# Damage Calculation

I’ve seen this calculations 4 months ago and could not understand what was happening. Now I’ve realised that you have calculated the effects of buffs separately and worked out the final percentage that will be applied to the final damage calculated without buffs.

Closure feels good

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You’ve multiplied by 415% instead of 365%

Kunchen as a tank always drop down theta close to 0.65

Note that Kunchen and Telluria do not obey maths and physics in general. They are Gods.

Unbuffed tile attacks
When I take only the tile attacks without any buffs/debuffs I get the following curve:

For this I used the simplified formula:
damage = damage_modifier x formula_to_be_found (total_attack / defense)

damage_modifier = 1 + colour_bonus
colour_bonus = 1 for strong colour, 0 for neutral colour, -0.5 for weak colour
total_attack = sum of the attack values of all heroes of the attacking tile colour
hero1 attack = hero1‘s attack value x (1 + troop attack bonus)
same for hero2 attack, etc

The curve starts as a straight line, then does kind of an “S” and then continues as a straight line.
Starting at an attack/defense ratio of approx 3, the damage shows considerable variation but remains clearly within a linear boundary.

attack buffs/debuffs, critical hits and tile combos
Now, if we add attack buffs/debuffs (Boldtusk/Ares/Richard, etc), critical hits and the tile combos, these (orange) data points add as follows:

damage = damage_modifier x formula_to_be_found (total_attack / defense)

damage_modifier = 1 + colour_bonus + critical_hit_bonus + tile_combo
colour_bonus = 1 for strong colour, 0 for neutral colour, -0.5 for weak colour
critical_hit_bonus = 1
total_attack = sum of the attack values of all heroes of the attacking tile colour
hero1 attack = hero1‘s attack value x (1 + troop attack bonus) x (1 + attack de/buff)
same for hero2 attack, etc

Formula
Now, what is the formula for this curve? It’s not an exponential curve, so what kind of curve type is it?

Only recently I stumbled across a formula for an “S” shaped curve.
Since start and end are nearly horizontal, I tried to add a straight line.

Unfortunately, as my excel clone doesn’t know how to add this kind of trendlines, I had to try manually and fit the curve myself somehow:

The formula for this fit is:
formula_to_be_found? = 350 x exp( -9 x exp( -0.9 x ADR)) + 80 x ADR

ADR = total attack/defense ratio

When the first part is multiplied with 0.6 or 1.4 the boundaries look quite good
formula_to_be_found? = 0.6 x 350 x exp( -9 x exp( -0.9 x ADR)) + 80 x ADR
formula_to_be_found? = 1.4 x 350 x exp( -9 x exp( -0.9 x ADR)) + 80 x ADR

closer look at the lower range:

How does the damage calculation with this formula perform for raid tile damage? Here’s the comparison between calculated damage and actual damage:

closer look at the lower range:

Clearly not as good as the DoT formula.

There is definitely more to it than this, but imho the formula works well so far. And most importantly, this curve type seems to point us in the right direction.

Now, this only took a look at tile damage, so this formula only applies to tile damage!

• no defender bonus for defense or anything has been taken into consideration here
• the formula doesn’t apply to specials, enemy slash attacks and enemy specials (I don’t have as much data on those yet as I have for tile damage)
• a few buffs/debuffs still need to be investigated in more detail (defense buffs/debuffs, Wu/Ranvir)
• it’s just a manual fit by someone with only basic skills in Excel

If you want to use this formula in Excel, you might have to separate the two exponential functions and make the calculation in two steps (that’s how I had to do it with my Excel clone).

Minion damage:
A preliminary analysis of enemy’s minion damage in raids shows a linear damage curve for them, similar to the linear bottom part of the tile damage curve.

(unfortunately, I have just Buddy and Noor as minion heroes, so I’m lacking data for the attack team.)

=> minion damage = damage_modifier x 90 x (attack / defense)

damage_modifier = 1 + colour_bonus + critical_hit_bonus
colour_bonus = 1 for strong colour, 0 for neutral colour, -0.5 for weak colour
critical_hit_bonus = 1
attack = caster’s attack value x (1 + troop attack bonus) x caster’s minion attack% x (Owner’s attack bonus)
defense = target’s defense x (1 + troop bonus) x (1 + defense buff/debuff x 4/5)

(the fudge factor of 4/5 for the defense buffs/debuffs is my current best guess to align minion and damage and also tile damage with the respective damage curve)

My observations so far:

• Enemy minion do more damage than attacker’s minions. Could be 20-25% more damage, something in this range
• All Minions attack a random target
• All Minions attack with the colour of the hero that they are “attached” to, their owner, and they get the colour bonus as if it would be a tile attack
• All minions can do critical damage, if their hero has a crit chance and they proc
• All minions get the attack buffs/debuffs that their owner’s have
• The minions damage depends on defense buffs/debuffs of their target
• Freya’s Minions attack buff for other minions applies to ANY other minion attached to their owner, i.e.two of Freya’s minions at one hero will give the +120% attack buff to each other
• The thorn minion of druid class seem to have approximately 15% attack power from their druid (should be in the range of 14-17% of the druid’s attack)
• I’d love to get Freya

I’ll try to get some data on minion damage with Wu’s buff. So far, I’m under the impression that Wu (and Ranvir) increase DAMAGE by 185% (195% respectively), not just the attack power like Boldtusk, Ares, CRigard, etc.

edit: corrected the factor in the damage formula to 90
edit2: corrected that minions do not get their owner’s attack buffs/debuffs

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If your numbers are correct: After getting shot by Lianna, your def-hero still has 369 HP left, he still benefits from higher def-stat. . The additional 144 HP from the HP-version dwindled to 12 extra HP.

You’ll realize that Liannas shot took only 74,74% of your def-boosted heroes total hp, while it took 76,26% of your hp-boosted heroes hp! And any additional damage will be similarly mitigated by the def-version.

Then there’s another often overlooked reason for choosing def over hp: The def stat benefits more from troops. No matter whether you choose mana troops like most (up to +18% def, 0% hp! ) or crit troops (+25% def, +9% hp), your heroes survivability benefits from choosing def over hp even more!

It’s good to see someone trying to complete the damage formula as the OP ended with the conclusion that it’s exponential function, which it is, but only to ±4 ADR - hence your findings of linear -> S curve -> linear.

I was tracking titan hits as I was wondering if rainbow titan team could be viable but I ended up with the same conclusion as you did - the damage begins to be linear quite early so rainbow is not that great even with the best attack/crit buffers and defense debuffers. And it’s quite hard to keep all the buffs/debuffs on all the time.

Minions - are you sure their damage goes up with buffs (defense debuffs on target definitely applies)? They might changed it but they inherited attack from casters base stats (hero card * troops). I’ll test it with Wu Kong, but I doubt it. And about your observation of minions on defense being stronger - do you count with the hidden +20% boost to attack and defense of defenders? Probably not

And Wu Kong is really increasing attack stat, not damage (attack boost is shown on hero cards during the fight).

Another thing you haven’t mention is combo bonus to attack - according to my data it seemed that its added to other attack buffs.

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I just checked for the few data points with attack boosts, and must admit that they are not conclusive if the owner’s attack boost actually applies to their minions.

The data on target’s defense buffs/debuffs the situation is clear, though. I have only data with 2 normal debuffs right now, but both definitely apply, because otherwise the damage is all over the place and not in line with the straight line that the rest forms.

I haven’t taken any boosts for the defender into account, yet. When there is enough data, such boosts will be easy to identify.

For the tile/slash attack, I already have some idea on the applicable boosts for the defender. Just not enough data to be certain. And the analysis takes time, especially as most of it is manual and I usually don’t have much time for it, and so on…

With this “S” curve function it could very well be that the defender gets boosts for

• attack by 30%
• defense by 30%
• damage by -45% (to compensate)
Not certain, just an idea of how the two tile/slash curves can be aligned.

Wu is really something. I went along for a long time with the indicated +185% attack boost and the increased attack that is indicated when you click on the hero during battle.
The Wu data was always all over the place and didn’t make sense.

Then I checked with my limited data what happens if I simply remove the +185% attack boost from the calculation and take a look:

Well, doesn’t that look like a simple factor to the damage?
So I decided to move his +185% boost from attack to damage and see what happens:

Nearly a perfect fit!
=> I take it from this that Wu might make some slight change to the attack value, but he certainly increases DAMAGE by +185%, that means 285% damage for each tile that hits, nearly triple damage, and even with the 32% miss rate, the average damage is nearly doubled (= 1,932 = (1 - 0,32) x 2,85)

The combo bonus works perfectly for me, if I add it to damage, not attack.

For raid and war a 3-2 team normally works great for me. Rainbow teams do very little damage while mono is very effective but risky. Recently I found some conclusive evidence to support this feeling.

Let’s say, as a basis an attack/defense ration of 1 gives approx. 100 damage. If you double the attack, like using 2 heroes of the same colour, you then expect 200 damage, and so on.
If I add such a line to the tile damage curve, I get areas below this and areas above this:

Let’s zoom in:

With some eyeballing the line crosses the damage curve at approx 1,3. Below this ratio the damage is punished and very low. Above 1.3 the damage is enhanced.

So at similar strength rainbow teams get punished considerably.
Teams with 2 heroes of the same colour with similar attack power as the defender’s defense get a damage boost.
This boost is even higher for 3,4 and 5 heroes of the same colour. So mono teams are rewarded the most, but are risky.

My preferred team of 3-2 is rewarded for both colours, and less risky.

Weak teams should use mono against strong opponents to get to this ratio of 1.3 and above.

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Well, with some more data, I can clearly say that minions don’t get the attack buff that their owner has. When considering the attack buff the data doesn’t fit with the rest.

When removing these attack buffs, the fit very well:

Also, Wu doesn’t work for the minions as my own Wu verified with Noor’s minions.
Neither does the extra HP boost work from Grevle (same should apply to CKasshrek and Heimdall).

The little data I have on thorn minions currently shows a good fit for 15% attack from the caster:

So what to expect from minions?
They get their HP and ATK from their caster, element and critical hit chance from their owner.
=> crit troops are better for minions

They act like shields, provide HP that help against direct damage and DoT, and do a little bit of damage.

How much damage can we expect from them? Depends on the target, of course. For a target with 1000 DEF the maximum damage should look like:

(please note that the defense debuffs have been reduced by 20% as this is my current best estimate on them)

And if you don’t have Athena, then Wilbur:

Or with one of the Ramming Pulverizers:

Can we apply this and make Minions a very effective tactic for raid and war?

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@Zack

That’s a lot of data! Are you able to draw any simple conclusions from your findings?

I thought this was answered when freya came out that has minions who buff other minions

But glad you confirmed it with data since sg has a habit of doin things that don’t make sense

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I would say that minions primarily act as extra HP that help their owner survive against direct damage and DoT, and support the team with a little bit of extra damage.

To maximise the minion’s effects, you could

• emblem the minion caster with a focus on HP and attack (as the minions get their attack and HP from this hero)
• emblem the other 4 heroes with a focus an defense (as the minions have the same DEF as their owner
• give the minion caster a crit troop for more HP, a good boost to ATK and the crit chance (from which the minions will profit as well)
• give the other team members crit troops as well for more DEF and the crit chance (the minions will profit from this as well)
• include Freya in your team, if possible, for the minion attack boost
• use strong colour heroes (as the minions get the colour bonus from their owner)
• include someone who reduces defense as much as possible (as the minion’s damage depends on the target’s defense).
• if reasonable, include an elemental defense debuffer (this will decrease the target’s defense even more)
• include someone who buffs the team’s defense (as the minions will survive longer)
• put the minion caster next to someone that increases mana generation, like Brynhild or put Ariel in the team (so that the minion caster summons faster)
• probably even more
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I should have read the Freya thread before, but I only became interested in minions since I got Noor.

Now I’m looking for a raid attack team with Noor (currently at 3-68) that is strong and fun. Competition is strong though with my favourite team consisting of Evelyn, Kingston, Athena, Vela and Kiril, especially since I got Kiril’s costume and will have it maxed soon.

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Today I tested the minion defense value to check if the minions get their defense from their owner, as assumed so far, or from their caster.

Short answer: minions get their defense from their owner

Here’s the relevant info from the raid battle with some screenshots below:
My Skittleskull-in-training has 593 defense and reduces enemy attack by 34%
My Noor has 793 defense

Khagan has 991 attack
Aegir has 782 attack
Leonidas has 862 attack

Skittleskull received one of Noor’s minions and got hit

• by Aegir with 157 damage
• by Leonidas with 98 damage while his attack was reduced by 34%
• by Khagan with 118 damage while his attack was reduced by 34%

Now, I added these points in my preliminary, yet unpublished damage diagram for slash attacks and used Noor’s defense (orange points) and Skittleskull’s defense (green points).

The difference in defense is large enough so that the points make a clear difference when compared to the rest of the slash attacks.
Noor’s higher defense pushes the points to the left and outside of the slash curve, while Skittleskull’s points are well in line.

=> Skittleskull’s minion get Skittleskull’s defense, not Noor’s
=> minions get their defense from their owner, not from their caster

Screenshots of my “close” loss:

(If anybody wonders: Khagan got healed by 139 instead of 118 because of his mana troop level 21 which gives +18% healing bonus)

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An additional question, if you have to decide to emblem a hero among 18 points of defense or 36 points of life, which one it’s worth more ? Based on this formula, for me it’s better to choose to emblem 36 points of life than 18 points of defense. 18% of defense using Grimm / Richard simulation, it would give a protection of only 4 more points of life (from 111 to 107) while embleming 36 of life it would give more protection and life to still alive. Am I correct ? Please comment

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Update on the minion damage:

Minion damage remains very linear. My guess is:
defender’s minion damage = 90 x ADR ±3
attacker’s minion damage = 68 x ADR ±3

ADR = attack/defense ratio

The defender’s minions’ damage is approx 32% larger than that of the attacker’s minions.

Minion’s defense
While fighting Derrics and Brands in bronze arena I got a nice case for the minions’ defense.

the damage

=> Perfectly clear that the minions get their defense from their owner

Bonus
I also found out that the minions take over (some of) the class ability from their owner. Kiril’s minion used jinx:

The normal minion damage against Bane is 58, but with jinx it went up to 69.
Besides wizards, minions might then also take over the class abilities from barbarians, rangers and sorcerers.
=> needs to be tested

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I suspect it’s a case of the game considering that to be a hit from the hero, so the talent can apply.

Only way to be sure would be from Barbarian, since the bleed would be VERY different if it’s based on minion damage.

It can be tested with some effort. The effects pop up as soon as the attack hits and when you ghost tiles or use tiles from a missing colour it is clear that the class effect can only come from the minion that currently attacks.

After several test runs in 8-7, 8-4 (elite enemies) and raid:

barbarian

My Grimm, Nordri and Gormek have a 30% chance to trigger the bleed damage. Their tile damage regularly triggered bleed damage, but their minions were unable to do so during dozens of attempts

=> minions cannot apply the barbarian‘s class special: bleed

sorcerer

My Sabina and my Gill-Ra have a 15% chance to trigger the reduced mana generation. Their tile damage applied this sometimes to enemies with mana bars. Their minions were unable to do so despite dozens of attempts.

=> minions cannot apply the sorcerer‘s class special: delay

ranger

My costumed Rigard has 25% chance for piercing, my Athena has 20%. During a long raid battle (timer went down to 02:11) there were 35 opportunities for their minions to pierce Vivica or Thorne, but they never succeeded. Athena and C-Rigard did with their tiles though.

=> minions cannot apply the ranger‘s class special: pierce

wizard

Since these other class specials didn‘t work, I wanted to test again for the wizard and included Kiril and Proteus in my raid team. Both have 25% chance for the 15% jinx extra damage per active buff of the targeted enemy.

Finally my team survived and Noor could hand out some minions for the test. A lonely Kadilen volunteered and the minions of Kiril and Proteus activated jinx damage. The jinx icon pops up when the attack hits, and when I ghost tiles it becomes perfectly clear that it can only be the minion attack that activates the jinx damage.

=> minions can apply the wizard‘s class special: jinx

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That’s bizarre. Enough so to be a bug IMO. It doesn’t make sense for only one talent to work.

Thanks for the testing!

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