Big List of AQ Formulas

**Additionally:** Often the explanation of the choice of a specific formula is convoluted or straight out doesn't exist, so just replace the text in the formula when needed, and input the numbers into a calculator.

## Introduction

For an example on how to calculate your damage, follow the DIY Calculation Guide.

## 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) Base/Random:

Taking Nemesis' Condemnation as an example.

Base Damage = 15

Max Damage = 29

Random Damage = Max Damage - Base Damage = 14

## Level Up Formulas

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

### Total Exp to Level Up:

If your level is **lower or equal to 135**:

```
Total EXP to next level = 10*[11*(1.1^I)]

```

If your level is **greater or equal to 136**:

```
Total EXP to next level = 10000*[0.011*(1.1^I)]

```

Cumulative Exp to Get **from Level 0 to F** (approximate):

```
Total EXP = 1100*(1.1^F - 1)

```

Cumulative Exp to Get **from Level I to F** (approximate):

```
Total EXP = 1100*(1.1^F - 1.1^I)

```

## Stat Damage Bonus (Per 100% Stat Bonus)

### Core Stat Damage

```
Melee Weapon: STR/8 + STR/80
Ranged Weapon: DEX/8 + STR/80
Magic Weapon: INT*3/32 + STR/80
Melee Skill/Spell: STR/4
Ranged Skill/Spell: DEX/4
Magic Skill/Spell: INT/4
Pets & Guests: CHA/15

```

Each hit of all player attacks (Weapons, Skills, and Spells) has a 10% chance of adding damage in the form of a Lucky Strike, which increases core stat damage by LUK\*3/8 for that hit.

* On average, this bonus results in an increase of LUK\*3/80.

In addition, Pets can also Lucky Strike, adding LUK/5 to core stat damage, averaging to LUK/50 for that hit.

If LUK is 0, Lucky Strikes do not activate. If LUK is negative, then the attacker instead takes a stat damage penalty when Lucky Strikes activate.

```
Minimum Stat Damage = 0.25 * (Core Stat Damage) * (Attack's Stat Multiplier)
Maximum Stat Damage = 0.75 * (Core Stat Damage) * (Attack's Stat Multiplier)

```

Where Attack's Stat Multiplier is the STAT% mentioned on the armor's page (For an armor with 559% we use 5.59).

For these formulas above, the minimum and maximum depend on whether Lucky Strikes activate. The minimum and maximum damage values for non-Lucky Strikes should exclude the +LUK\*3/8 bonus, and the minimum and maximum values for Lucky Strikes should include the +LUK\*3/8 bonus.

### Average Core Stat Damage, with Lucky Strikes Included

```
Melee Weapon: STR/8 + STR/80 + LUK*3/80
Ranged Weapon: DEX/8 + STR/80 + LUK*3/80
Magic Weapon: INT*3/32 + STR/80 + LUK*3/80
Melee Skill/Spell: STR/4 + LUK*3/80
Ranged Skill/Spell: DEX/8 + LUK*3/80
Magic Skill/Spell: INT/4 + LUK*3/80
Pets: CHA/15 + LUK/50
Guests: CHA/15

```

#### Average Stat Damage

```
Average Stat Damage = 0.5 * (Core Stat Damage) * (Attack's Stat Multiplier)

```

## Stat Bonus to Hit

Stat Bonus to Hit adds to the likelihood the attacker's hit lands against a target.

**Melee**: STR\*4/25 + LUK/50

**Ranged**: DEX\*4/25 + LUK/50

**Magic**: INT\*4/25 + LUK/50

**Pets** & **Guests**: CHA\*3/40 + DEX\*3/40 + LUK/40

## Blocking Ability

Blocking Bonus from Stats: DEX/50 + LUK/50.

* Monsters only receive LUK/50 to blocking.

This reduces the effective BtH of an attack by the resulting amount.

## HP, MP, & SP Formulae

Level is the player's level

PowLevel is the player's "power level" as modified by Guardian status. A player who is a Guardian gains at least three levels on top of their usual level.

```
Player HP = [23.8 * ((5.25 + 0.5625 * Level + 0.00375 * Level^2) + (1 + 0.066 * Level) * END/16) * 1/1.4]
Player MP = [4.1 * (32 + (6.1 + 2.3375 * Level + 0.01125 * Level^2) * MIN(1, INT / MIN(Level * 2.1462 + 5.7076, 250)))]
Max MP = [4.1 * (33 + (5.1 + 2.3375 * Level + 0.01125 * Level^2) * MIN(1, INT / MAX(MIN(2 * Level + 4, 250), 10)))]
Player Max SP = [2.25 * (38.1 + 2.3375 * MPLevel + 0.01125 * MPLevel^2)]
Player SP Regeneration = [0.15 * (38.1 + 2.3375 * MPLevel + 0.01125 * MPLevel^2)]

```

For balance purposes, these conversion rates were set up: 1 HP = 1.125 SP = 1.5 MP

Player Fleeing Cost = Monster's Current SP

## Who Strikes First?

At the start of battle, a hidden stat roll is performed to determine which party strikes first. The roll, which varies between 1 and 100, is also affected by stats and Initiative bonus of both the player and the monster:

The stat formula for initiative is (LUK + STR/2 + INT/2 + DEX/2)/2.

Player Stats + Initiative = P

Monster Stats + Initiative = 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. This means that if P exceeds M by 101 or more, the Player will always strike first.

### Chance of First Strike Formula:

C = Chance Player Goes First

X = P - M

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

## Special Charisma Related Info

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

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.

Pets released 2012 or later also use a Training Difficulty of -66. Some older pets will have attack rates specific to them.

## Assumed Stat Training Regimen

```
Available Stat Points = Level*5

```

The expected stats to have, based on your level, distributed between your Main, Secondary, and Tertiary stats. i.e. a level 34 Warrior with STR,DEX and LUK, should have his Primary (STR), Secondary (DEX), and Tertiary (LUK) at 100, 70 and 0 respectively.

```
Primary = MAX(MIN(MROUND(2 * Level + 30, 5), 5 * Level, 250), 10)

Secondary = MAX(MIN(MROUND(4 * Level + 32 - Primary, 5), 5 * Level - Primary, 250), 0)

Tertiary  =MAX(5 * Level - Primary - Secondary, 0)

```

## Standard Monster Defense

Defense = [0.259\*Level + 15]

This reduces the effective BtH of the player by the resulting amount.

 For those interested in a Standard Adjusted Monster Defense, an exact formula is not available, but an excellent approximation is: Standard AMD = 0.5\*Level + 15

## 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 Float between 0 and 100.

```
Defender Value (Player) = Blocking Defense + DEX/50 + LUK/50
Defender Value (Monster) = Blocking Defense + LUK/50

```

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).

## Calculating 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 = 3/80\*LUK

### Base Damage

#### Average Damage

```
Average Normal Weapon Base = (Weapon Base) * (Armor Base) + (Weapon Random) * (Armor Random) / 2 + (Stat Damage) * (Armor Stat) / 2
Average Weapon Special Base = (Weapon Base) * (Special Base) + (Weapon Random) * (Special Random) / 2 + (Average Lucky Strike Stat) * (Special Lucky Strike) / 2
Average Spell Base = Base + Random / 2 + (Stat Damage) * (Spell Stat) / 2
Average Pet/Guest Base = Base + Random / 2 + (Stat Damage) * (Pet/Guest Stat) / 2

```

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. Your Weapons and Armours will vary in their Base/Random multipliers. You can find this information on their AQ encyclopedia entries or, if they entries don't yet exist, in the info submission section (which you can find here)

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.

#### Minimum Damage

For calculating Minimum Damage use these instead:

```
Minimum Normal Weapon Base = (Weapon Base) * (Armor Base) + (Stat Damage) * (Armor Stat) / 4
Minimum Weapon Special Base = (Weapon Base) * (Special Base) + (Average Lucky Strike Stat) * (Special Lucky Strike) / 4
Minimum Spell Base = (Hit Rate) * [Base + (Stat Damage) * (Spell Stat) / 4]
Minimum Pet/Guest Base = Resistance * (Hit Rate) * [Base + (Stat Damage) * (Companion Stat) / 4]

```

#### Maximum Damage

And as for Maximum Damage:

```
Maximum Normal Weapon Base = (Weapon Base) * (Armor Base) + (Weapon Random) * (Armor Random) + (Stat Damage) * (Armor Stat) * 3 / 4
Maximum Weapon Special Base = (Weapon Base) * (Special Base)  + (Weapon Random) * (Special Random) + (Average Lucky Strike Stat) * (Special Lucky Strike) * 3 / 4
Maximum Spell Base = Resistance * (Hit Rate) * [Base + Random + (Stat Damage) * (Spell Stat) * 3 / 4]
Maximum Pet/Guest Base = Resistance * (Hit Rate) * [Base + Random + (Stat Damage) * (Companion Stat) * 3 / 4]

```

### Additive Damage Multiplier

When certain items provide additive damage, multiply your average damage by the following:

```
Additive Multiplier = 1 + Sum of All Additive Damage

```

### Multiplicative Damage Multiplier

```
Multiplicative Multiplier = Product of All Multiplicative Damage

```

### Average Damage

```
Weapon Average Damage = [(1 - Special Rate) * (Average Weapon Base) * (Weapon Hit Rate) + (Weapon Special Hit Rate) * (Special Rate) * (Average Weapon Special Base)] * (Additive Multiplier) * (Multiplicative Multiplier) * (Resistance)
Average Spell Damage = (Average Spell Base) * (Hit Rate) * (Additive Multiplier) * (Multiplicative Multiplier) * (Resistance)
Average Pet/Guest Damage = (Average Pet/Guest Base) * (Hit Rate)* (Additive Multiplier) * (Multiplicative Multiplier) * (Resistance)

```

Also see: DIY Calculation Guide

## Potion Recovery

### Health Potion Healing

```
HP recovered drinking one Health Potion = 2 * 0.85 * ((10.5 + 1.125 * Level + 0.0075 * Level^2) + (1 + 0.066 * Level) * END/16) HP

```

Note: There's a 10% chance of that END/16 being replaced by END/16 + LUK \* 3/16.

### Mana Potion Healing

```
MP recovered drinking one Mana Potion = 2 * 0.8 * (38.1 + 2.3375 * Level + 0.01125 * Level^2)

```

## 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.

## EXP/Gold Caps

```
AQ Daily Exp Cap = (1.055^Level + 8 + 1.055^(Level^1.085)) * 900 * 1.5
AQ Daily Gold Cap = (1.055^Level + 8 + 1.055^(Level^1.085)) * 300 * 1.5
AQ X-Guardian Daily Exp Cap = (1.055^Level + 8 + 1.055^(Level^1.085)) * 990 * 1.5
AQ X-Guardian Daily Gold Cap = (1.055^Level + 8 + 1.055^(Floor(Level^1.085))) * 330 * 1.5

```

## Status Conditions

### Status System Save Roll Formula

```
Level: (InflictLevelStatistic - ResistLevelStatistic)/2
Major: (MajorInflictStatistic - MajorResistStatistic)/5, minimum -20, maximum +20
Minor: (MinorInflictStatistic - MinorResistStatistic)/10, minimum -10, maximum +10
Additional Modifiers: (NetInflictModifiers - NetResistModifiers)
If a monster tries to inflict a status, players gain an additional END/50 as a resist modifier.

```

```
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.

## Notable Post-Sweep Equipment Standards

### Definitions

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]

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. Using a Wild of 0 will sometimes result in an attack receiving Random damage of -1. In this event, Base is effectively decreased by 1 and Random is effectively increased from -1 up to 1.

Melee Power: Melee Power designates the amount of damage done by a Melee weapon supported by stats but disregarding the weapon's special, excluding the effect of Lucky Strikes. This amount of damage is similar to what a Melee weapon does in an armor with an Offensive Lean of 0.9 (often called "mid-defensive") when including the weapon's special. A mid-defensive armor is commonly assumed when considering sources of damage not coming from a player's weapon, so this unit "Melee Power" plays an important role in balance.

### Spells

```
Spell Base Damage = [2*(1 - Wild)*(5.25 + 0.5625*PLvl + 0.00375*PLvl^2)]
Spell Random Damage = [4*(5.25 + 0.5625*PLvl + 0.00375*PLvl^2)] - 2*(Spell Base Damage)
Spell Stat Multiplier = 1 + 0.066*PLvl
BTH per Hit = [PLvl/4]
MP Cost = [38.1 + 2.3375*MPLvl + 0.01125*(MPLvl^2)]

```

Spells fully supported by stats will do roughly 2 \* (Melee Power).

### Weapons

```
Weapon Base Damage = [(1 - Wild)*(5.25 + 0.5625*PLvl + 0.00375*PLvl^2)/(1 + 0.03*PLvl)]
Weapon Random Damage = [2*(5.25 + 0.5625*PLvl + 0.00375*PLvl^2)/(1 + 0.03*PLvl)] - 2*(Weapon Base Damage)
BTH per Hit = [PLvl/8]
Special Base/Random: (1+10/PROC)*(1+0.03*PowLvl)*(1+MIN(2*PowLvl+30, 5*PowLvl, 250)*(1+0.066*PowLvl)/16/(0.00375*PowLvl^2+0.5625*PowLvl+5.25))
Special Lucky Strike: (1 + PowLvl*0.066)*(1+10/proc)
Special BtH =PowLvl/4 + MIN(0.2*PowLvl+1.6, 25)

```

Note: Specials should deal [0.1+(Proc)]/(Proc) in (Melee Power) which is 1.5 \* (Melee Power) at 20% proc.

### Armors

```
Base Multiplier = [1 + 0.03*PLvl] * OffLean
Random Multiplier = [1 + 0.03*PLvl] * OffLean
Stat Multiplier = [100 + 6.6*PLvl]/100 * OffLean
BTH per Hit = [PLvl/8]

```

### Pets

```
Pet Base Damage = [0.4*(1 - Wild)*(5.25 + 0.5625*PLvl + 0.00375*PLvl^2)]
Pet Random Damage = [0.8*(5.25 + 0.5625*PLvl + 0.00375*PLvl^2)] - 2*(Pet Base Damage)
Pet Stat Multiplier = (100 + 6.6*PLvl) * 0.75 / 100
BTH per Hit = [PLvl/4]

```

Pets fully supported by stats have power roughly equal to 0.4 \* (Melee Power). Pets not supported by CHA are assumed to be worth 0.2 \* (Melee Power).

### Guests

```
Guest Base Damage = [0.6*(1 - Wild)*(5.25 + 0.5625*PLvl + 0.00375*PLvl^2)]
Guest Random Damage = [1.2*(5.25 + 0.5625*PLvl + 0.00375*PLvl^2)] - 2*(Guest Base Damage)
Guest Stat Percentage = (100 + 6.6*PLvl) * 1.125 / 100
BTH per Hit = [PLvl/4]
Upkeep MP Cost = [[38.1 + 2.3375*MPLvl + 0.01125*(MPLvl^2)]*0.175]

```

Guests fully supported by stats have power roughly equal to 0.6 \* (Melee Power).

### Miscs

All Miscs receive a MODIFIER on the bonuses they receive, with each bonus' modifier being independent.

```
CORE: 0.00000995*PowLvl^3 -0.00292*PowLvl^2 +0.2846*PowLvl

```

#### Bonus

```
Resistance is x[100 - 5*CORE*MODIFIER]%, min x50%
Attribute bonuses are +5*CORE*MODIFIER, max +50
Damage boosts are +(0.02*CORE*MODIFIER), max +0.2
Blocking and BTH are +(CORE*MODIFIER), max +10

```

#### Cost

Formulas for MP cost. For SP costs, multiply by 0.75:

```
Blocking: 49.11*2*(1-(70-BONUS)/70)*1.193
Resistance: (0.85*2*(39.385-(OLD+13.3104))*295.8965/100)*1.193 where OLD=[-CORE*MODIFIER]
BTH bonus: 49.11*2*(BONUS/100)*1.193
Attributes: (49.11+0.16*BONUS)*2*BONUS/16*1.193/100+0.16*BONUS*2*1.193
Damage boosts: 20.746*(1+BONUS)^3 -130.83*(1+BONUS)^2 +301.67*(1+BONUS) -191.33

```

Where Bonus is the value you get from the value from the value formulas.

The cost for guardians is reduced by 1.

### Assumed Equipment Replacement

These assumptions are not hard requirements but rather an average assumed baseline of what will happen. These assumptions are also not necessarily the most-efficient use of gold. For example, you will probably find it useful to replace armors more frequently and shields less frequently at higher levels, and warriors will have much less use for spell upgrades, so act as you see fit.

Weapon: One upgrade per level, so each item is replaced every 7 levels.
Spell: One upgrade per level, so each item is replaced every 8 levels.
Pet: One upgrade per two levels, so each item is replaced every 16 levels.
Misc: One upgrade per two levels, so each item is replaced every 16 levels.
Armor: One upgrade per three levels, so each element is replaced every 21 levels.
Shield: One upgrade per three levels, so each element is replaced every 21 levels.

### Common Damage Multipliers

SP Cost (instead of MP): \*0.75 (applied before rounding)

Magic Weapon Base/Random Damage: \*0.75 (applied before rounding)

Mastercraft (if bonus is applied to damage): \*1.05

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)

All elements: \*132/109

Choice of Two Elements: \*0.9 (for all attack types, applied to spells before rounding)

Element-Seeking: \*0.8

Element randomized at the start of battle: \*1.1

Generic trigger: \*1.1 (can vary depending on prevalence of triggering targets)

Generic downtrigger: \*0.95 (sometimes varies)

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)

Theoretical Weapon Special Advantage: \*(1 + 0.1/Proc) (Proc is the weapon special rate. For the default 20% rate, the multiplier is 1 + 0.1/0.2 = 1.5. The exact effect is different because weapon specials typically ignore player stats and will do extra base/random damage to compensate.)

No-special weapon: \*1.08 (specials are stronger than regular attacks, so a lack of a special is accounted for this way)

"100% special" weapon: \*1.1 (the lack of a normal special means the weapon does less damage than normal)

Damage to MP: \*1.5

Damage to SP: \*1.125

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 more versatile will generally be made weaker in other ways. Likewise, items that are harder to use effectively will generally be made more powerful.

#### Status Effect / Damage Compensation

Attacks without status effects are the "standard" actions. If a player does an action that applies or attempts to apply a negative status effect on the enemy, the particular item will directly do less damage than a standard action. The usual rule is:

Damage Reduction: (Expected Status Attempt Rate) \* [50 - (Enemy's Save Bonus)] \* (Effect Value)

The Expected Status Attempt Rate is almost always affected by the attack's hit rate. If a special with a BtH Mod of -5 requires both of its hits in a two-hit special to connect to attempt a status effect, and the status effect is only attempted 50% of the time when that condition is met, then the Expected Status Attempt Rate is 0.8 (first hit lands) \* 0.8 (second hit lands) \* 0.5 (50% chance to try) = 0.32.

The Effect Value is a measure of the status effect's usefulness. Some examples are included below.

Turn Loss with no extra effect: 1.4 \* (Melee Power)

Frozen/Petrification: 1.6 (Melee Power)

Poison/Burn/etc: (Turns of Poison/Burn/etc) \* (Poison/Burn/etc's Damage Per Turn)

Blind: [(BtH Reduction)/70] \* (Turns of Blinding) \* 1.4 \* (Melee Power)

Damage reductions apply before multi-element multipliers.

#### Enemy Power Multipliers

Monsters may receive difficulty multipliers to place them above or below standard. Below are common multipliers:

Mook: 0.5

Champion: 1.25

Elite: 1.5

Boss: 2

However, monsters are not required to use these multipliers in particular. Monsters with power multipliers of 1.4 or 0.9 are possible in their own right.

### 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.

## Elemental Compensation

Elemental compensation has two variations. The old variation (used for items like Moglord, White Knight Z, etc) and for newer (recent) stuff.

It is not immediately apparent which piece of gear uses which elecomp formula (old or new), but it can be roughly guesstimated based on the released date of the piece of gear. Anything newer than 2016 is guaranteed to use the new formula with the exception of some of the (now perma-rare) Guardian Dragon Forms.

**For Spell (or Old Lean) based skills, you multiply the damage by the elemental compensation. For Weapon-Based skills there are additional steps in each section.**

### New Formula

Calculate the following for **each element**.

```
$element_Compensation_Mod = (Damage_Taken_Mod / Damage_Dealt_Mod) * Blocking_Mod * Armor_lean_Mod / 0.9

```

Where:

```
Damage_Taken_Mod = ( [Your current $element resistance, with an expected shield] / [Expected resistance, with an expected shield] )
Expected shield resistance is -0.00000948*PowLvl^3 + 0.003356*PowLvl^2 - 0.426364*PowLvl -4*PowLvl/150
Expected armour resistance is 100 + ROUND(ROUND(0.0015*PowLvl*PowLvl -0.6*PowLvl) -4*PowLvl/150))

```

```
Blocking_Mod = ( (85 - [The average of the armour's Defences] +[Expected armour defence])/85 )
Expected armour defences = round((0.5*PowLvl - 0.5) / 3) + 25

```

```
Damage_Dealt_Mod = ( [an $element monster's expected resistance to $skill_element] / [monster's top expected resistance] )
Expected resistances are:
Element: 70
Allied Elements: 85
Neutral Elements: 100
Poorly Related Elements: 115
Opposite Element: 130

```

Elemental Wheel

**The monster's top expected resistance is always 130.**

```
Armor_lean_Mod = ( ([Armor Lean] - 1)/2 +1 )

```

We now find the minimum of the former values:

```
Elemental_Compensation_Mod = MIN($element_Compensation_Mod)

```

Meaning the elemental compensation **modifier** is the minimum among all values.

And Finally:

```
Elemental Compensation = 5*( Elemental_Compensation_Mod / (4 + Elemental_Compensation_Mod) )

```

For spell-based skills you multiply your **damage** by the elemental compensation above. For weapon based skills you instead follow the additional steps below and modify the **cost**.

#### Weapon Based Skill

If this is a weapon based skill, we perform the following **additional** steps to calculate the new cost:

```
Cost_Elecomp_Mod = Elemental_Compensation_Mod * 0.9 / Armor_lean_Mod

```

Same as for regular elemental compensation:

```
Cost_Hyperbole_Mod = 5*( Cost_Elecomp_Mod / (4 + Cost_Elecomp_Mod ) )

```

And finally:

```
Cost_Mod = (2 / Cost_Hyperbole_Mod - MRM_Mod) / 1.25

```

When MRM\_Mod is 1 when dealing Melee / Ranged damage, and 0.75 and doing Magic damage.

The Cost\_Mod is then multiplied by the expected cost for a skill.

### Old Formula

Calculate the following for **each element**.

```
$element_Compensation_Mod = (Damage_Taken_Mod / Damage_Dealt_Mod) * Blocking_Mod

```

Where:

```
Damage_Taken_Mod = ( [Your current $element resistance, with an expected shield] / [Expected resistance, with an expected shield] )
Expected shield resistance is -0.00000948*PowLvl^3 + 0.003356*PowLvl^2 - 0.426364*PowLvl -4*PowLvl/150
Expected armour resistance is 99 + 0.0015*PowLvl*PowLvl -0.6*PowLvl -4*PowLvl/150

```

```
Blocking_Mod = ( (85 - [The average of the armour's Defences] +[Expected armour defence])/85 )
Expected armour defences is round((0.5*PowLvl - 0.5) / 3) + 25

```

```
Damage_Dealt_Mod = ( [an $element monster's expected resistance to $skill_element] / [monster's top expected resistance] )
Expected resistances are:
Element: 70
Allied Elements: 85
Neutral Elements: 100
Poorly Related Elements: 115
Opposite Element: 130

```

Elemental Wheel

**The monster's top expected resistance is always 130.**

Finally:

```
Elemental Compensation = MIN($element_Compensation_Mod)

```

Meaning the elemental compensation is the minimum among all values.

If this is a weapon based skill, we perform the following additional steps to calculate the new cost:

```
Cost_Mod = MAX(1 - 2*(Elecomp - Lean)/1.25, (Lean*2*Damage_Dealt_Mod / Damage_Taken_Mod-0.75)/1.25)

```

**Incomplete.**

## House Value

```
Value = [Price * (0.9 + [Days Owned]/1400)]

```

"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/2)% of the purchase price, updated daily based off the time of day you purchased the house.

## Stat Training Costs

```
Gold Cost = floor(10 * 1.25(statLvl+5)/5)

```

"statLvl" is the current value of the stat. E.g., when training from 245 to 250, statLvl is 245.

floor(x) means that you round down x. floor(10.7) = 10.

min(x, y) means the lowest value of x and y. min(10, 2) = 2.

max(x, y) means the greatest value of x and y. max(69, 2) = 69.