Damage Calculation

I believe the OP “Special skill” is the offense hit.

I believe so also. that is why I asked. It ‘may’ be that special offense/defense are same compute, and then the simple difference is offensive tiles, vs defensive strikes. But I wanted to ask as I also need the defensive special powers to better match teams for personal raiding.

One thing that is more tough to compute, is odds of a special actually going off, and if so, HOW many times it will be used, before the hero is killed. That is not something simple math can achieve, it takes looking at the entire team dynamics, how well they heal, how well they block how well they complement each other, and how well they counter the other teams special powers (AND biggest of all, how dam lucky you get in tiles, lol, which can not be computed upfront).

But having all attacker / defender attacking ‘real’ values in an easy to compute set of rules is critical to being able to give insight to these much harder to compute values (i.e. team help / enemy hurt specials vs opposite for enemy team).

I gathered the special skills of attack and defense.
In my calculations the values of the attackers are slightly lower than those of the defenders. But it is not statically significant.
So I think the calculation is the same.

EDIT : My apologies, the post of RedPython a little further allowed me to realize my mistake. Everything is calculated in fact with a single formula, it is the defense of the teams managed by the AI which is increased …

Wow. That is one BOSS spreadsheet! =-]

Hm… @SolemnWolf I’ve just seen this:

I’m not sure if I saw that part in the post with the examples Damage Calculation

How this info affects the formula? :thinking:


That’s why the coefficient on the Defense damage is 101, while on offense it’s 78. Ogives that the exponent values are also different, benefitting offense.

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Thanks for the clarification :wink:

A big thank you to you @RedPython!
I didn’t know anything about this increased defense of the AI-led team.
How does this information affect the formula? Take a look at the first post on this topic and you’ll know it!


(as only 20 characters can be)

Amazing. Thanks for updating the original (and now unified) formula.

Kudos to @RedPython for helping reveal the final key to this puzzle. :slight_smile:

@SolemnWolf The new formula definitely makes more sense, tho is θ an evenly distributed random between e^-0.5 and e^0.5 or is it a curve such that it’s usually around 1? I think you had something about a Guassian curve in your older version of the post? Most low damage hits seem to be near each other in my experience, otherwise even for low damage hits near 30 we’d see more 15 and 58 damage hits when θ was 0.6 or 1.6.

So maybe a full version of the formula would be?:

100 * TileD * ((θ * AttackSum / DefenseSum) ^ 1.35) * ( ColorBonus + Crit)

AttackSum = (Attack Stats of a hero * Troop buffs) for each hero * Skill% * Combos * Buffs
DefenseSum = Defense Stat of target * EnemyBonus * Buffs

TileD = 1/3 if it’s a tile, else 1
Combos = 1, 1.1, 1.2 etc depending on cascading combo multiplier for tiles, else 1
Skill% = skill stat in decimal form, else 1 if not a skill
Buffs = 1 + Skill Buffs [only 1 buff/debuff of the same type can be active at once]
EnemyBonus = 1.2 if the target is an enemy of the active player in PVP, else 1
ColorBonus = 2, .5, or 1 for tile damage depending on color strengths/weaknesses, else 1 for non tiles
Crit = 1 if it’s both a tile and rolled a crit (base 0 chance, increased with troops / skills), else 0
θ = a random number between e^-0.5 and e^0.5 with a Guassian curve distribution of σ^2=1
Note: The special effects of certain skills can change a number of these stats

Or did I mis-order something?

Edit: Fixed ColorBonus / Crit interaction via Kerridoc’s and SolemnWolf’s help. Thanks!


The way you incorporate the crit bonus is wrong. The crit bonus is color-blind. The right hand terms of the equation should be (colorBonus + Crit) where Crit = 1 if crit, 0 otherwise.

Now I know exactly what happened here, other than my poor judgment that I can defeat this team and pressing the attack button. Thank you @SolemnWolf for this great efforts.

You faced an all yellow team with ONE purple and to make it funnier he was a healer :joy::joy::joy:


It was Sartana ,… I believe.
But I killed her… Rawr!

I’m saying on YOUR team! :rofl::joy::joy::rofl:

This is a beautiful work Lutrinae, personally I didn’t want to go into much detail because there are many exceptions with all the effects of special skills (some are powerful and without weaknesses, buffs can be cumulated if they are slightly different…).
The only (possible) error is that identified by Kerridoc: It seems that critics cancel the weakness.
Moreover, the bonus of 20% for the AI certainly concerns only the PvP fights (but we have no way to check it because the stats are only accessible in PvP …).
Finally, if you’re looking for detail for θ, the best approach I’ve found is:
θ = exp (χ)
And χ follows a Gaussian law centered at 0 with a variance of 1.07%, so in 68% of cases -10% <χ <10% -> 0.90 <θ <1.11.
But this is only a statistical approach!

Is there an error in the defense value? should it be 20% more, right?
In which case does this % def. increase apply? In the prevoius example it was not cnsidered^^ Thanks :slight_smile:

@Oracle83, this bonus applies to AI defense for each player attack (but apparently only for PvP).
The bonus is well applied in the calculation examples (post # 13), the defense of the AI is increased by 20% from the start (Def x 120%)

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