Formulae

Note: Page under construction. Feel free to add any additional information. If you don't know how to use the math mode, just put the raw, I (#Sacrezar#9802)'ll modify it.

XP required per level

$XP_{Class}\quad \ \ =\left\lfloor \left(15+{lvl}^{1.9}+11\times lvl\right)\times \left(1.208-\min \left\{0.164,{\frac {0.215\times {lvl}}{{lvl}+100}}\right\}\right)^{lvl}-15\right\rceil$

$XP_{OtherSkills}\ =\left\lfloor \left(15+{lvl}^{2}+13\times lvl\right)\times \left(1.225-\min \left\{0.18,{\frac {0.135\times {lvl}}{{lvl}+50}}\right\}\right)^{lvl}-30\right\rfloor$

$XP_{Smithing}\ =\left\lfloor \left(15+{lvl}^{2}+13\times lvl\right)\times \left(1.225-\min \left\{0.164,{\frac {0.135\times {lvl}}{{lvl}+50}}\right\}\right)^{lvl}-26\right\rfloor$

${\rm {XP}}_{Construction\left(Lv<71\right)}=\left(\left(10+{\rm {lvl}}^{2.81}+4\ast l\ v\ l\right)\ast {\frac {1.117-\left(0.135\ast l\ v\ l\right)}{lvl\ +\ 5}}^{lvl}-6\right)\ast {\frac {1\ +\ {\rm {lvl}}^{1.72}}{300}}$

${\rm {XP}}_{Construction\left(Lv>71\right)}=\left(\left(10+{\rm {lvl}}^{2.81}+4\ast l\ v\ l\right)\ast {\frac {1.003}{2.35}}^{lvl}-6\right)\ast {\frac {1\ +\ {\rm {lvl}}^{1.72}}{300}}$

${\rm {XP}}_{Worship}=\left(15+{\rm {lvl}}^{1.3}+6\ast l\ v\ l\right)\ast \left(1.17-Min\left\{0.07,\ {\frac {0.135\ *\ lvl}{lvl\ +\ 50}}\right\}\right)^{lvl}-26$

${\mathrm {XP} }_{Breeding}=\ \left(10\ +\ {\mathrm {lvl} }^{1.9}\ +\ 10\ \ast \ lvl\right)\ \ast \ {1.11}^{lvl}$

${\mathrm {XP} }_{Laboratory\left(Lv<5\right)}=\ 6.4\ \ast \ lvl\ \ast \ {1.6}^{lvl}$

${\mathrm {XP} }_{Laboratory\left(Lv>5\right)}=\left(10+{\rm {lvl}}^{1.3}+10\ast l\ v\ l\right)\ast {1.11}^{lvl}$

${\mathrm {XP} }_{Sailing}=\left(10+{\rm {lvl}}^{1.6}+5\ast l\ v\ l\right)\ast {1.08}^{lvl}$

${\mathrm {XP} }_{Divinity}=\left(9+{\rm {lvl}}^{1.4}+3\ast l\ v\ l\right)\ast \left(1.1\ -\ {\frac {0.08\ *\ lvl}{lvl\ +\ 20}}\right)^{lvl}$

${\mathrm {XP} }_{Gaming}=\left(10+{\rm {lvl}}^{1.6}+3\ast l\ v\ l\right)\ast {1.13}^{lvl}+{1.13}^{Max\left(0,lvl-20\right)}$

Skilling

Mining

${\rm {MiningSpeed}}_{3>MiningSpeed}=Max\left({\frac {\left(5.7+\left(4-MiningSpeed\right)^{2.2}-\left({\frac {0.9*{\rm {MiningLv}}^{0.5}}{{\rm {MiningLv}}^{0.5}+250}}+{\frac {0.6*MiningLv}{MiningLv+40}}\right)\right)}{1+{\frac {MineSpdFood+MineSpdCards+ActionFrenzyTalent+MineSpdEquip+Round\left({\frac {EmeraldNavetteJewel}{20}}\right)}{100}}}},0.57\right)$

${\rm {MiningSpeed}}_{3<MiningSpeed}=Max\left({\frac {\left(5.7-{0.2*MiningSpeed}^{1.3}+\left({\frac {0.9*{\rm {MiningLv}}^{0.5}}{{\rm {MiningLv}}^{0.5}+250}}+{\frac {0.6*MiningLv}{MiningLv+40}}\right)\right)}{1+{\frac {MineSpdFood+MineSpdCards+ActionFrenzyTalent+MineSpdEquip+Round\left({\frac {EmeraldNavetteJewel}{20}}\right)}{100}}}},0.57\right)$

Choppin

${\rm {ChoppinSpeed}}_{3>ChoppinSpeed}=Max\left({\frac {\left(5.7+\left(4-ChoppinSpeed\right)^{2.2}-\left({\frac {0.9*{\rm {ChoppinLv}}^{0.5}}{{\rm {ChoppinLv}}^{0.5}+250}}+{\frac {0.6*ChoppinLv}{ChoppinLv+40}}\right)\right)}{1+{\frac {ChopSpdFood+ChopSpdFood+ActionFrenzyTalent+ChopSpdEquip+Round\left({\frac {EmeraldNavetteJewel}{20}}\right)}{100}}}},0.57\right)$

${\rm {ChoppinSpeed}}_{3<ChoppinSpeed}=Max\left({\frac {\left(5.7-0.2*{\rm {ChoppinSpeed}}^{1.3}+\left({\frac {0.9*{\rm {ChoppinLv}}^{0.5}}{{\rm {ChoppinLv}}^{0.5}+250}}+{\frac {0.6*ChoppinLv}{ChoppinLv+40}}\right)\right)}{1+{\frac {ChopSpdFood+ChopSpdCards+ActionFrenzyTalent+ChopSpdEquip+Round\left({\frac {EmeraldNavetteJewel}{20}}\right)}{100}}}},0.57\right)$

Fishing

${\rm {FishingSPD}}_{3>FishingSpeed}=5.7-\left(Min\left(\left({\frac {FishingEfficiency}{FishingEfficiency+300}}\right)\ast 1.7,0.8\right)+Min\left(\left({\frac {FishingEfficiency}{FishingEfficiency+1000}}\right)\ast 2,1.7\right)\right)$

${\rm {FishingSpeed}}_{3>FishingSpeed}=Max\left(FishingSPD+\left(4-FishingSpeed\right)^{2.2}-\left({\frac {0.9*{\rm {FishingLv}}^{0.5}}{{\rm {FishingLv}}^{0.5}+250}}+{\frac {0.6*FishingLv}{FishingLv+40}}\right),0.57\right)\ast$ $\left({\frac {15}{1+{\frac {FishSpdFood+ToolkitSpd+FishSpdCards+ActionFrenzyTalent+FishSpdEquip+Round\left({\frac {EmeraldNavetteJewel}{20}}\right)}{100}}}}\right)$

${\rm {FishingSpeed}}_{3<FishingSpeed}=Max\left(FishingSPD-0.2\ast {\rm {FishingSpeed}}^{1.3}+\left({\frac {0.9*{\rm {FishingLv}}^{0.5}}{{\rm {FishingLv}}^{0.5}+250}}+{\frac {0.6*FishingLv}{FishingLv+40}}\right),0.57\right)\ast$ $\left({\frac {15}{1+{\frac {FishSpdFood+ToolkitSpd+FishSpdCards+ActionFrenzyTalent+FishSpdEquip+Round\left({\frac {EmeraldNavetteJewel}{20}}\right)}{100}}}}\right)$

Catching

${\rm {CatchingSpeed}}_{3>CatchingSpeed}=Max\left(5.7+\left(4-CatchingSpeed\right)^{2.2}-\left({\frac {0.9*{\rm {CatchingLv}}^{0.5}}{{\rm {CatchingLv}}^{0.5}+250}}+{\frac {0.6*CatchingLv}{CatchingLv+40}}\right),0.57\right)\ast$ $\left({\frac {2}{1+{\frac {CatchSpdFood+CatchSpdCards+ActionFrenzyTalent+Min\left(5,FruitSaladAchieve\right)+CatchSpdEquip+Round\left({\frac {EmeraldNavetteJewel}{20}}\right)}{100}}}}\right)$

Cooking

${\begin{matrix}{\text{luckVAL = [1, 0.2, 0.1, 0.05, 0.02, 0.01, 0.004, 0.001, 0.0005, 0.0003]}}\\{\textbf {NewMealChance}}=\\{\textbf {EachFromtheRight}}{\begin{pmatrix}{\text{Owned}}&=&{\text{luckVAL}}\\{\text{New}}&=&{\text{luckVAL}}*\left(1+{\frac {5*{\mathit {StationLuckVal}}^{0.85}}{100}}\right)*1.5^{FireLevel}\end{pmatrix}}\end{matrix}}$
luckVAL is accessed by the index of the meal in the list. Example: The 5th meal has a base luckVAL of 0.02.

Actual luck depends on the previous (to the right) meal's failure. So the second in a list of 5 would need meals 3, 4, and 5 to all fail and then it's own to succeed. Without fire level or luck factoring in that would be:

(1-0.02) * (1-0.05) * (1-0.1) * 0.2 = 16.758%

Fighting formula

Damage done

${Damage}_{max}=$ [(1/9)*(WP^2)+Flat_Dmg_bonus]*Damage_%

${Damage}_{min}={Damage}_{max}\times Mastery$

$Mastery\ =\ Min\left\{0.8,0.35-{\frac {MasteryUpTalent}{100}}+LilBigDamageBubble+SandGiantCard+MasteryUpTalent+EfauntRibcageShirt+ChizoarBodyplateShirt+ChizoarScaledLeggingsPants+ChizoarWalkersShoes\right\}$

Crit Chance

${\rm {AgilityCritChance}}_{1000\ >\ AGI}\ =\ {\frac {\left(AGI\ +\ 1\right)^{0.37}\ -\ 1}{40}}$

${\rm {AgilityCritChance}}_{1000\ <\ AGI}\ =\ \left({\frac {AGI\ -\ 1000}{AGI\ +\ 2500}}\right)\ \ast \ 0.5\ +\ 0.255$

${Crit\ Chance}$ $=5+HyperionNebulaCardset+RatCard+XyloboneCard+$ $FlombeigeCard+MegaCritTalent+EfauntTrunculusRing+$ $FrozenTartChainKeychain+MegalodonTrophy+EclecticOrdealFisticuffs+$ $CircularCriticalsPrayer+MuttonMeal+BeholderStatue+$ $TheFallenTitanStarSign+ISeeYouTalent+MegaCritTalent+DungeonWallopAchievement+$ $CivilWarShipment+OveraccurateCritTalent+\left(\left({\frac {AgilityCritChance}{2.3}}\right)\ast 100+CheapShotBubble\right)$

Crit Damage

${\rm {StrengthCritDamage}}_{1000\ >\ STR}\ =\ {\frac {\left(STR\ +\ 1\right)^{0.37}-\ 1}{40}}$

${\rm {StrengthCritDamage}}_{1000\ <\ STR}\ =\ \left({\frac {STR\ -\ 1000}{STR\ +\ 2500}}\right)\ \ast \ 0.5\ +\ 0.255$

${Crit\ Damage}$ $=\ 1.2\ +\ KnucklebusterTalent\ +\ KachowStatue\ +\ FarsightTalent\ +\ KapowStamp\ +$ $\ {\frac {100\ *\ StrengthCritDamage}{1.8}}\ +\ BappityBoopityBubble\ +\ MashedPotatoCard\ +$ $\ ThermisterCard\ +\ EggCapsuleCard\ -\ CircularCriticalsPrayer\ +\ CritikillTalent\ +$ $\ AdornmentoftheHighPriestHelmet\ +\ TheIceBreakerSpear\ +\ DeuscytheSpear\ +\ BlizzardBow\ +$ $\ BlackholeBow\ +\ SprigglyStormWand\ +\ GreyGatsbyWand\ +\ DivineInterventionTalent$

Boss Damage

${\rm {WisdomBossDamageMulti}}_{1000\ >\ WIS}\ =\ {\frac {\left(WIS\ +\ 1\right)^{0.37}-\ 1}{40}}$

${\rm {WisdomBossDamageMulti}}_{1000\ <\ WIS}\ =\ \left({\frac {STR\ -\ 1000}{STR\ +\ 2500}}\right)\ \ast \ 0.5\ +\ 0.255$

Attack Speed

${\rm {SPD}}_{25>Class\ Lv}\ =\ \left({\frac {75-lvl}{25}}\right)\ast 1.8\$

${Wait\ Time\ Speed}_{25>Class\ Lv}=Min\left(13,SPD+AttackSpeed\right)$

${Wait\ Time\ Speed}_{25<Class\ Lv}=Min\left(13,2+AttackSpeed\right)$

$Fisticuffs\ N\ Spear={\frac {\frac {\left(0.6\ +\ \left({\frac {10-WaitTimeSpeed}{5}}\right)+0.35\right)}{\left(MidnightStopwatchRing+BalloonDogChain+CauliflowerMeal+PotatoChip+HyperSwiftBubble+DeathsStorageUnitShipment\right)}}{100}}+1$

$Bow={\frac {\frac {0.7\ +\ \left({\frac {10-WaitTimeSpeed}{5}}\right)+0.1}{MidnightStopwatchRing+BalloonDogChain+CauliflowerMeal+PotatoChip+HyperSwiftBubble+DeathsStorageUnitShipment}}{100}}+1$

$Wand={\frac {\frac {0.16\ +\ \left({\frac {10-WaitTimeSpeed}{5}}\right)+1.2}{SpeedyBookTalentBuff+MidnightStopwatchRing+BalloonDogChain+CauliflowerMeal+PotatoChip+HyperSwiftBubble+DeathsStorageUnitShipment}}{100}}+1$

$AFKAttackSpeed=Max\left(0.1,{\frac {\frac {1\ +\ \left({\frac {10-WaitTimeSpeed}{5}}\right)}{SpeedyBookTalentBuff+MidnightStopwatchRing+BalloonDogChain+CauliflowerMeal+PotatoChip+HyperSwiftBubble+DeathsStorageUnitShipment}}{100}}+1\right)$

Food Consumption

Healing Food

${Consumption}_{Grassland}=$

${Consumption}_{Desert}=$

${Consumption}_{Tundra}=$

Damage taken per hit

$Damage=\left\lceil {\frac {{attack}_{enemy}-2.5\times {defense}^{0.8}}{\max \left\{1,1+{\frac {{defense}^{1.5}}{100}}\times {\frac {defense}{\max \left\{1,{attack}_{enemy}\right\}}}\right\}}}\right\rceil$

Alchemy

P2W Tab

Cauldrons

$regen_{\%}={\frac {16+0.5\times (regenLvl-1)}{15}}\times regenLvl\times 3$

$newBubble=1+{\frac {newBubbleLvl\times 2.5}{newBubbleLvl+100}}$

$boostReqLow_{\%}=70\times {\frac {boostLvl}{100+boostLvl}}$

Liquid

$regen_{\%}=400\times {\frac {regenLvl}{100+regenLvl}}$ $cap=capLvl$

Vials

$cap=capLvl$

$rng=250\times {\frac {rngLvl}{100+rngLvl}}$

Player

$AlchSpeed_{\%}=35\times {\frac {AlchSpeedLvl}{100+AlchSpeedLvl}}$

$ExtraXP_{\%}={\frac {11+0.5\times (ExtraXPLvl-1)}{10}}\times ExtraXPLvl$

Liquid

$liquid_{/hour}=\left(1+{\frac {decant_{\%}+RLP2W_{\%}+vial_{\%}}{100}}\right)\times \left(1+{\frac {stamp_{\%}+\sum \left((alchLvl*2+4)^{0.65}\right)}{100}}\right)$

• $RLP2W_{\%}$ is P2W Liquid Regen

Multiply this by 1.5 if you have the corresponding gem upgrade.

Misc

Drop Rate

${\rm {DropRateLuck}}_{1000>LUK}={\frac {\left(LUK+1\right)^{0.37}-1}{40}}$

${\rm {DropRateLuck}}_{1000<LUK}=\left({\frac {LUK-1000}{LUK+2500}}\right)\ast 0.5+0.297$

$DropRate={\mathrm {IslandExplorerPack} }_{1.2}\ast \left(1.4*DropRateLuck+{\frac {FlatDropRateSources+BossBattleSpilloverTalent*WeeklyBossesDefeated+5*FauxJewelsDreamLevels}{100}}+1\right)$ $\ast \left(1+\left({\frac {ArchlordOfThePiratesTalentLevel*6}{ArchlordOfThePiratesTalentLevel+150}}\right)*LOG10\left({\frac {PlunderousMobKills}{100}}\right)\right)$

${\rm {DropRate}}_{Grounded\ Processor\ Nanochip}=Min\left(5,DropRate+{\frac {60}{100}}\right)$

Teleportation cap

${TP}_{cap}=21(1+n)$

Where 'n' is the number of time you bought Daily Teleports.

Statues

$Cost=\left\lfloor lvl^{1.17}\times 1.35^{\frac {lvl}{10}}+1\right\rceil$

$Bonus=\left\lfloor Base\times lvl\right\rceil$

Stamps

$baseCost_{Coin}=Price_{base}\times (1-{\frac {bribe}{100}})$

As of v1.14, the bribe effect is 8%, not 5%.

${Cost}_{Coin}=\left(1-{\frac {vial_{\%}}{100}}\right)\times \left\lfloor baseCost_{Coin}\times \left(i_{10}-\left({\frac {lvl}{lvl+5*lvlRange}}\times 0.25\right)\right)^{lvl\times {\frac {10}{lvlRange}}}\right\rfloor$

${Cost}_{Material}=\left\lfloor baseCost_{Material}\times {i_{8}}^{\left\lfloor {\frac {lvl}{lvlRange-1}}^{0.8}\right\rceil }\right\rfloor \times \max \left\{0.1,1-{\frac {vial_{\%}}{100}}\right\}$

• $vial_{\%}$ is the Blue Flav vial effect.
• $lvlRange$ is the number of time you can lvl up a stamp before having to pay using materials.
• $i_{8}$ and $i_{10}$ are value you can find in the code or in the wiki, look for data-i in the .stampdiv of the stamp you want to know about.

Worship

w = ((5+highest wave)/10)^2.6

f= Food bonus

Souls from Totem = 5(1+Bonus souls on map)*w*f

Gaming

$AmountOfMails=1+Floor\left(1+random\left(0,1\right)+{\frac {SnailLvl}{100}}\right)$

Functions

$addLower=t+i\ast \left(n+l\right)$

$decay={\frac {\left(t\ast n\right)}{\left(n+i\right)}}$

$decayLower={\frac {\left(t\ast \left(n+l\right)\right)}{\left(n+l+i\right)}}-{\frac {\left(t\ast n\right)}{\left(n+i\right)}}$

$decayMulti=l+{\frac {\left(t\ast n\right)}{\left(n+i\right)}}$

$addLower=t+i\ast \left(n+l\right)$