# Adventure Quest Game Formulae Master List

Adventure Quest Game Formulae Master List by Kaelin

Notes

1) Symbol Key:

^ means ‘to the power of’. So 10^3 = 1000.
>= means ‘greater than or equal to’.
<= means ‘less than or equal to’.

2) Order of Operations:

As in all mathematics, expressions are simplified in the order below.
[a] Parentheses: Anything inside parentheses takes priority. When there are multiple layers of parentheses, simplify the innermost layers first.
[b] Exponents: Exponents come next. Work left to right.
[c] Multiplication and Division: Both of these operations are done next. Work left to right.
[d] Addition and Subtraction: Both of these operations are last. Work left to right.

Example:
3 – 4 * (5 + 3 ^ 3) / 8
= 3 – 4 * (5 + 27) / 8 = 3 – 4 * (32) / 8 = 3 – 4 * 32 / 8
= 3 – 128 / 8 = 3 – 16
= -13

3) Rounding:

No colored brackets = Rounding not required or undetermined
[ ]” = Round off the contents in the brackets to the nearest integer.
[ ]” = Round down the contents in the brackets to the nearest integer.
[ ]” = Round up the contents in the brackets to the nearest integer.

4) Taking Nemesis’ Condemnation as an example.

Base Damage = 15
Max Damage = 29
Random Damage = Max Damage – Base Damage = 14

Thanks to .*. .*. .*. for the updated “Nemesis” weapon information.

[1] Level/Exp Related Formula
[2] Stat Damage Bonus
[3] Stat Bonus to Hit
[4] Blocking Ability
[5] HP & MP Formulae
[6] Treasure Chest Size
[7] Who Strikes First?
[8] Special Charisma Related Info
[9] Cost of Training Stats
[10] Monster Encounter Levels
[11] Monster Scaling
[12] Hit or Miss? (Accuracy Formulas)
[13] Calculating Average Damage Per Turn
[14] Potion Recovery
[15] Stat Rolls
[16] Monster Pack EXP/Gold
[17] EXP/Gold Cap
[18] Status Conditions
[19] Skill Points Formulae
[20] Notable Post-Sweep Equipment Standards
[21] Gold from Ballyhoo per Run
[22] House Value

[1] Level Related Formula

I = Initial level (current level), F = Final Level (the level you plan to reach) , E = Exp

No. of Available Stat Points = I*5

Total Exp to Level Up:

If level <= 102: E = 10*[11*(1.1^I)]
If level >= 103: E = 2000000

Cumulative Exp to Get from Level 0 to F:

If level <= 103 (approximate): E = 1100*(1.1^F – 1)
If level >= 104: E = (F – 103)*2000000 + 20175090

Cumulative Exp to Get from Level I to F = [Cum. Exp LEVEL 0->F] – [Cum. Exp LEVEL 0->I]

Here are (updated) values for level up in chart form:
http://img219.imageshack.us/img219/7949/xpchart136.jpg

[2] Stat Damage Bonus (Per 100% Stat Bonus)

Stat Damage increases the damage an attacker does against a target. As presently implemented, Stat Damage only adds “random” (variable) damage and not “base” (guaranteed) damage. The increase to your damage can be as large the amount below (scaled by the target’s Resistance and the stat% of your attack) or as small as 0.

Core Stat Damage

Melee Weapon: STR/8
Ranged Weapon: STR/10 + DEX/40
Magic Weapon: INT*3/32
Melee Skill: STR/4
Ranged Skill: STR/5 + DEX/20
Magic Skill: INT*3/16
Spells: INT/4
Pets & Guests: CHA/15

All player attacks (Weapons, Skills, and Spells) have a 10% chance of increasing Stat Damage by LUK/2. On average, this bonus results in an increase of LUK/20. Pets and Guests do NOT receive this bonus.

Average Stat Damage, with Lucky Strikes Included

Melee Weapon: STR/8 + LUK/20
Ranged Weapon: STR/10 + DEX/40 + LUK/20
Magic Weapon: INT*3/32 + LUK/20
Melee Skill: STR/4 + LUK/20
Ranged Skill: STR/5 + DEX/20 + LUK/20
Magic Skill: INT*3/16 + LUK/20
Spells: INT/4 + LUK/20
Pets & Guests: CHA/15

A few skills and spells use different formulas for stat damage. Most notably, the Heal Wounds spell series uses END/4 instead of INT/4. Other than weapons that use their “special” attack every turn, most weapons do NOT take stat damage on their specials. In the future, players are expected to get Lucky Strike stat damage on their special attacks. In this event, the stat multiplier will be the weapon’s built-in Special Lucky Strike value.

Lucky Strike information thanks to Westwind and Aelthai.

[3] Stat Bonuses to Hit

Stat Bonus to Hit adds to the likelihood the attacker’s hit lands against a target. The increase will not guarantee that you will land more hits, but the chance of any attack landing will improve accordingly.

Melee Weapon/Skill: [STR/16 + DEX/16 + LUK/20]
Ranged Weapon/Skill: [DEX/8 + LUK/20]
Magic Weapon/Skill: [INT/16 + DEX/16 + LUK/20]
Spells: [INT/16 + DEX/16 + LUK/20]
Pets & Guests: [CHA*7/60]

A few skills and spells use different formulas for stat bonus to hit. Other than weapons that use their “special” attack every turn, most weapons do not take stat bonus to hit on their specials.

[4] Blocking Ability

Blocking Bonus from Stats: [DEX/10 + LUK/20]

[5] HP & MP Formulae

L = Level, E = Endurance, I = Intellect

Player HP: [5*L + 0.05*L*E + E + 100]
Player MP: [5*L + 0.05*L*I + I + 100]

MonsterSetHP/MP = Each monster has a set amount of HP/MP they get as a “base” amount (Example: a Frogzard has a set HP of 30).

Monster HP = (MonsterSetHP + E*1.5) * Random Number Between 0.950-1.050
Monster MP = (MonsterSetHP + I*1.5) * Random Number Between 0.950-1.050

[6] Treasure Chest Size

* A Character < LEVEL 30 receives a Small Treasure Chest (25 Gold / 0 Exp), doesn’t fight a boss and doesn’t get a star (in the Crossroads Quest).

N = Char Level + LUK/5

N = 30 to 49: Treasure Chest (40 Gold / 0 Exp)
N = 50 to 64: Big Treasure Chest (76 gold / 25 Exp)
N = 65 to 84: Huge Treasure Chest (812 Gold / 125 Exp)
N = 85+: Treasure Hoard (1200 Gold / 250 Exp)

Thanks to Sora Aeragorn for correction. Thanks to Ward_Point for the updated information.

[7] Who Strikes First?

Player Luck = P
Monster Luck = M

First Strike Roll:

Player: X = Random # Roll (1,100) + P
Monster: Z = Random # Roll (1,100) + M

If X > Z, player goes first. If X = Z then there is a 50% chance of either player or monster going first. If Z >X, monster goes first.

Chance of First Strike Formula:

C = Chance Player Goes First

If P >= M + 100,
C = 1

Else If P <= M – 100,
C = 0

Else If P <= M,
C = (100 + P – M)^2 / 20000

Else If P > M,
C = 1 – (100 – P + M)^2 / 20000

All answers of C will be in decimal form. To change to a percentage, multiply by 100.

Thanks to Kalanyr, Yagno2000, and Captain Rhubarb.

[8] Special Charisma Related Info

Attack Rate = 67 + (CHA – Training Difficulty)/2

Formula from Chii via Sora Aeragorn.

Charisma Needed for 100% Attack Rate = 66 + Training Difficulty

Some pets have a negative Training Difficulty but will display a value of 0, so the true attack rate may be higher. “Friendly” pets will usually have a Training Difficulty of -66.

Some older pets will have attack rates specific to them.

[9] Cost of Training Stats

I = Initial Stat , F = Final Stat, TG = Total Gold needed to train

Cost to Raise by 5 Points: TG = 0.8*(I^2)

Cumulative Cost to Raise a Stat from Zero to F: TG = 0.8*{ (1/15)F^3 – (1/2)F^2 + (5/6)F }

Cumulative Cost to Raise a Stat from I to F: TG = 0.8*{ (1/15)[F^3-I^3] – (1/2)[F^2-I^2] + (5/6)[F-I] }

Thanks to CodeLabMaster for discovering how to simplify this formula.

Cost of Training Stats with Z-Tokens: = TG/20

Training Costs Spreadsheet (Thanks to lx4000):

[10] Monster Encounter Levels

Random Encounter Monster List

Single Monsters

Min Monster Level = [0.75*CharacterLevel] – 5
Max Monster Level = [1.15*CharacterLevel] + 1

Pack Monsters

Min Monster Level = [0.75 * (CharacterLevel – 20)]
Max Monster Level = CharacterLevel – 18

Note: Yonder lowers the Min Monster Level by 5 and increases the Max Monster Level by 5.

[11] Monster Scaling

Level = Your Level + 5
NOTE: Level-scaling maxes out at the original level * 2.5 . If the monster would be scaled above that point, then it is simply set at the maximum. This can set the level at a fraction.

Strength = (Current Level/Normal Level)*Normal Strength
Dexterity = (Current Level/Normal Level)*Normal Dexterity
Intellect = (Current Level/Normal Level)*Normal Intellect
Endurance = (Current Level/Normal Level)*Normal Endurance
Charisma = (Current Level/Normal Level)*Normal Charisma
Luck = (Current Level/Normal Level)*Normal Luck

[12] Hit or Miss? (Accuracy Formulas)

Attacker Value (weapon) = [Weapon BTH + Armor BTH + Stat BTH]
Attacker Value (weapon special) = [Weapon BTH + Weapon Special BtH]
Attacker Value (spells) = [Spell BTH + Stat BTH]
Attacker Value (pet/guest) = [Pet/Guest BtH + Stat BtH]
Roll = Rolls a Random # (1-100)
Defender Value = [Blocking Defense + Dex/10 + Luk/20]

If Attacker Value + Roll > Defender Value, then it hits. Otherwise it misses. Certain special actions, like healing spells, will always hit.

Chance to Hit

Chance to Hit = (100 + Attacker Value – Defender Value) / 100

Chance to Hit is in decimal form. It will always lie between 0 and 1 (inclusive).

Big thanks to Aelthai for rounding mechanics.

[13] Calculating Average Damage Per Turn

For the calculations below, convert all Resistance, Special Rate, hit rates, base%, random%, and stat% (include Special Lucky Strike%) into decimals.

Average Lucky Strike Stat = LUK/20

Normal Weapon Power = (Weapon Base) * (Armor Base) + (Weapon Random) * (Armor Random) / 2 + (Stat Damage) * (Armor Stat) / 2
Weapon Special Power = (Weapon Base) * (Special Base) + (Weapon Random) * (Special Random) / 2 + (Average Lucky Strike Stat) * (Special Lucky Strike) / 2

Average Weapon Damage = Resistance * [Weapon Hit Rate * (1 – Special Rate) * (Normal Weapon Power) + (Weapon Special Hit Rate) * (Special Rate) * (Weapon Special Power)]

Average Spell Damage = Resistance * (Hit Rate) * [Base + Random / 2 + (Stat Damage) * (Spell Stat) / 2]

Average Pet/Guest Damage = Resistance * (Hit Rate) * [Base + Random / 2 + (Stat Damage) * (Companion Stat) / 2]

Special Lucky Strikes are currently not enabled.

When calculating average damage for weapons with a 100% special rate, disregard Weapon Special Power. Just calculate Normal Weapon Power using the built-in Base/Random/Stat multipliers as the Armor Base/Random/Stat multipliers, and then calculate Average Weapon Damage using Special Rate = 0.

Besides weapons with a 100% special rate, a handful of older weapons deal stat damage on their special. For these weapons, add (Stat Damage) * (Weapon Stat) to the Weapon Special Power.

For player weapon and armor comparisons, Dev’s Weapons Spreadsheet is available.

For player spell comparisons, JMill’s Spell Comparison Spreadsheet is available.

For player pet comparisons, JMill’s Pets and Guests Spreadsheet is available.

Thanks to Everest for the updated damage comparison links.

[14] Potion Recovery

Health Potion Healing

HP recovered drinking one Health Potion = (50 + Level/3) to (100 + Level/3 + LUK/2 + END/2)
HP recovered drinking two Health Potions = (100 + Level/3) to (200 + Level/3 + LUK/2 + END/2)

Mana Potion Healing

MP recovered drinking one Mana Potion = (50 + Level/3) to (100 + Level/3 + LUK/2 + INT/2)
MP recovered drinking two Mana Potions = (100 + Level/3) to (200 + Level/3 + LUK/2 + INT/2)

[15] Stat Rolls

Roll: Rolls a Random # (1-100)
Bonus: A bonus added to the roll. Usually Bonus = Stat/5, where Stat is the value of the stat used for the roll.
Difficulty: The value the player must reach to win a roll

If Roll = 100, the roll instantly succeeds. If Roll = 1, the roll instantly fails.
Otherwise, if Roll + Bonus >= Difficulty, then the roll succeeds.
If the roll still has not succeeded, the roll will fail unless the player can defy the roll (see Roll Defiance below).

Probability of Success = 1.01 + Bonus – Difficulty.

Probability is in decimal form. 0.01 <= Probability <= 0.99 due to Instant Failures and Instant Successes when rolling 1 and 100.

Roll Defiance: If a stat roll neither succeeds nor instantly fails, a player may be allowed to pay SP to “defy” a stat roll. When available, the player must pay [0.3*Point] for each point the player fell short of the roll Difficulty. For example, a player that gets a Roll + Bonus of 84 against a Difficulty of 88 must pay a cost of [0.3*85] + [0.3*86] + [0.3*87] + [0.3*88] = 26 + 26 + 27 + 27 = 106 SP.

Fast Defiance Cost Formula = [0.15 * ((Difficulty + 2)^2 – (Roll + Bonus + 2)^2)]

If a player lacks the SP to defy the roll or declines to pay the cost, the roll will fail. If the player defies the roll, the player will win the stat roll and lose the required SP.

Note: The Fast Defiance Cost Formula will produce an error of 1 SP in 10% of possible outcomes.

[16] Monster Pack EXP/Gold

EXP = Normal EXP Amount * Number of Monsters * 1.5
Gold = Normal Gold Amount * Number of Monsters * 1.25
(10% X-Guardian boost added after multiplication)

[17] EXP/Gold Cap

Daily Exp Cap = (3300 * Your Character Level + 500)
Daily Gold Cap = (2000 * Your Character Level + 500)

X-Guardian Daily Exp Cap = (3300 * Your Character Level + 500) * 1.1
X-Guardian Daily Gold Cap = (2000 * Your Character Level + 500) * 1.1

Thanks to BlackAces/Dev/TCO for the updated caps.

[18] Status Conditions

Old Paralysis

Chance to Resist Paralysis = [END/2.5]

0 END = 0% chance of resisting
50 END = 20% chance of resisting
100 END = 40% chance of resisting
200 END = 80% chance of resisting

Newer equipment uses the new status effect system detailed below.

Status System Save Roll Formula

Major: (MajorInflictStatistic – MajorResistStatistic)/5, minimum -20, maximum +20
Level: (InflictLevelStatistic – ResistLevelStatistic)/5, minimum -20, maximum +20
Minor: (MinorInflictStatistic – MinorResistStatistic)/10, minimum -10, maximum +10

Save Roll Difficulty = 51 + (Major + Level + Minor + Additional Modifiers)

Resist Status Roll = Random # Roll (1,100)

If Resist Status Roll < Save Roll Difficulty, the status condition is applied. Otherwise the status condition is not applied.

Poison Damage

Base Damage: [[4 + 0.5*PoisonLevel + 0.005*(PoisonLevel^2)]/2] * 0.1

Random Damage: {[[13 + 1.25*PoisonLevel + 0.005*(PoisonLevel^2)]/2] + [(200 + 8.8*PoisonLevel)/200] * [[[(2.1462*PoisonLevel + 10.399)/5]*5] / 8]} * 0.1

= Min 10, Max 200

Poison damage is applied for ten turns.

Burn Damage

Base Damage: [[4 + 0.5*BurnLevel + 0.005*(BurnLevel^2)]/2] * 0.2

Random Damage: {[[13 + 1.25*BurnLevel + 0.005*(BurnLevel^2)]/2] + [(200 + 8.8*BurnLevel)/200] * [[[(2.1462*BurnLevel + 10.399)/5]*5] / 8]} * 0.2

= Min 10, Max 200

Burn damage is applied for five turns.

New status condition info thanks to In Media Res.

[19] Skill Points Formulae

L= Character Level

Max Skill Points = 50+ 5L

Skill Points Regeneration = 10 + (L / 5)

Thanks to ZzlzhtT for these formulas.

Fleeing: SP Cost of Fleeing = Monster’s Current SP

This Flee cost is capped at 150 SP.

Thanks to Z.324 for this formula.

[20] Notable Post-Sweep Equipment Standards

Note: Sweep standards are always in flux. Some “swept” equipment may now be on outdated standards.
Note: This section is a work in progress.

Level: Equipment Level

Equipment level is the level a piece of equipment is intended for purchase.

PLvl: Power Level

The Power Level for an item is the equipment’s intended purchase level plus any bonuses. Guardian-only and Ballyhoo equipment will get a bonus of at least 3 levels. Equipment bought with Tokens gets a bonus of at least 10 levels.

MPLvl: MP Level = [PLvl*3/4 + Level/4]

Wild: Wild Factor

OffLean: Offensive Lean on an armor. It can range from “Defensive” (0.8, in other words “80%”) up to “Offensive” (1.25, in other words “125%”). The most common lean on swept armors is “Average” (1, in other words “100%”). The Offensive Lean of an armor indirectly affects how good an armor can be in terms of Defense and Resistance.

Wild Factor is a value between 0 and 1 describing the distribution of power between “base” damage (guaranteed damage, if the attack hits) and “random” damage (extra damage potentially awarded if the attack hits). An “average” attack will use a value of 0.5 .

SCP: Standard Core Power = 5.25 + 0.5625*PLvl + 0.00375*(PLvl^2)
SABRM: Standard Armor Base/Random Multiplier = [100 + 3*PLvl]
SS: Standard Stat% = [100 + 6.6*PLvl]

Standard Core Power is the average power of a regular Melee attack with a PLvl level weapon and a “neutral” PLvl level armor without factoring stat damage. Standard Armor Base/Random Multiplier is the damage multiplier a weapon receives to Base and Random when the player attacks wearing a standard PLvl level armor. Standard Stat% is the standard stat damage multiplier used for most player attacks.

Spells

Spell Base Damage = [2*(1 – Wild)*SCP]
Spell Random Damage = [4*SCP] – 2*(Spell Base Damage)
Spell Stat Multiplier = SS
BTH per Hit = [Level/4]
MP Cost = [38.1 + 2.3375*Level + 0.01125*(Level^2)]

Weapons

Weapon Base Damage = [(1 – Wild)*SCP/SABRM]
Weapon Random Damage = [2*SCP/SABRM] – 2*(Weapon Base Damage)
BTH per Hit = [Level/8]

Armors

Base Multiplier = [(100 + 3*PLvl) * OffLean]
Random Multiplier = [(100 + 3*PLvl) * OffLean]
Stat Multiplier = [(100 + 6.6*PLvl) * OffLean]
BTH per Hit = [Level/8]

Pets

Pet Base Damage = [0.4*(1 – Wild)*SCP]
Pet Random Damage = [0.8*SCP] – 2*(Pet Base Damage)
BM Pet Stat Percentage = SS*0.75
Non-BM Pet Stat Percentage = SS*0.5625
BTH per Hit = [Level/4]

Guests

Pet Base Damage = [0.6*(1 – Wild)*SCP]
Pet Random Damage = [1.2*SCP] – 2*(Guest Base Damage)
Pet Stat Percentage = SS*1.125
BTH per Hit = [Level/4]
Upkeep MP Cost = [[38.1 + 2.3375*Level + 0.01125*(Level^2)]*0.175]

Common Damage Multipliers

Any multipliers “applied before rounding” are applied to SCP (Standard Core Power) and SS (Standard Stat%). The other multipliers are applied to the final (unrounded) damage/healing numbers.

SP Cost (instead of MP): *0.75 (applied before rounding)
Magic Weapon Base/Random Damage: *0.75 (applied before rounding)
“Friendly” (non-Beastmaster) Pet Stat Damage: *0.75 (applied before rounding)
Two Forced Allied Elements: *1.05, or *1.1 on the less powerful elemental attack (for all attack types, applied to spells before rounding)
Two Forced Neutral Elements: *1.1, or *1.2 on the less powerful elemental attack (for all attack types, applied to spells before rounding)
Two Forced Poorly-Related Elements: *1.155, or *1.31 on the less powerful elemental attack (for all attack types, applied to spells before rounding)
Two Forced Opposite Elements: *1.2, or *1.4 on the less powerful elemental attack (for all attack types, applied to spells before rounding)
Choice of Two Elements: *0.9 (for all attack types, applied to spells before rounding)
Harm-element: *0.9 (for all attack types, applied to spells before rounding)
Auto-Hit: *0.85
Healing: *0.9 (also receives *0.85 for Auto-Hit)
Accuracy Lean (BtH Mod = Equipment BtH – Standard BtH Per Hit): *85/(85 + BtH Mod)

Golden Rule of Multipliers: Multipliers are used so any two pieces of equipment with the same PLvl in the same equipment category have similar levels of usefulness. Items with behaviors that make them weaker or harder to use generally get multipliers to increase their output, and items with behaviors that make them strong or easier to use generally get multipliers to decrease their output.

Elemental Wheel

The Elemental Wheel is used to describe the relationship of elements. Pairs of elements that are close on the wheel are said to be more related than those farther away.

Earth and Light are considered to be three positions apart since they are connected through Light Energy Fire Earth.

For equipment that is forced to attack with two elements, the distance of those two elements determines how much (more) damage the attack can do.

Allied Elements: 1 position apart
Neutral Elements: 2 positions apart
Poorly-Related Elements: 3 positions apart
Opposite Elements: 4 positions apart

Attacks that force more than two elements will receive multipliers according to the difficulty of using such attacks effectively. The more elements used and the farther apart the elements are on the wheel, the greater the damage multiplier.

Other bits

“Heal Wounds” spells have +20 added to their PLvl and MPLvl and receive a *1.3 multiplier instead of the *0.9 *0.85 that the sweep standards call for. These spells were given stats based off an old standard, but their influence on the game makes them worth mentioning.

Thanks to the Knights of Order for the publishing these standards. Thanks to BexnDan for finding an omission and Roblos for fixing BtH on weapon/armor.

[21] Ballyhoo

Gold:

Y = Gold per Run
X = Player Level

Y = [6.5*X + 10]

Note: Max gold achievable is 894 at level 136.

Experience:

Y = Experience per Run
X = Player Level

Y = 10*X + 50

Note: Unlike gold, the character’s chance to get experience is not 100%. Experience is only awarded to players under level 100.

Thanks to Captain Rhubarb via etching for the updated formula.

[22] House Value

Value = [Price * (0.9 + [Days Owned]/700)]

“Price” is the original purchase Z-Token price, “Value” is the current Z-Token sellback, “Days Owned” is the number of days the player has owned the house.

Put more plainly, a house’s value is about (90 + Weeks Owned)% of the purchase price, updated daily based off the time of day you purchased the house.