplicative but even still I should have a defense against that hit far greater. For reference against an unbuffed rigard with 747 defense alasie hit for 930.

ochartier · December 19, 2018, 12:55pm

This comes from the random parameter in the formula. The 700 damage is most probably because she hit close to the top of the random variable (the zero with a line in it).

In your situation, where she has a really high attack %, it can make the damage margin really large. She could probably have done as low as under 400 damage if she hit the bottom of the random parameter.

ochartier · December 19, 2018, 1:08pm

good point, The formula indicates that for a 1/1 attack on defense ratio, the damage range would be between 50 and 196… @SolemnWolf are you sure there is not an error in the formula or do data really show such a great variability?

PHATDIAMOND · December 19, 2018, 8:27pm

It’s not 1:1, had the 75% “defense against special skills” buff on top of the advertised defense score.

Zack · January 4, 2019, 5:39pm

Is it possible that the damage formula has been adjusted?

The damage with my Leonidas, Magni and Caedmon over the last 2 weeks or so seems lower than what the curve in the initial post shows. I’ve collected some data (the values for damage and the attack and defense values of the heroes when you click on them during the raid battle) and put the two together. This is how it looks (I hope the upload works):
grafik

Here is my curve with damage over the attack-defense ratio.

So far, I have only found a good polynomial fit:
attack-defense ratio = 4,994E-17 x^6 – 1,988E-13 x^5 + 2,642E-10 x^4 – 1,218E-07 x^3 +1,297E-05 x^2 + 1,038E-02 x
with x = damage
grafik

and
Damage = 1,91029E-07 x^8 – 2,88399E-05 x^7 + 1,79085E-03 x^6 – 5,85549E-02 x^5 +1,06369E+00 x^4 -1,01844E+01 x^3 + 3,94013E+01 x^2 + 7,07666E+01 x
with x = (total attack / total defense)

Not as elegant as the exponential formula above

Maybe somebody can check this and verify that the damage formula has been adjusted?

Garanwyn · January 4, 2019, 9:54pm

Are you accounting for the 20% defense boost that AI-run defense teams get?

Zack · January 4, 2019, 11:25pm

During the raid battle when I click on the hero it shows the current attack, defense and HP:

This Grimm has now 397 defense, which I used for my diagram. When I check him in the watchtower again, his initial defense is 361 and his troop provides a 10% defense boost, which results in 361 x 1,1 = 397 defense.

So there is no 20% defense boost shown and therefore I didn’t use a 20% defense boost for my diagram. Any boost like Magni’s defense boost, Boldtusk’s attack boost or Wu Kong’s boost are shown when I click on the hero (and is then be considered in my diagram).

Is the 20% boost applied but not shown?
When I add 20% defense, the curve is shifted slightly to the left but doesn’t merge with the initial curve:
grafik

So I’m a little bit confused. If applicable, I would expect such a 20% defense boost to be shown in the stats when I click on a hero during battle, but I may very well overlook something.

Argon · January 5, 2019, 12:23am

I made the same mistake, that 20% defense bonus doesn’t show up on raid defense team and therefore skew the whole calculation.

Garanwyn · January 6, 2019, 4:42am

There look to be at least two curves embedded there, to my eye. You can see how there are two discrete blue curves in there toward the high damage end. Are you combining hits against you from the defense team with hits by you against the defense?

Also, how are you getting Att/Def ratios in the neighborhood of 30 to 50? That seems remarkably high.

Zack · January 6, 2019, 11:12am

The high Att/Def ratios come from 3 star enemy heroes and lower. I dropped in raid to get more data points and am currently at (close to) 0. There are even some non-leveled 1 stars there and my Magni (at 3-70) is happy

The curve now consists of something like

40 normal attacks from my team
26 normal attacks from the enemy team
4 special attacks from the enemy team
330 special attacks from my team
6 normal attacks from my team during war
17 special attacks from my team during war

The single gem damages were tripled. Weak damage values were also doubled, strong damage values were halved.

So yes, I combined hits from my own team with those from the enemy team, both fit well with each other.

A few points are now included in orange from the current war:

grafik

It looks to me like those war points fit very well with the raid points. For those war points I did the same procedure.

take the attack values and defense values by tapping on the heroes during battle
Att values for special attacks are calculated as: Att = indicated Att x Special attack multiplier (e.g. Magni has 799 Att with his troops, so 799 x 4,2 = 3355; with Boldtusk and Wu Kong bonus it’s (799 + 1857) x 4,2 = 11,155)

Also for war the values shown during battle are: initial hero’s stat x troop boost x current boost from special

Here’s the updated logarithmic curve with the added curve for a 20% defense boost (in yellow) and the few new war points (in orange)

=> it looks to me like there is no 20% defense boost for raid battles

Garanwyn · January 6, 2019, 11:58am

So I think I can explain the two curves I’m seeing then. There’s also a 20% attack boost that the defenders get, but which doesn’t appear if you click on them. That will probably push the two curves together.

Zack · January 6, 2019, 2:18pm

Please explain. I can’t see two different curves for attacker and defender yet.

There is some variability in the damage, which becomes evident when I attack the same target twice (with low to moderate damage so that the target is not one shotted). This is probably from this random parameter θ that the damage formula has.

Only 4 data points are from enemy specials, the rest is from my own team, so practically the complete curve above Att/Def ratio of 1 is from my own team.

Initially, it was found that the raid defense team receives a 20% defense boost. But for me

this boost is currently not visible
it also seems to not show when I compare with the few war battles (I’ll try to collect more data during the next war)
if there is an extra defense boost, it seems to apply for war and raid
when I apply an extra 20% defense boost for the Att/Def ratio ( Att/Def ratio = total attack / (total defense x 1.2 ) the curve gets pushed considerably to the left (yellow points), but even doesn’t fit with the original data points

What do I need to incorporate then to make my curve fit with these data points in the first post of this thread?

Garanwyn · January 6, 2019, 3:37pm

These points here appear to be part of a different curve than the main body of points you have:

20190106_082011

So there are two questions I’m trying to understand:

Why does it look like there are two curves in your data points?
Why does your data set as a whole not align with the earlier research into damage calculation?

I don’t have a good answer on #2 yet, but I think I may understand #1.

You have 30 total attacks from the enemy in your graph (26 normal, 4 special). These attacks should have a 20% attack boost applied to them, which doesn’t show up in the attributes if you click on the hero icon, but which SG is apparently using just like the 20% defense buff.

I think if you apply this boost to those 30 defender attacks in your data, that the collection of points I circled will fall in line with the main body of points. That will leave you with a single curve well-fitted by an exponential equation, but one which doesn’t align with the earlier damage curve generated by @SolemnWolf.

With respect to the war data, I agree with you that it does look like it aligns well with the raid data. Can you help me understand why you don’t think there’s a 20% defense boost in there?

Zack · January 6, 2019, 7:27pm

Ok right, I see. That part there is very strange indeed.

My data includes a tiny bit of extra info that lets me identify whether it was an enemy attack or not. The points for the enemy attack fit ok when I apply 20% defense, but this doesn’t make that curve fall in line, unfortunately
grafik

A 20% attack boost for the defender would push these points too far to the right…

=> So it looks like the defender still gets the 20% defense boost in raid and war

Regarding that strange curve part, maybe some of the heroes do not fully achieve the indicated damage for their special attacks?

Still no answer yet why the curve doesn’t fit with the original.
grafik

(Sorry for the diagram overload)

Eddard · January 22, 2019, 2:00am

So with this data is it safe to assume that added defense is worth more vs added health considering upgrades from emblems as it pertains to damage mitigation/survivability?

zephyr1 · January 22, 2019, 2:15am

Yes, to a tipping point, as @Kerridoc would say:

MrSanshiro · January 30, 2019, 10:07am

Very nice work! Thanks a lot… now I have example question… which team will make bigger damage: Grimx3, Triton, Kiril or… 3xLJ, Ohara, Brienne. And why…

What you think?

TWAndrews · February 2, 2019, 2:35pm

I love that you Spotfire for this. I worked for them for a long time.

Dandcoug · February 12, 2019, 2:06pm

Can someone give me a basic breakdown of damage is dealt? How do the modifiers help both defense and offense?