Damage Calculation

After several months of statistical analysis of raid and AW fighting, here is my conclusion.
The damage can be estimated from the attack / defense ratio with a power function.


EDIT : After the post of RedPython, it made me think and I redid my calculations …
And finally, everything is clearer! all my previous calculations are merged into one formula, so I modified the original message. Again thank you @RedPython!


:crossed_swords: Damage ≈ 100 x ( θ x Att / Def ) ^ 1.35 :crossed_swords:

:point_right: Tile damage is divided by three
:point_right: The defense of the team managed by the AI is increased by 20% (certainly only concerns PvP fights)
:point_right: θ is a random parameter between exp(-.5)=0.606 and exp(.5)=1.649.

I have no way of being sure of the formula used by the game algorithm, but these estimates are reliable for the 1047 cases studied. They allow us to deduce interesting things.

:point_right: As long as the attack is inferior to the defense, the damage is ‘compressed’ between 1 and 33 for the tiles and 1 and 100 for the special skills and attacks of the defenders.
:point_right: On the other hand, once the attack is superior to the defense, the damage can fly away with no known maximum.
(This also explains the impression of ‘levels’ felt on the map and against the titans. Once our heroes have evolved so that their attack is superior to the opposing defense, everything becomes easier!)
:point_right: Having several heroes of the same color only increases tile damage. They are calculated by adding the attacks of these heroes
:point_right: Lowering the enemy defense is more effective than increasing the attack.
:point_right: Combining defense penalties and attack bonuses has a devastating effect.

I hope they will not change the calculation right away …

152 Likes
Damage per tile
How to calculate the defense
Hero durability - statistics
No more silent nerfs
Upgrade Boldtusk now or Natalya later?
Calculations of attacks on enemies
Best snipers in the game?
Damage calculation+
Attack damage % question
What does 100% damage mean?
:rice: Talents: defense points or health points?
Titan Attack Fundamentals - (new player Titan guide)
How many tiles to remove tank
Mechanics Questions
What does a percentage damage mean on a hero special?
Thoughts on Kage, guys?
How is Team power calculated?
Analyse Heroes ala RedPython
Please review Gobbler and his low defense
Zimkitha or Isarnia, which one should I fire off first?
Favorite Hero Combos
After upgrading 12 raids - 12 losses. WHAT IS IT LIKE?
Does this stack?
What does X% damage means?
Time for a big change - STOP Mono Colour
Alliance Wars Matchmaking (Discussion & Developer Response) MASTER
Ascension and team decisions, help!
Hero card showing stats with full leveled hero
Hero against hero. How or why is this possible
Calculating damage
Help with specials
Pattern in the raids
Wu Kong or Tarlak + Boldtusk
Calculate Hero Attack and Received Damage
...and minor damage to nearby enemies
What do stats do?
Question regarding elemental link - elemental defense up and special - elemental defense up
:test_tube: Early Information on the October 2019 HOTM (Kingston)
Embleming Strats for 4& Heroes
Clarification on Special Attack %
Best approach - boost attack or defence
Flawed damage?
Boomer holy defense not accurate
Slow heroes are dead
:moyai: Guardian Gazelle: Guardians of Teltoc – Thoughts, Discussion & Summon Results with Feedback
Need help calculating damage taken in raid
Jabberwocky - 600% Damage Against Titans?
Gorilla (Blue Shield) – How does the defense buff work?
Let’s take a minute to appreciate Caedmon
TILES: Attack damage inflicted from tiles
A good use for Thorne?
Wu Kong needs a new haircut (NERF WK?)
Wu kong khiona and tarlak stacking
Can heroes be ranked objectively?
Wrath of the Titans
Khiona's special skill not working?
Thoughts on Kage, guys?
Just how bad is Elkanen?
Shout out to our Veterans of old
Alliance Wars Matchmaking (Discussion & Developer Response) MASTER
Thoughts on Kage, guys?
Damage points
Athena vs strong color pulverizer
Combat damage algorithm definition
What do stats do?
What am I doing?
Error in raid matchmaking algorithm – FrancescoDarkness‘s feedback and discussion on Raiding
What are the raid attacks based on?
Bane Costume - what's the point?
Frida + Athena stacking- Sum or Multiple?
Question about Attack rating
Clarissa – 5* Dark/ Purple - May 2020 HOTM (Hero of the Month)
Understanding DoT (Damage over Time)
:test_tube: Early Information on the April 2020 HOTM (Malosi)
Error in raid matchmaking algorithm – FrancescoDarkness‘s feedback and discussion on Raiding
Special powers of the diminishing heroes
Costumes... Whats the Point? Which is Better?
Danni raid senza logica
Reduced damage?
Costumed Gunnar for epic/legendary challenge events: wich emblems path?
Jabberwocky - 600% Damage Against Titans?
Lianna and Wu Damage not Adding Up
Understandimg atack damage Help
Empires & Puzzles RPG Quest (Bugs at ZERO poits) at Titans
Attack damage when hitting all targets
Celebrating 500 days since Hero Academy first teased
Tile damage doubled with 2 heroes of same color?
Jabberwock damage inconsistencies
What is the best 1-2 punch / Hero Pairings in the game?
Elemental Down or Wu Kong?
Analysis of Power Creep of Hero Stats - Long Read Warning
:balance_scale: Hero Balance Discussion: Noor
:test_tube: Early Information on Season 3 Heroes [Part of The Beta Beat V26 & V27]
Any love for Domitia?
Jean-François – 5* Fire/ Red - February 2020 HOTM (Hero of the Month)
Titans - what is your strategy, heros to always bring/avoid
Titan Damage Boosters: Miki vs. Tarlak vs. Ranvir vs. Wu Kong vs. Guardian Gazelle
Master List of E&P Links & Player Guides
JF 94% ice defense doesn’t work
:balance_scale: Hero Balance Discussion: Noor
Question about TORIL
Costume brienne help me understand
Rigged Raids and Other Game Flaws the Devs Will Continue to Ignore
Kage full and half damage
Where to find stats about stacking
Where to find stats about stacking
Maybe guardian gazelle bug
Clarissa – 5* Dark/ Purple - May 2020 HOTM (Hero of the Month)
Damage calculation vs titans
Help with understanding tiles
Time to ask Embarrassing Questions
Why is nothing being done about Kadilen's Eclipse Shield special?
Season 3 heroes stat buffs
Bug with defence down?
Rigged Raids and Other Game Flaws the Devs Will Continue to Ignore
Rigged Raids and Other Game Flaws the Devs Will Continue to Ignore
Stones' colour distribution is NOT random
Troop Comparison & Summary! -- Including New Ninja Troops
What happens in a red color stack when Marjana is blinded, Ares has a crit buff and Gravemaker has 30% wound? OR Color stacking and RNG ( buffs, debuffs and talents )
How to determine elemental attack/defense calcs
No attack power is added to the tournament
Damage calculation spreadsheet
Stones' colour distribution is NOT random
:japanese_castle: Ninja Hero Thoughts & Discussion Thread
Talent Grid Boril Help
Help with Season 1: Province 17+ and more help please
Defense vs Health
Hero Costumes Discussion
:tea: Riddles of Wonderland: Jabberwock – Thoughts, Discussion & Summon Results with Feedback
:tea: Riddles of Wonderland: Jabberwock – Thoughts, Discussion & Summon Results with Feedback
1*+19 Heroes and 1* troops in tourneys or Attack/ HP, Attack troops, and maybe Brand in the center
Broken damage calculations
:tea: Riddles of Wonderland: Jabberwock – Thoughts, Discussion & Summon Results with Feedback
Damage output
Stones' colour distribution is NOT random
Damage reduction : -25% Atk or +25% defense?
Special skill - percent of what?
Glenda – 5* Ice/ Blue - November 2020 HOTM (Hero of the Month) -- Initial Release
One hero hits the other 2 times, but with different strengths: how is this possible?
Do regular defense buff and elemental defense buff stack? And how?
Hero gains +94% defense
Who gets the Tabard’s? Victor or Jabberwock?
:rabbit: Springvale 2019: Master Lepus – Thoughts & Discussion
Guide "Increased damage against elements - how much?⁷
Kashhrek is too powerful in raids
Sartana damage bug?
Neith, Musashi, or Ranvir?
Monochrome teams, attack bonus?
Can someone explain this for me?
I'm NEVER coming back! See you tomorrow! Vent thread
Margaret / Kashhrek Defence against fire... Confused!
:tea: Riddles of Wonderland: Jabberwock – Thoughts, Discussion & Summon Results with Feedback
Buff booster tournament rule is baloney?
Problems with my Scarlett's full power
Understanding attack power?
Ranking of the best hitters (snipers) to 7th June 2020
Telluria Emblems -- heart path... Or shield path...?
Common troops + titanium shield tactic
Freya emblems
Help need for my Troops
Does guardian gazelle increase special attack of allies by 100%
Farewells - MASTER List - Add your favourite past forum great or player who quit [WIKI]
Gravedigger (Gravemaker) on steroids? – Why is the amount of Burn Damage different in battle than what the card says?
Damage Calulation Stones and Buffs
Where to find stats about stacking
3* Blue Sniper - Rankings
:test_tube: Early information on the December 2020 HOTM (Reuben)
What is the percent sign in the damage reverring to?
Tile damage question
Tile damage question
Help with Reds!
Best emblem path for Drake?
Difference in Emblems
Hero's Attack
Hero Damage
Serious error in the game code
Just the place for a Snark! I have said it once
Damage calculation possible error
Deciding where to spend your class emblems - Tourney update 2019-Mar [Math, Analysis]
Kageburado damage not correct
Alliance Wars Matchmaking (Discussion & Developer Response) MASTER
Can classed wu kong beat Tarlak?
Anzogh – New April 2019 HOTM (Hero of the Month): First Thoughts & Discussion
Descriptive Index of Empires & Puzzles Resources
"How better" is +18 DEF than +36 Health right now? In what cases it's resonable to go for the HP instead?
Anzogh – New April 2019 HOTM (Hero of the Month): First Thoughts & Discussion
Is there a list of tile damage per heroe?
Boldtuks attack buff not working with specials?
Questions about xp and heroes power

Can you translate the three French parts?

Défense = Defense

Compétences Spéciales = ?

Tuiles = ?

special abilities, tiles?

1 Like

Special skill / tiles

That’s right. I replaced the graphic with the English version in the first post.

4 Likes

So, if I may, I want to check if I understand you (@SolemnWolf) right:
Attack is the Attack-Stat (including all bonuses from troops, color, …) of the attacking Hero?
Defence is the Defence-Stat (Shield) (again including all bonuses) or the defending Hero?
The ± 50% are taken from the ratio?

So, it seems, that for tiles the damage per tile is actually one third (maybe you’d like to try a factor of 33 instead of 30, although that might not make a big difference), because you need at least 3 tiles to “shoot”.
Very interesting. Big thank you to @SolemnWolf for sharing that information.

2 Likes

This is great. Thanks for putting in all the work to gather the data and approximate the function. It’ll be interesting to play with this in mind now. Makes sense why tactics like Wu Kong are so effective.

Semi-related note: Is a X% attack buff really a X^1.35 % damage buff? i.e. Kiril’s 30% attack buff is a 42.5% damage buff? Kiril’s 30% defense buff is a 30% damage decrease.[i.e. (1/1.3)^1.35]

1 Like

It’s almost that.
Attack is Attack-Stat of the attacker with all the bonuses, penalties and combos
Defense is Defense-Stat of the defender with all the bonuses and penalties
±50% is a random coefficient varying from 0.5 to 1.5 and applied to the Attack/Defense ratio
On the other hand, the effects of colors and critical hits are applied after the indicated calculation.
For the cases studied, critical hits only appeared for tiles and in less than 4% of cases.

2 Likes

That’s right @flyingsolow,
Att +30% = Damage +42.5%
Def -30% = Damage +60%
Att +30% & Def -30% = Damage +131%
Att +30% & Def -30% & Wu Kong = Damage +662% !!!

24 Likes

This information is amazing! Thank you for sharing. It must have been quite a bit of work to put this together :).

3 Likes

I think I understand but can you put some numbers behind this using a couple of heroes with like 3 tiles and a special skill

1 Like

Ahh, Thank you for pointing that out.
Again, @SolemnWolf, thank you so much for sharing this information.

1 Like

Examples of calculations


EDIT : The examples were taken again following the simplification of the first post


  1. Defense


    Attacker 1: Richard (Att=650)
    Defender 1: Grimm (Def=600)
    :point_right: Calculated damage: 100x(650/600)^1.35=111 - Damage found: 112
    Attacker 2: Elena (Att=788)
    Defender 2: Zeline (Def=619)
    :point_right: Calculated damage: 100x(788/619)^1.35=139 - Damage found: 149

  2. Special Skills


    Attacker: Zeline (Att=724x154%=1108, the capture dates from before the reduction of Zeline’s special skill)
    Defender 1: Richard (Def=783x120%=940, powerful attack)
    :point_right: Calculated damage: (100x(1108/940)^1.35)x2=250 - Damage found: 212
    Defender 2: Elena (Def=578x120%=694)
    :point_right: Calculated damage:100x(1108/694)^1.35=188 - Damage found: 181
    Defender 3: Kadilen (Def=734x120%=881)
    :point_right: Calculated damage: 100x(1108/881)^1.35=136 - Damage found: 144
    Defender 4: Domitia (Def=682x120%=818)
    :point_right: Calculated damage: 100x(1108/818)^1.35=151 - Damage found: 163
    Defender 5: Vivica (Def=699x120%=839)
    :point_right: Calculated damage: 100x(1108/839)^1.35=146 - Damage found: 154

  3. Tiles (1 hero of the attack color)


    Forward: Wu Kong (Att=834)
    Defender: Kadilen (Def=734x120%=881)
    :point_right: Calculated damage: 1/3x100x(834/881)^1.35=31 - Damage found: 35 & 35 & 33

  4. Tiles (2 heroes of the attack color)


    Attackers: Kiril & Grimm (Att=(725 + 844)x1.1=1726)
    Defender 1: Rigard (Def=733x120%=880)
    :point_right: Calculated damage: 1/3x100x(1726/880)^1.35=83 - Damage found: 98
    Defender 2: Little John (Def=642x120%=770, weak attack)
    :point_right: Calculated damage: (1/3x100x(1726/770)^1.35)/2=50 - Damage found: 58
    Defender 3: Gormek (Def=632x120%=758, powerful attack)
    :point_right: Calculated damage: (1/3x100x(1726/758)^1.35)x2=202 - Damage found: 206 & 218 & 203

42 Likes

Have you adjusted for crits?

1 Like

Yep. Critical hits only appear for tiles (~ 3.5% of cases) and have the same effects as a powerful color attack (x2 damage).
I have never had a powerful and critical color attack at the same time.

2 Likes

So having heroes with good defense and strong attack would be better ? What about heroes who have high attack power and low defense like Elena ? would it be worth it to fully level her up ? I think she’s the one red 5* who has strong power attack and low defense though if I don’t make mistake !

1 Like

Exceptional work @SolemnWolf. I look forward to seeing what further conclusions can be drawn.

Very interesting to see that lowering defence is more valuable than raising attack.

7 Likes

Isn’t crit chance dependant on troops? Also weak spot on titans always crits.

1 Like

I think weak spot on Titan does not always critic… I’m pretty sure!!!

2 Likes

@Paizo101, I do not think my work is a good starting point for choosing heroes.
The tactic is more important. For example, Elena’s special skill is very interesting.
Look at the side of this topic

2 Likes

Cookie Settings