Thank you for your check on my procedure.
Now I understand how to use your formula.
I will test some more case and report to you!
Not when you use this formula. The formula fits only with the tile damage and doesnât apply any bonuses. This would be different, if the formulas design would also incorporate the defenderâs slash damage.
The distant target is, of course, to get a formula that works for tile damage, slash damage and specials damage. My preliminary data shows that the curves are similar, but different. I havenât found a simple relation yet. There seems to be something else than just a 20% boost for attack and defense of the defender.
That would be great. Iâm curious, if this this formula will indeed hold up to expectations
That is right. Nevertheless, these are only 3 data points.
The min and max I suggest for that situation (ADR = 3,05) indicate a large range from approx 241-346.
When I compare these data points with my own tile damage date it fits quite well:
(fumitomoâs tile damage is multiplied by 3/2 to adjust for tiles and strong colour)
So more testing is very welcome 
Can you link the post where the 20% defense bonus for the defender is confirmed? I only remember that other players assumed such a bonus and others went along with it.
If you only look at the damage in one situation (tile damage) then it doesnât matter if there are any extra bonuses or not, because the fomula you get already includes all of them.
When you extend the situation and include the defenderâs slash attacks into your formula, then you have to take into account all of the bonuses that apply to the defender to be able to align their damage output to the attackerâs damage.
I already did some checking in this regard for my data, but I wasnât able to align the tile and slash damage curves with only +20% attack and +20% defense for the defender. My best manual fit so far was with something like
- +30% attack boost for the defender
- +30% defense boost for the defender
- -45% damage reduction for the defender
Of course, this is far from a nice and simple relation, so itâs probably wrong.
I am so sorry to have cluttered up the discussion with such nonsense. I did not examine your formula closely. I see what you mean now.
The way I recall it, the confirmation was one of those damndably brief drive-by comments in the wake of the discovery of the 20% increase to DoT on defence. The amount was not confirmed, just something like âYes, this is realâ. I wish I had bookmarked it, but I wasnât even a Forum member at the time. I remember being excited, like the stats crew had caught the staff out on some kind of big secret! Now I understand that SGG is just bizarrely secretive about trivial things.
Does it count when Staff says âgood conributionâ? 
No problem at all, the damage calculation still needs discussion and analysis for better understanding, and you reminded me that I wanted to investigate this further. (too much life happened in the meantimeâŠ)
The 20% increase in DoT damage for the defender is proven, yes.
My recent investigation into this found that the DoT formula is rather simple:
DoT/turn = heroâs DoT factor x heroâs attack value x (1 + troop attack bonus) / DoT turns x defense team bonus
=> you can use the +20% for the damage or for the defenderâs attack, both give the same result
I got burned when I initially investigated raid damage and treated tile damage, slash damage and specials damage equally. The resulting damage curve wasnât really that useful (see my earlier posts in this thread).
So I then decided to separate them and check each on their own, which gave much better results, especially after finding the formula for the Gompertz curve to describe the âSâ shaped curveâŠ
When I look at the minion damage they also seem to have a rather straight and simple damage formula. Defender gets a damage or attack boost there as well, their factor is approx 90 compared to 68 for the attacker:
Minion damage = 68 x casterâ attack power x casterâs troop bonus x casterâs minion attack % x (1 + minion attack buff) / (targetâs defense x targetâs troop defense bonus x (1+defense buff/debuff x 4/5) x (1+elemental defense buff/debuff x 4/5) x damage_modifier
90/68 = 1,32
So there seems to be an attack or damage boost in the range of 30-35% for the defender. Is the defenderâs bonus different for every formula? Or do 20% attack boost always apply for the defender and there are additional modifiers?
You could apply 20% attack bonus and then add another +50% bonus for minion damage to get the 30% damage increase for the defender (1,2 x 1,5 = 1,3)
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Great thread and big thanks to the author!
Surely this has been discussed somewhere before, but I couldnt find it⊠My question is about color stacking and damage.
As (n * x)^1.35 = n^1.35 * x^1.35 , can this be directly applied to color stacking and tile damage?
So 2 same color same strength heroes is not 2x damage, itâs 2^1.35=2.55 times the damage, 3 heroes is 3^1.35=4.4 times, 4 heroes is 6.4 times and 5 heroes is 8.8 times the tile damage. So for mono, you get 8.8 for the price of 5
Is this correct? Thanks!
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This is all excellent! Thanks for your effort @Zack
All minions give a percentage
of HP and Attack, from the caster
Replicator: 18% HP, 15% ATK
Forest Familiar: 9% HP, 13% ATK
Sparrow: 25% HP, 25% ATK
Raven: 20% HP, 20% ATK
And you discovered defense comes from owner, awesome!
But is it 100%?
Thank you @Pompitous!
That is a very good question!
So I now checked a dozen of my raid videos on minion damage and looked for a damage comparison for the same situation with and without minions:
Enemy Hu Tao hits my Caedmon (no minion) for 91 damage.
Enemy Hu Tao hits my Caedmon (minion) for 94 damage.
Enemy Hu Tao hits my Caedmon (no minion) for 95 damage.
Enemy Vivica hits my Caedmon (no minion) for 114 damage.
Enemy Vivica hits my Caedmon (minion) for 121 damage.
Enemy Vivica hits my Caedmon (no minion) for 118 damage.
My blue stack hits Delilah (no minion) for 167 damage at a 1.2 combo multiplier, so it would normally be 139 damage (=167 / 1.2)
My blue stack hits Delilah (minion) for 154 damage at a 1.1 combo multiplier, so it would normally be 140 damage (=154 / 1.1)
My blue stack hits Lady of the Lake (no minion) for 73, 74 and 70 damage (1.1 combo is shown for the next set of tiles in the cascade)
My blue stack hits Lady of the Lake (minion) for 69 damage.
Iâll check some more videos tomorrow, but imho this already points in the direction of the minions getting 100% defense from their owners.
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Damage isnât calculated against the minion but is calculated against the hero they are attached to.
The minion just intercepts the damage (up to their current HP).
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thanks 
After checking 4 more videos I have one more case:
my blue stack hits Freya (no minion) for 144 damage
my blue stack hits Freya (no minion) for 133 damage
my blue stack hits Freya (no minion) for 133 damage
my blue stack hits Freya (minion) for 136 damage
my blue stack hits Freya (minion) for 144 damage
my blue stack hits Freya (minion) for 144 damage (pierce)
Itâs late again, so Iâll leave it at that and
=> I accept that the minion gets 100% defense from his owner, just like we probably all assumed so far 
Unless somebody can find some counter evidence! ^^
(should be as unlikely like, for example, the âimpossibly unluckyâ evidence of a 4* whose special is still at 7 at level 4-31, despite me always feeding 10x 1* or 2*. He looks as surprised as me: dâoh⊠
)
I made a video on that subject. In a table I realized when the tankâs defense was over 850 the formula changes, because I tested several heroes.
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Have you ever thought about sharing the form?
good job interest I would like to analyze the calculations you made
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anyone here did any research on the random element in special attacks? I get a feeling that the max dmg output is capped differently. Maybe it uses a different RNG range on specials?
So far I would say that the random element seems to be very similar for tile attacks, specials and opponent specials. Only the slash attacks seem to have much less variability.
What exactly makes you feel that special attacks behave different than the other attack types?
because especially for snipers, the dmg range is so very wide, and I doubt Iâve ever rolled so low or so high as numbers potentionally present
Iâve collected some data on damage and can confirm that the damage can vary substantially once the attack/defense ratio goes beyond 3. This seems to be similar to tile damage, for example, though.
Hereâs a preliminary diagram with two versions showing tile damage and special damage (reduced to 85%) and they seem to align quite well.
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Nice work! Sounds like a lot of effort !
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Thanks! That it was!
At least, the work finally payed off and I made good progress in understanding how the most common buffs/debuffs work. Iâll soon be able to make a post about the results.
For example, it looks like the attack buff and Wuâs buff are applied differently for tile damage and special damage.
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