Note |
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This guide is mostly a copy-paste from Kaelin's guide on the forums, with minor formatting, and an additional damage calculation guide.
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:
^: 'to the power of' e.g., 10 ^ 3 = 1000 >: 'greater than or equal to' <: 'less than or equal to' Floor(x): Round down x e.g., Floor(10.7) = 10. Min(x, y): The lowest value of x and y e.g., Min(10, 2) = 2 Max(x, y): The greatest value of x and y e.g., Max(69, 2) = 69
2) Base/Random. Taking Nemesis Destroyer as an example:
Base (i.e. Min damage): 21 Random: 22 Max Damage: 21 + 22 = 43
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 Ranged Weapon: DEX/8 Magic Weapon: INT*3/32 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 + LUK * 3 / 80 Ranged Weapon: DEX / 8 + LUK * 3 / 80 Magic Weapon: INT * 3 / 32 + LUK * 3 / 80 Melee Skill/Spell: STR / 4 + LUK * 3 / 80 Ranged Skill/Spell: DEX / 4 + 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)
Note |
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A few weapons, 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. However, weapons do take Lucky Strikes on specials (at the usual 10% rate). |
Style Bonuses
Style bonuses are additional benefits provided to players that invest at least 150 points into a stat. They start at 25% of their maximum value, and scale up to their maximum power at 250 points. The following bonuses below assume maximum investment.
STR [Warrior]: Weapon attacks deal +10% damage. This does not affect weapon specials or bow attacks.
Note |
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Warriors also possess access to Warrior Lean, where Melee weapons are unaffected by the damage reduction of Fully Defensive armours. This is not a style bonus and Melee attacks receive the full benefit even if the player possesses no STR. |
DEX [Ranger]: Weapon specials and bow attacks receive the following damage bonus:
Bonus: +15 * Log(rate) / Log(100) %
Log refers to the natural logarithm. This boost also applies to weapon attacks/specials that don't receive weapon effects (e.g., Lt. Lore's Shield).
INT [Mage]: Spells and Spell-type skills increase in damage when hitting an element that the monster possesses <100% resistance to:
Bonus: +[ ( 100 - Resistance ) / 130 ]%
Resistance in the above formula refers to the percentage value.
Stat Bonus to Hit
Stat Bonus to Hit adds to the likelihood the attacker's hit lands against a target.
Melee: STR * 4 / 25 Ranged: DEX * 4 / 25 Magic: INT * 4 / 25 Pets & Guests: CHA * 3 / 40 + Max(STR, DEX, INT) * 3 / 40
Note |
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A few weapons, 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. |
Ranged Accuracy Multiplier
Each time you successfully hit with a Ranged attack will decrease the accuracy lean of your attacks. Each time you miss, your accuracy lean will increase instead. Each miss is worth twice as much as a hit. Your total accuracy modifier is calculated as:
Accuracy Modifier: -(85 * Total) / (Total^2 + 32 * Total).
Where 'Total' refers to the combined number of Ranged hits and misses dealt by the player from battle start [e.g., For 5 hits and 2 misses, Total = (-1 * 5 * 1) + (+1 * 2 * 2) = -1] . You then receive adequate damage compensation [e.g., for -10 BTH you deal *85 / (85 - 10) damage].
Where 'Total' refers to the combined number of Ranged hits and misses dealt by the player from battle start [e.g., For 5 hits and 2 misses, Total = (-1 * 5 * 1) + (+1 * 2 * 2) = -1] . You then receive adequate damage compensation [e.g., for -10 BTH you deal *85 / (85 - 10) damage].
Note |
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The above formula has no cap, but if the BTH modifier exceeds +20, any downside above the limit is doubled [e.g., -30 lean deals *(85 / 55) damage, but you take -40 BTH. The -10 BTH downside above the lean is doubled |
In addition, due to Ranger Style bonus, all attacks also gain up to +4.25 BTH. You receive 25% of this value at 150 DEX, which scales linearly to receive the full value at 250 DEX.
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
Note |
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The Fleeing cost is capped at 150 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
X <= -100 | -100 < X < 0 | 0 <= X <= 100 | X > 100 |
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C = 1 | C = (100 + X)^2 / 20000 | C = 1 - (100 - X)^2 / 20000 | C = 1 |
All answers of C will be in decimal form. To change to a percentage, multiply by 100.
Charisma Related Info
Style Bonus
Charisma's Style Bonus means that Guests deal +5% damage, as well as having a 20% chance to perform a Ferocious strike, in which damage is doubled. As with other style bonuses, this starts at 25% of maximum strength at 150 CHA and scales to the quoted values when CHA is maximised at 250.
[Outdated] Training Difficulty
MAJOR NOTE |
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In AQ's history, Pets did not always take their turn. Their chance to attack depended upon Player charisma and the "Training Difficulty" stat. However, this system is now in the process of being phased out. Pets in the future will always get their turn (unless some unique circumstance take it away). |
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: Floor[Level / 4 + 55]
'Floor' in the above formula means "round down". Monster defenses reduce the effective BTH of the player by the resulting amount.
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 Defender Value (Monster): Blocking Defense
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
Daily Exp Cap: (1.055 ^ Level + 8 + 1.055 ^ (Level ^ 1.085)) * 900 * 1.5 Daily Gold Cap: (1.055 ^ Level + 8 + 1.055 ^ (Level ^ 1.085)) * 300 * 1.5 X-Guardian Daily Exp Cap: (1.055 ^ Level + 8 + 1.055 ^ (Level ^ 1.085)) * 990 * 1.5 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
Save Roll Difficulty: 51 + (Major + Level + Minor + Additional Modifiers)
Where:
Level: (InflictLevelStatistic - ResistLevelStatistic)/2 Major: (MajorInflictStatistic - MajorResistStatistic)/5, minimum -20, maximum +20 Minor: (MinorInflictStatistic - MinorResistStatistic)/10, minimum -10, maximum +10 Additional Modifiers: (NetInflictModifiers - NetResistModifiers)
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.
Note |
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If a monster tries to inflict a status, players gain an additional END/50 as a resist modifier. |
[Outdated] Poison and Burn Damage
In the modern game, a Power 1 poison can be expected to provide 10% Melee (10% of an expected Melee attack) of damage. However, there are some outdated calculations regarding how poison and burn previously functioned. As is noted, these statuses assume specific durations:
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 turn
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 [A.K.A.: Armour Lean]: 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. Please note that, due to Warrior's Style Bonus, Melee weapons deal *1 Damage even in Defensive leaning armours
Wild Factor: 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. A similar term, %Melee, refers to Melee power expressed as a percentage.
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)
NB: Weapon Specials should deal *(1 + 0.1 / Proc) Damage. Proc refers to the decimal chance of the weapon special occurring e.g., 20% chance = 0.2.
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: Max([100 - 5 * Core * Modifier], 50)% Attribute bonuses: Min([5 * Core * Modifier], 50) Damage boosts: Min([0.02 * Core * Modifier], 0.2) Blocking and BTH: Min([Core * Modifier], 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 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 [applied to damage]: *1.05 Two Forced Allied Elements: *1.05, *1.1 on the less powerful elemental attack (applied to spells before rounding) Two Forced Neutral Elements: *1.1, *1.2 on the less powerful elemental attack (applied to spells before rounding) Two Forced Poorly-Related Elements: *1.155, *1.31 on the less powerful elemental attack (applied to spells before rounding) Two Forced Opposite Elements: *1.2, *1.4 on the less powerful elemental attack (applied to spells before rounding) All elements: *132/109 Choice of Two Elements: *0.95 (applied to spells before rounding) Element-Seeking: *0.8 (*1.2 is also typically applied to cost. This is considered the 'Omni-elemental Penalty') Element Randomised at the Start of Battle: *1.1 Generic Trigger: Downtrigger * -2 Player Controlled Trigger: Downtrigger * -1.5 Generic Downtrigger: *0.95 (5% damage) Harm-element: *0.9 (applied to spells before rounding) Autohit: *0.85 (Some old items have values of either *0.6375 or *0.8 due to outdated stat assumptions) Healing: *0.9 (also receives *0.85 for Auto-Hit) Accuracy Lean (BTH Mod: Equipment BTH - Standard BTH Per Hit): *85/(85 + BTH Mod) Weapon Special Advantage: *(1 + 0.1 / Proc), where Proc is the weapon special rate. For the default rate: 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) 0-proc (0% Weapon special rate): *1.08 100-proc (100% Weapon special + lack of a 'true' special): *1.1 Damage to MP: *1.5 Damage to SP: *1.125
The Golden Rule: 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. Damage reductions apply before multi-element multipliers.
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)
Enemy Power Multipliers
Monsters may receive difficulty multipliers to place them above or below standard. Below are common multipliers:
Mook: 0.5 Regular: 1 Champion: 1.25 Elite: 1.5 Boss: 2 Champion Boss: 2.5-3 Champion Elite Boss: 3.5-4 Exceptional: 5+
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: -0.00000948 * PowLvl ^ 3 + 0.003356 * PowLvl ^ 2 - 0.426364 * PowLvl -4 * PowLvl / 150 Expected armour resistance: 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: ([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
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 - Blocking_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: -0.00000948 * PowLvl ^ 3 + 0.003356 * PowLvl ^ 2 - 0.426364 * PowLvl - 4 * PowLvl / 150 Expected armour resistance: 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: Round((0.5 * PowLvl - 0.5) / 3) + 25
Damage_Dealt_Mod: ( [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
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)
NB: This is 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.