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Durability Formulas

Max Health MH \([ HP]\)

\(MH=MH_{0}+2\times lvl+20\times mh=MH_{0}+2\times\left(lvl+10\times mh\right)\)

\(MH_{0}\) Base Max Health (health at lvl 0)
\(lvl\) Level
\(mh\) Max Health Stat
Body Strength BS \([1]\)

\(BS=1+\frac{1}{5}\times bd\)

\(bd\) Body Damage Stat
Durability D \([S]\)

\(D=\frac{1}{4}\times MH\times BS\)

\(MH\) Max Health
\(BS\) Body Strength
Durability Bullet \(D_{b}\) \([S]\)

\(D_{b}=Bf\times\left(\frac{7}{10}+\frac{3}{10}\times dm\right)\times\left(1+\frac{3}{4}\times bp\right)=Bf\times DS\times PP\)

\(Bf\) Bulletfactor
\(dm\) Bullet Damage Stat
\(bp\) Bullet Penetration Stat
\(DS\) Bullet Strength
\(PP\) Penetration Potential

credits to lyw318


The 3 laws of Collision Mechanics

1. Every object deals a specific and constant amount of damage per loop.

2. If the HP of an object is lower then the DPL (DPL'') of the opponent the corresping DPL of it is proportional to the ratio of its health and the opponent's DPL (DPL'').

\(GH\leq DPL''\rightarrow DPL \sim\frac{GH}{DPL''}\)

3. Every collision can only last a natural number of loops.

           

fundamental equation:

\(GH_L = GH''\times\frac{DPL''}{DPL}\)

\(GH_L\) General Health Loss per Loop
General Durability D \([S]\)

\(D=\frac{1}{80} \times GH \times DPL\)

\(GH\) General Health
\(DPL\) Damage per Loop
Bullet Penetration BP \([HP]\)

\(BP=20 \times\frac{Bf}{Df}\times PP=20 \times Pf\times PP\)

with \(Bf=Df \times Pf\)

\(Bf\) Bulletfactor
\(Df\) Damagefactor
\(Pf\) Penetrationfactor
\(PP\) Penetration Potential
Penetration Potential PP \([1]\)

\(PP=1+\frac{3}{4}\times bp\)

\(bp\) Bullet Penetration stat
Bullet Strength DS \([1]\)

\(DS=\frac{7}{10}+\frac{3}{10}\times dm\)

\(dm\) Bullet Damage Stat
Reload BR \([\frac{1}{s}]\)

\(BR=\frac{1}{D_{b}}\times\left(\frac{D_{o}}{t}+RR\right)\)

Necromancer :

\(N_{D}=22+2\times br\)

\(D_{b}\) Durability Bullet
\(D_{o}\) Durability Object
\(t\) Time
\(RR\) Regeneration
\(N_{D}\) Number of Necromancer Drones
\(br\) Reload Stat
Reload Time RT \([s]\)

\(RT=\frac{1}{BR}\)

Reload-Loop-Equation \([x]\) :

\(RT=\lceil\frac{X_{0}}{1,875^{br}}\rceil\leftarrow\) credits to Cx for finding it

\(BR\) Reload
\(X\) Reload Time in multiples of 0,04s
\(X_{0}\) Technical Base Reload Time
\(br\) Reload Stat
Recoil Rc \([gu]\)

\(Rc=\frac{s}{BR\times t}\)

\(Rc=\frac{\rho}{BR}\)

Reload Speed \(V_{Rc}\) \([\frac{gu}{s}]\) :

\(V_{Rc}=Rc\times BR=\frac{Rc}{RT}\)

\(s\) Distance
\(BR\) Reload
\(t\) Time
\(\rho\) Radius
\(RT\) Reload Time
Regeneration RR \([\frac{S}{s}]\)  

\(RR=\frac{1}{30}\times D\times\left(\frac{3}{100}+\frac{12}{100}\times rr\right)\leftarrow\) credits to La Faucheuse for generalizing it

Regenerated Durability per Loop HPT \([\frac{S}{x}]\) :

\(DT=\frac{1}{25}\times\frac{1}{30}\times D\times\left(\frac{3}{100}+\frac{12}{100}\times rr\right)\)

Regenerated Health per Loop HPT \([\frac{HP}{x}]\) :

\(HPT=\frac{1}{25}\times\frac{1}{30}\times MH\times\left(\frac{3}{100}+\frac{12}{100}\times rr\right)\)

Regenerated Health per Second HPS \([\frac{HP}{s}]\) :

\(HPS=\frac{1}{30}\times MH\times\left(\frac{3}{100}+\frac{12}{100}\times rr\right)\)

for mh=0 and lvl 11 :

\(RR=\frac{1}{30}\times\left(\frac{144}{100}+\frac{6}{100}\times lvl+\frac{84}{10}\times rr\right)\)

for shapes :

\(RR=0\)

\(D\) Durability
\(rr\) Regeneration Stat
\(MH\) Max Health
\(mh\) Max Health Stat
\(lvl\) Level
Health Loss \(MH_{L}\)\([HP]\) after one collision from a bullet :

general formula :

\(GH_{L}=\frac{80 \times D''}{DPL}\)

for tanks :

\(MH_{L}=\frac{4\times D_{b}}{BS}\)

for spike :

\(MH_{L_{S}}=\frac{4\times D_{b}}{BS_{S}}\)

for bullets :

\(BP_{L}=20\times \frac{D_{b}''}{Df\times DS}\)

\(GH_{L}\) General Health Loss
\(D''\) Durability Opponent
\(DPL\) Damage per Loop
\(BS\) Body Strength
\(MH_{L_{S}}\) Health loss Spike
\(BS_{S}\) Body Strength Spike
\(BP_{L}\) Bullet Health loss
\(Df\) Damagefactor
\(D_{b}''\) Bullet Durability Opponent
\(DS\) Bullet Strength
Damage reduction dr \([1]\)

general formula :

\(dr=1-\frac{DPL_{0}}{DPL}\)

damage reduction tank / shapes :

\(dr=1-\frac{4}{10\times BS}\)

for spike :

\(dr=1-\frac{4}{10\times BS_{S}}\)

\(DPL_{0}\) Base Damage per Loop
\(DPL\) Damage per Loop
\(BS\) Body Strength
\(BS_{S}\) Body Strength Spike
Damage reduction bullet \(dr_{b}\) \([1]\)

\(dr_{b}=1-\frac{4}{2\times Df\times DS}\)

\(Df\) Damagefactor
\(DS\) Bullet Strength
Acceleration A \([\frac{du}{x^{2}}]\)

\(A=A_{0}\times\frac{1,07^{v_{m}}}{1,015^{lvl}}\)

for Tanks :

\(A_{0}=2,58825\)

\(A_{0}\) Base Acceleration
Movement Speed \(V_{M}\) \([\frac{gu}{s}]\)

\(V_{M}=\frac{s}{t}\)

General Top Speed \(V_{M_{T}}\) \([\frac{gu}{s}]\) :

\(V_{M_{T}}=10\times A_{0}\leftarrow\) credits to Cx

Top Speed \(V_{M_{T}}\) in \([\frac{gu}{s}]\) :

\(V_{M_{T}}=5\times 2,58825*\frac{1,07^{v_{m}}}{1,015^{lvl}}\leftarrow\) credits to Cx

Top Speed \(V_{M_{T}}\) in \([\frac{du}{x}]\) :

\(V_{M_{T}}=10\times 2,58825\times\frac{1,07^{v_{m}}}{1,015^{lvl}}\leftarrow\) credits to Cx

\(s\) Distance
\(t\) Time
\(A_{0}\) Acceleration
\(v_{m}\) Movement Speed Stat
\(lvl\) Level
Damage per second DPS \([\frac{S}{s}]\)

\(DPS=D_{b}\times BR\)

\(D_{b}\) Durability Bullet
\(BR\) Reload
Damage per loop DPL \([\frac{HP}{x}]\)

general formula :

\(DPL=4\times Df\times DS\)

for all other bullets :

\(DPL=10\times Bf\times DS\)

for triplet :

\(DPL=\frac{10}{0,7}\times Bf\times DS\)

for twin :

\(DPL=\frac{100}{9}\times Bf\times DS\)

for skimmer (small bullet),rocketeer (main bullet) :

\(DPL=2\times\sqrt{50\times Bf}\times DS\)

for skimmer (main bullet),rocketeer (small bullet) :

\(DPL=\frac{10}{3}\times Bf\times DS\)

for gunner (manuall bullet) :

\(DPL=\frac{1}{3}\times\sqrt{1000\times Bf}\times DS\)

for drones / destroyer / hybrid (bullet) / annihilator :

\(DPL=5\times Bf\times DS\)

for necromancer :

\(DPL=20\times Bf\times DS\)

for factory (drone bullet) :

\(DPL=25\times Bf\times DS\)

for factory (drone) :

\(DPL=2,5\times Bf\times DS\)

for traps :

\(DPL=\sqrt{50\times Bf}\times DS\)

for tanks / shapes :

\(DPL=20\times BS\)

for spike :

\(DPL=20\times BS_{S}\)

\(Df\) Damagefactor
\(Bf\) Bulletfactor
\(DS\) Bullet Strength
\(BS\) Body Strength
\(BS_{S}\) Body Strength Spike
Angular velocity \(\omega\) \([\frac{1}{s}]\)

\(\omega=\frac{2\times\pi}{t_{r}}=1\)
with \(t_{r}=2\times\pi\)

\(\pi\) 3,14159265...
\(t_{r}\) Time for one Rotation
Bullet speed \(V_{b}\) \([\frac{gu}{s}]\)

\(V_{b}=\frac{\rho_{V_{b}}}{t_{b}}\)

for drone classes :

\(V_{b}=\rho\times\omega\)

\(\rho_{V_{b}}\) Distance an Bullet can fly before Decay
\(t_{b}\) Time until Decay
\(\rho\) Radius
\(\omega\) Angular Velocity
Area damage density u \([\frac{S}{gu^{2}\times s}]\)

\(u=\frac{DPS}{a}=\frac{180\times D_{b}\times BR}{\arcsin\left(\frac{h}{V_{b}\times t_{b}}\right)\times \pi\times\left({V_{b}\times t_{b}}\right)^{2}}\)

\(DPS\) Damage per Second
\(a\) Area
\(D_{b}\) Durability Bullet
\(BR\) Reload
\(h\) Height of the Triangle
\(V_{b}\) Bullet Speed
\(t_{b}\) Time until Decay
\(\pi\) 3,14159265...
Scattering rate w \([1]\)

\(w=\frac{h}{\rho_{v_{b}}}\)

\(h\) Height of the Triangle
\(\rho_{V_{b}}\) Distance an Bullet can fly before Decay
Probability to get target by a dominator \(p\left(D\right)\) \([1]\)

\(p\left(D\right)=\frac{\left(\rho_{a}-S_{n}\right)}{\left(N\times \rho_{a}-\sum_1^NS_{i}\right)}\)

quadratic assumption :

\(p\left(D\right)=\frac{\left(\rho_{a}-S_{n}\right)^{2}}{\left(N\times \rho_{a}^{2}+\sum_1^NS_i^2-2\times \rho_{a}\times \sum_1^NS_i\right)}\)

\(\rho_{a}\) Activition Radius Dominator
\(S_{n}\) Distance to the Dominator
\(N\) Number Players closer to the Dominator than \(\rho_{a}\)
Knockback KB \([gu]\)

\(KB=L\times Kf\times DS=\lfloor\frac{BP}{DPL''}\rfloor\times Kf\times DS\)

for Drones/Tank Bodies :

\(\frac{KB}{L}\) = constant for all dm/bd

\(L\) Number of Loops
\(Kf\) Knockbackfactor
\(DS\) Bullet Strength
\(BP\) Bullet Health
\(DPL''\) Damage per Loop Opponent
\(dm\) Bullet Damage Stat
\(bd\) Body Damage Stat
Size \(Z [gu]\)

\(Z=2\times1,01^{lvl-1}\leftarrow\) credits to Biohazard-Flames

\(lvl\) Level
Field of view FOV \([gu^{2}]\)

\(FOV=\frac{1}{Ff^{2}}\times\left(\frac{1920}{0,55}\times\sqrt{1,01}^{lvl-1}\right)\times\left(\frac{1080}{0,55}\times\sqrt{1,01}^{lvl-1}\right)
=\frac{1}{Ff^{2}}\times\frac{1920\times1080}{0,55^{2}}\times1,01^{lvl-1}\leftarrow\) credits to MegaScythe

\(Ff\) Fieldfactor
\(1920\times1080\) Resolution of the screen
\(0,55\) Conversionfactor between Pixel and du
\(lvl\) Level
Arena Length AL \([gu]\)

\(AL=\lfloor\sqrt{N_{P}}\times50\rfloor\)

\(N_{P}\) Number of Players
\(\lfloor...\rfloor\) rounded down to the nearest even integer
Shape Count \(N_{SH}\) \([1]\)

\(N_{SH}=\lfloor{12,5\times N_{P}}\rfloor\)

\(N_{P}\) Number of Players

Unit System of Diep:
Unit of time \(t : Second [s]\)
Unit of loop \(L : Loop [x] = \frac{1}{25} s\)
Unit of distance
(squares on the grid)
\(s : Grid Units [gu]; Diep Units [du] = \frac{1}{50} gu\)
Unit of general health
can be MH or BP
\(GH : Health Points [HP]\)
Unit of max health \(MH : Health Points [HP]\)
Unit of penetration \(BP : Health Points [HP]\)
Unit of Durability
(equal to 1 hit from a Square)
\(D : Squares [S]\)
\([1]\) means it's dimensionless

Tanks Bulletfactor
Tanks Bulletfactor
Destroyer, Annihilator, Hybrid (Bullet) 6
Mega Trapper 5,12
Rocketeer (Large Bullet) 5
Skimmer (Large Bullet) 3
Factory (Drone) 2,8
Trapper, Tri-Trapper, Overtrapper (Trap), Gunner Trapper (Trap), Auto Trapper (Trap) 2
Overlord, Overseer, Manager 1,4
Basic Tank, Flank Guard, Sniper, Assasin, Ranger, Stalker, Tri-Angle (Front Bullet), Booster (Front Bullet), Fighter (Front Bullet), Spread Shot (Large Bullet) 1
Hybrid (Drone), Overtrapper (Drone) 0,98
Necromancer 0,84
Fighter (Side Bullet) 0,8
Quad Tank, Hunter, Predator 0,75
Machine Gun, Triple Shot, Sprayer (Large Bullet) 0,7
Octo Tank 0,65
Spread Shot (Small Bullet) 0,6
Twin 0,585
Penta Shot 0,55
Twin Flank, Triple Twin, Gunner Trapper (Bullet) 0,5
Triplet 0,42
Auto 3, Auto 5 0,4
Auto Gunner (Auto Bullet), Auto Trapper (Auto Bullet), Auto Smasher (Auto Bullet) 0,3
Gunner, Auto Gunner (Manual Bullet) 0,225
Streamliner, Tri-Angle (Rear Bullet), Booster (Rear Bullet), Fighter (Rear Bullet) 0,2
Skimmer (Small Bullet), Rocketeer (Small Bullet) 0,18
Factory (Drone Bullet) 0,16
Battleship 0,15
Sprayer (Small Bullet) 0,1

credits to lyw318

Tanks Damagefactor
Tanks Damagefactor Damage per Loop (1 dm)
Destroyer, Annihilator, Hybrid (Bullet) 7,5 30 HP
Necromancer 4,2 16,8 HP
Mega Trapper 4 16 HP
Basic Tank, Flank Guard, Sniper, Assasin, Ranger, Stalker, Tri-Angle (Front Bullet), Booster (Front Bullet), Fighter (Front Bullet), Spread Shot (Large Bullet), Trapper, Tri-Trapper, Overtrapper (Trap), Gunner Trapper (Trap), Auto Trapper (Trap), Skimmer (Large Bullet), Rocketeer (Large Bullet) 2,5 10 HP
Fighter (Side Bullet) 2 8 HP
Quad Tank, Hunter, Predator 1,875 7,5 HP
Machine Gun, Triple Shot, Sprayer (Large Bullet), Overlord, Overseer, Manager, Factory (Drone), Hybrid (Drone), Overtrapper (Drone) 1,75 7 HP
Octo Tank, Twin 1,625 6,5 HP
Triplet, Spread Shot (Small Bullet), Skimmer (Small Bullet), Rocketeer (Small Bullet) 1,5 6 HP
Penta Shot 1,375 5,5 HP
Twin Flank, Triple Twin, Gunner Trapper (Bullet), Gunner, Auto Gunner (Manual Bullet) 1,25 5 HP
Auto 3, Auto 5, Factory (Drone Bullet) 1 4 HP
Auto Gunner (Auto Bullet), Auto Trapper (Auto Bullet), Auto Smasher (Auto Bullet) 0,75 3 HP
Streamliner, Tri-Angle (Rear Bullet), Booster (Rear Bullet), Fighter (Rear Bullet) 0,5 2 HP
Battleship 0,375 1,5 HP
Sprayer (Small Bullet) 0,25 1 HP
Tanks Penetrationfactor
Tanks Penetrationfactor Bullet Health (0 bp)
Rocketeer (Large Bullet) 2 40 HP
Factory (Drone) 1,6 32 HP
Mega Trapper 1,28 25,6 HP
Skimmer (Large Bullet) 1,2 24 HP
Annihilator, Hybrid (Bullet), Destroyer, Trapper, Tri-Trapper, Overtrapper (Trap), Gunnertrapper (Trap), Auto Trapper (Trap), Overlord, Overseer, Manager 0,8 16 HP
Hybrid (Drone), Overtrapper (Drone) 0,56 11,2 HP
Basic Tank, Flank Guard, Machine Gun, Sniper, Assassin, Ranger, Stalker, Tri-Angle, Booster, Fighter, Spread Shot,Quad Tank, Hunter, Predator, Octo Tank, Penta Shot, Twin Flank, Triple Twin, Gunner Trapper (Bullet), Triple Shot, Auto 3, Auto 5, Streamliner, Battleship, Sprayer, Auto Gunner (Auto Bullet), Auto Gunner (Auto Bullet), Auto Smasher (Auto Bullet) 0,4 8 HP
Twin 0,36 7,2 HP
Triplet 0,28 5,6 HP
Necromancer 0,2 4 HP
Gunner, Auto Gunner (Manuell Bullet) 0,18 3,6 HP
Factory (Drone Bullet) 0,16 3,2 HP
Rocketeer (Small Bullet), Skimmer (Small Bullet) 0,12 2,4 HP
Tanks Knockbackfactor
Tanks Knockbackfactor Knockback per Loop (1 dm)
Smasher, Landmine, Spike, Auto Smasher (Body), All Tank Bodies - 1,6 gu
Overseer, Overlord, Manager, Necromancer, Factory (Drone), Hybrid (Drone), Overtrapper (Drone) - 0,8 gu
Mega Trapper 1,0666... 1,0666... gu
Basic Tank, Flank Guard, Sniper, Assasin, Ranger, Stalker, Tri-Angle (Front Bullet), Booster (Front Bullet), Fighter (Front Bullet), Spread Shot (Large Bullet), Trapper, Tri-Trapper, Overtrapper (Trap), Gunner Trapper (Trap), Auto Trapper (Trap) 0,666... 0,666... gu
Fighter (Side Bullet) 0,5333... 0,5333... gu
Quad Tank, Hunter, Predator 0,5 0,5 gu
Machine Gun, Triple Shot, Sprayer (Large Bullet) 0,4666... 0,4666... gu
Octo Tank, Twin 0,4333... 0,4333... gu
Triplet, Spread Shot (Small Bullet), Skimmer (Small Bullet), Rocketeer (Small Bullet) 0,4 0,4 gu
Penta Shot 0,3666... 0,3666... gu
Twin Flank, Triple Twin, Gunner Trapper (Bullet), 0,333... 0,333... gu
Auto 3, Auto 5, Factory (Drone Bullet) 0,2666... 0,2666... gu
Auto Gunner (Auto Bullet), Auto Trapper (Auto Bullet), Auto Smasher (Auto Bullet), Destroyer, Hybrid (Bullet) 0,2 0,2 gu
Streamliner, Tri-Angle (Rear Bullet), Booster (Rear Bullet), Fighter (Rear Bullet) 0,1333... 0,1333... gu
Battleship, Annihilator 0,1 0,1 gu
Sprayer (Small Bullet), Skimmer (Large Bullet), Rocketeer (Large Bullet) 0,0666... 0,0666... gu

Tanks Fieldfactor
Tanks Fieldfactor
Ranger 0,7
Assassin, Stalker 0,8
Hunter, Streamliner, Predator 0,85
Sniper, Overseer, Overlord, Necromancer, Manager, Overtrapper, Battleship, Factory, Trapper, Tri-Trapper, Gunner Trapper, Mega Trapper, Overtrapper, Auto Trapper, Smasher, Landmine, Auto Smasher, Spike, Skimmer, Rocketeer 0,9
All other tanks 1

Tanks Recoil
Tanks Recoil
Annihilator 6,8 gu
Destroyer, Hybrid (Bullet) 6 gu
Sniper, Assasin, Ranger, Stalker, Skimmer (Large Bullet), Rocketeer (Large Bullet) 1,2 gu
Fighter (Rear Bullet), Booster (Inner Rear Bullet), Tri-Angle (Rear Bullet) 1 gu
Basic, Machine Gun, Gunner Trapper (Trap/Bullet), Sprayer (Large Bullet), Manager, Factory (Drone), Overtrapper, Hybrid (Drone), Tri-Trapper, Mega Trapper, Auto Trapper (Trap), Factory (Drone Bullet) 0,4 gu
Twin 0,3 gu
Penta Shot 0,28 gu
Triplet 0,2 gu
Auto 3, Auto 5, Auto Smasher (Auto Bullet), Auto Gunner (Auto Bullet), Auto Trapper (Auto Bullet), Hunter, Predator 0,12 gu
Streamliner, Gunner, Auto Gunner (Manual Bullet), Tri-Angle (Front Bullet), Fighter (Front Bullet), Booster (Front Bullet), Booster (Outer Rare Bullet) 0,08 gu
Spread Shot (Large/Small Bullet) 0,04 gu
Sprayer (Small Bullet) 0 gu

Tanks Technical Reload Time
Tanks Technical Reload Time Reload Time (0 br)
Rocketeer (Small Bullets) 3 x 0,12 s
Skimmer (Small Bullets) 5,4 x 0,24 s
Machine Gun, Sprayer (Large Bullet) 7,5 x 0,32 s
Basic, Twin, Flank Guard, Triple Shot, Twin Flank, Octo Tank, Quad Tank, Tri-Angle, Booster, Fighter (Front/Rear Bullet), Auto 3, Auto 5, Triple Twin, Penta Shot, Triplet, Gunner, Auto Gunner (Manual/Auto Bullet), Streamliner, Gunner Trapper (Bullets), Auto Smasher (Auto Bullet), Auto Trapper (Auto Bullet), Battleship, Factory (Drones), Sprayer (Small Bullet) 15 x 0,6 s
Sniper, Fighter (Side Bullet), Trapper, Tri-Trapper, Auto Trapper (Trap) , Overtrapper (Trap) 22,5 x 0,92 s
Spread Shot, Assasin, Ranger, Stalker 30 x 1,2 s
Hunter 37,5 x 1,52 s
Manager, Factory (Barrel), Gunner Trapper (Trap), Predator 45 x 1,8 s
Mega Trapper 49,5 x 2 s
Destroyer, Hybrid, Annihilator, Skimmer (Large Bullet), Rocketeer (Large Bullet) 59,9 x 2,4 s
Overlord, Overseer, Hybrid (Drone), Overtrapper (Drone) 90 x 3,6 s

special thanks to die ♤ bitch, you die ♤ sorry, m♤utarde, ♤ la Faucheuse ~ parangon ♤, Licht ♤, Cx, lyw318, MegaScythe and Biohazard-Flames for supporting, helping and assisting

If you have further questions or want to make suggestions about the physics you can write me an email to aznatf@spade- squad.com or contact me in the diep.io subreddit /u/aznatf