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DragonFable Stats and Formulas

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7/16/2018 2:38:50   
Sakurai the Cursed

By Sakurai the Cursed
Previously by dracojan

Main Stats

Every time a player levels up, they get 5 stat points. These points can be invested into your main stats by talking to Rolith in Oaklore Book 1 and 2, Maya in Oaklore Book 3, Sir Render in Falconreach, or Clyde the Stats Moglin in your House if you've bought him and placed him there, at a cost of the player's level in gold per point (meaning, if you're level 50, it will cost 50 gold per point you invest). They can be untrained for 1,000 gold only by Sir Render or Clyde the Stats Moglin; after untraining, all stat points are removed and players can invest them again.
There is no hard cap on main stats, but they can only be trained up to 200. Additional bonuses or penalties to stats can come from equipment, consumables, or buffs/debuffs from yourself, allies or enemies, with alterations to the main stats summed up and shown on the character sheet after the base invested amount as blue additions if the total alteration is positive, or red subtractions if the total alteration is negative (or, if you've enabled Simple Stat Info in the options, the base and alterations will be summed up and shown as one value, keeping the same coloring scheme). The effects of the main stats are as follows:

STR (Strength) - Increases Melee damage, Immobility resistance, and overall damage from stats

STR/10 = bonus damage with Melee weapons/skills, STR/5 = increased immobility resist, STR/5 = percentage bonus to stat damage

So at 200 Str you'd have +20 Melee damage, +40% to all damage given from stats (including the +20 from itself), and +40 Immobility resistance.

INT (Intelligence) - Increases Magic damage, Critical Hit damage, and chance to hit

INT/10 = bonus damage with Magic weapons/skills, INT/10 = Bonus to Hit, INT/1,000 = bonus to Critical damage multiplier

So at 200 INT you'd have +20 Magic damage, +20 Bonus, and +0.2 Critical damage multiplier added on to the base of 1.75, for 195% total Critical damage. Specific classes such as Cryptic have higher base Critical Hit modifiers than 1.75, but this bonus is additive so will always simply raise the final modifier by INT/1,000; in Cryptic's case with 200 Int, this would be 2.0->2.20.

DEX (Dexterity) - Increases Pierce damage and Damage over Time, and decreases incoming Glancing Blow damage

DEX/10 = bonus damage with Pierce weapons/skills, DEX/10 = flat bonus damage to Damage over Time effects (not affected by multipliers), DEX/1,500 = decrease to Glancing Blow damage modifier

So at 200 DEX you'd have +20 Pierce damage, +20 damage per turn to DoT effects, and -0.133~ from the base Glancing Blow modifier of 0.25, for ~11.66% damage received on Glancing Blows.

Note: For the most part, whether an attack is Melee, Pierce or Magic damage is based on your choice of weapon; swords/axes/maces and the like inflict Melee damage, daggers/claws and the like inflict Pierce damage, and staves/wands and the like inflict Magic damage. However, there are two exceptions to this: first, there are specific skills on specific classes that will always do one particular type of damage regardless of weapon or stats, which will be noted on the class' Encyclopedia entry; second, weapons categorized as scythes (though they can take any shape) don't have their own damage type but rather will use the damage type of whatever stat is highest: Melee for STR, Pierce for DEX, or Magic for INT. If you have multiple stats with equal values, the priority is Magic>Pierce>Melee.

CHA (Charisma) - Increases Pet and Guest damage, Gold and Exp gain when using Guests, and the chance of activation and power of certain Pet skills

CHA/10 = bonus damage to Pet and Guest attacks, CHA/1,000 = bonus to Gold and Exp modifier per Guest used

So at 200 CHA you'd have +20 damage to pets/guests and +0.2 to the Gold and Exp modifier per Guest added on to the base of -0.1 per Guest, for +0.1 or +10% Gold and Exp gain. This is on a per-guest basis, so with two guests, this would become +20%. CHA's increase to the chance and power of certain Pet skills is determined on a case-by-case basis, for example the Atgasedd Doll using CHA/20 and CHA/40 to determine the strength of its debuffs and buffs respectively, or the Pet Dragon using CHA/10 and LUK/10 to boost its skill use chance. Since this is unique per pet that makes use of it, it can't be accurately noted here, but will be included in the Encyclopedia entry for each pet that it pertains to, if known.

Note: CHA will only raise Pet/Guest damage in quests released after engine version 9.0.0 was implemented.

LUK (Luck) - Increases Critical Hit chance, Melee/Pierce/Magic defenses, Direct Hit chance, pet dragon skill use chance, and various dice rolls in minigames

LUK/10 = bonus Crit, LUK/25 = bonus Melee, Pierce, and Magic defenses, LUK/25 = bonus Direct Hit

So at 200 Luk you'd have +20 Crit, +8 Melee, Pierce and Magic defenses, and +8 Direct Hit. The effect of LUK's bonus to dice rolls is on a case-by-case basis, so can't be accurately noted here.

END (Endurance) - Increases maximum HP

END*5 = bonus to maximum HP

So at 200 END you'd have +1,000 maximum HP. A simple stat, but effective.

WIS (Wisdom) - Increases maximum MP and the strength of incoming heals

WIS*5 = bonus to maximum MP, WIS/20 = percentage bonus to incoming heal strength

So at 200 WIS you'd have +1,000 maximum MP and +10% Health and Mana recovery. This does not affect negative damage received from having over 100 resistance to a damage type, only effects of the "Health" or "Mana" element.

Secondary Stats

These cannot be directly invested in, but are determined by main stats, equipment, class, skills, buffs, debuffs, etc. and an understanding of them is required to understand how your character functions in combat:

Level - Represents the level of power of your character. Raised by defeating enemies and acquiring Experience, this determines what equipment and classes you can use, your HP and MP values, and how many stat points you have available.

Level*20 = bonus to maximum HP, level*5 = bonus to maximum MP, (level-1)*5 = available stat points

HP (Health Points) - Represents the physical endurance of your character; damage dealt to your character lowers this, and if it falls to 0 then you're defeated and will have to try again from the beginning of the quest, though defeated enemies will not need to be fought again. Base HP is 60, raised by your level and END stat.

MP (Mana Points) - Represents the magical endurance of your character; using the various spells and skills available to your class will diminish this, and they will not be usable without enough of it. Base MP is 190, raised by your level and WIS stat.

MPM (Melee / Pierce / Magic Defense) - Represents your chance to completely avoid Melee, Pierce or Magic attacks, respectively. Checked against Bonus.

1.5 Melee / Pierce / Magic = +1% evasion chance

BPD (Block / Parry / Dodge Defense) - Represents your chance to receive Glancing Blows on Melee, Pierce and Magic attacks, respectively. Checked against Bonus and Crit.

1.5 Block / Parry / Dodge = +1% incoming glancing blow chance

Bonus - Increases your chance for an attack to hit and to deal full damage. Checked against opponent MPM and BPD.

1.5 Bonus = +1% chance to hit, -1% chance of outgoing glancing blows

Glancing Blow - A hit that deals reduced damage and does not inflict status effects that must hit to be inflicted. Base glancing blow damage is 25%.

Direct Hit - Represents your minimum chance to hit. When activated, ignores MPM, BPD and Bonus checks and automatically hits. Because of the way the hit/miss system works in DragonFable, this stat doesn't come into effect unless your normal hit chance is lower than your direct hit chance; in other words, if your direct hit chance is 10%, it does nothing to improve your accuracy until your normal hit chance would fall below 10%. Base direct hit chance is 0.66~%.

1.5 Direct Hit = +1% minimum chance to hit

Critical Miss - Represents your minimum chance to miss. When activated, ignores MPM, BPD and Bonus checks and automatically misses. Base critical miss chance is 0.66~%, and cannot currently be increased or reduced.

Crit - Represents your chance to land a Critical Hit.

2 Crit = 1% chance to deal critical damage, capped at 50% possible from items (Cap does not affect LUK, skills, buffs or passive class effects)

Critical Hit - A hit that deals increased damage and cannot be a glancing blow. Base Critical damage is 175%, but can differ between classes.

Dmg (Damage) - The sum of your weapon damage and stat damage, used as a base to be multiplied by the various attacks you can use.

Boost - Increases your outgoing damage.

1 Boost = +1% damage

Resistances - Lowers the incoming damage of [element], or in the case of Shrink and Immobility, lowers the chance of such effects working. Health and Mana resistances lower the 'damage' of Health and Mana recovery effects, thus reducing their power and making positive values for these resistances undesirable. "All resistance" effects include Shrink, Immobility, Health and Mana as well.

1 resistance = 1% reduction in effect of [element/status], capped at 80% possible from items (This cap only applies to each single resistance, and since All Resistance is considered its own resistance you can for example combine 50 Fire and 50 All to have 100% total reduction of Fire damage. Buffs from skills and consumables are unaffected by this cap)

< Message edited by Sakurai the Cursed -- 3/14/2019 12:01:36 >
AQ DF MQ AQW Epic  Post #: 1
11/3/2018 1:46:19   
Sakurai the Cursed

Practical Applications

Reader beware, math ahead! This section is purely for those interested and isn't necessarily required to understand the game, only to assist in mathematic comparisons and evaluations.

Now that we've defined the parameters of all the various stats, let's detail how they interact and lay out some practical formulae you can use to determine actual damage and hit chance.

First, damage: The flat damage received from Str, Dex or Int always rounds down, but the final stat damage after applying Str's percentage boost always rounds up, and this final stat damage is added to both your minimum and maximum weapon damage to provide the damage displayed on your character sheet (Dmg):

Note: "ceiling()" and "floor()" mean to round the number inside of their parentheses up to the next highest whole number (for ceiling) or down to the next lowest whole number (for floor); for example, ceiling(12.1) = 13 and floor(72.9) = 72
Dmg = Weapon Damage + ceiling(floor(Str or Dex or Int / 10) * (1 + Str / 500))

So for example, using a Melee weapon with 75-100 weapon damage and 109 STR, you'd have:

75-100 + ceiling(floor((109 / 10)) * (1 + 109 / 500))
75-100 + ceiling(floor(10.9) * 1.218)
75-100 + ceiling(10 * 1.218)
75-100 + ceiling(12.18)
75-100 + 13 = 88-113

Note that pet/guest damage is much the same as your own damage, just using their own stats (listed on the item description for pets or the character sheet for guests) instead of yours, with the obvious exception of your Cha. The vast majority of pets simply do 100% damage per hit making the number of hits paramount for Cha builds, however there are exceptions and guests can be as variable as your own classes, so this all applies to them as well; just add in "+ floor(Your Cha / 10))" at the end.

This base is then multiplied by the attack/skill used, any boost you may have, and your critical modifier if you land a critical hit. Additionally, from a gameplay perspective, every attack or effect in DragonFable will have an associated element to it; this can range from mundane materials like Metal or Stone, to traditional elemental archetypes like Fire or Light, moral concepts like Good or Fear or even the enigmatic "???". In fact, even the lack of an element is considered an element of its own, called simply "None". All of these are mitigated by their respective elemental resistance, though some don't have any sources of resistance for themselves in particular, but all are affected by the "All" resistance. And lastly, all final damage numbers are always rounded up (only relevant if a final damage value is not a whole number).

So, taking these together, a simple formula for base damage would look like this:

Base damage = ceiling(Dmg * Skill Multiplier * (1 + Boost / 100) * (100 - Relevant Resistances) / 100)

To use the aforementioned example of 88-113 dmg, with a 200% skill multiplier and assuming the attack is of the Metal element with the enemy having -30 Metal Resistance but 10 All Resistance, we'd have:

ceiling(88-113 * 2 * (100 - -30 - 10) / 100)
ceiling(176-226 * (120) / 100)
ceiling(176-226 * 1.2)
ceiling(211.2-271.2) = 212-272 damage

Critical hits then multiply that damage by 175% plus any class or stat modifiers, however they do so before the final ceiling, so if the skill crits we'd use this:

Crit damage = ceiling(Base damage * (1.75 + Class Crit Modifier + Int / 1,000))

Let's assume the Cryptic class which has +25% critical damage and 200 Int:

ceiling(211.2-271.2 * (1.75 + 0.25 + 200 / 1,000))
ceiling(211.2-271.2 * (2 + 0.2))
ceiling(211.2-271.2 * 2.2)
ceiling(464.64-596.64) = 465-597 final damage

If we want to find the average damage we should expect while ignoring chance to hit, for example if we know our hit-rate will be the max anyway (and, to be honest, it generally is at higher levels, outside of challenge fights), we just need to take crit chance into account (note that we don't round up here because these aren't actual inflicted damages, just expected averages:

Note: "median(x,y,z)" means to use whichever variable within the parentheses is the middle (median) value of the given options when arranged in numerical order from smallest to largest, or largest to smallest. So, for example, median(0, 1.5, 1) = 1, or median(0.1, 0.05, 0.9933) = 0.1
Average raw damage = Base damage * (1 + median(0, (Crit / 200), 1) * (0.75 + Class Crit Modifier + Int / 1,000))

So, continuing on from the previous examples and assuming 120 Crit for 60% critical chance, we'd have:

212-272 * (1 + median(0, (120 / 200), 1) * (0.75 + 0.25 + 200 / 1,000))
212-272 * (1 + median(0, 0.6, 1) * 1.2)
212-272 * (1 + 0.6 * 1.2)
212-272 * 1.72 = 364.64-467.84 damage on average, or to take it a step further, 416.24 average damage

DoTs (Damage over Time...s) are effects inflicted on a target which deal damage to them at the start of each of their turns for a set number of turns; they're isolated and somewhat unique from other damage in that they can't crit or miss and are unaffected by any Boost you may have (though the hit that inflicts this effect on the enemy is treated as any normal skill), so the formula is rather unconnected to the rest. They're also rather unique in that, whereas almost all 'standard' skills have the same multipliers for both weapon damage and stat damage, DoTs in particular have a tendency to use differing percentages of the two, often only making use of weapon damage and ignoring stat damage entirely, other than Dex's secondary flat DoT damage bonus which is always applied the same way (except when it isn't applied at all, like with DoTs that deal damage based on your HP...). This does vary on a skill by skill basis, and is honestly not often documented in Encyclopedia entries either as nailing down the exact mechanics is difficult. When DoT effects do make use of stat damage, the stat damage is determined by the hit that inflicts the DoT, not the type (Melee, Pierce or Magic) of the DoT itself; if, for example, a DoT does Magic damage, but the hit that inflicts the DoT was Melee, the DoT will make use of your Str rather than your Int. So, while DoTs are very convoluted and not often fully documented, if you do know the details then you can make use of this formula for whatever ratio of weapon:stat damage that they may have:

DoT damage = ceiling((Weapon Damage * Weapon Multiplier + floor(Str or Dex or Int / 10) * Stat Multiplier + ceiling(Dex / 10)) * (100 - Relevant Resistances) / 100))

Using the previous stats; Metal Melee weapon with 75-100 weapon damage and 109 Str, let's add in 250 Dex and assume a DoT effect that does 25% weapon damage and 0% stat damage, against -30 Metal but 10 All Resistance:

ceiling((75-100 * 0.25 + floor(109 / 10) * 0 + ceiling(250 / 10)) * (100 - -30 - 10) / 100))
ceiling((18.75-25 + 0 + 25) * (120 / 100))
ceiling((18.75-25 + 25) * 1.2)
ceiling(43.75-50 * 1.2)
ceiling(52.5-60) = 53-60 damage per turn

Now of course, sometimes we're not trying to figure out damage inflicted in a particular situation but just want to do a comparison between two classes/skills and nothing else, so don't care about the enemy or our weapon or stats (though crit chance and crit damage still need to be taken into account since those things do vary between classes/skills); in that case, we'd use this:

Average skill damage = Skill Multiplier * (1 + Boost / 100) * (1 + Crit / 200 * (0.75 + Class Crit Modifier + INT / 1,000))

So, assuming the same crit chance as before of 60% and 200 INT for crit damage, say we have a skill that does 150% damage, and the class has a 30% Boost buff and a +25% Crit Modifier, and we want to compare it to a skill that does 120% damage with +20% crit chance (+40 Crit) on a class that has a 50% Boost buff, but no bonus to critical damage:

1.5 * (1 + 30 / 100) * (1 + 120 / 200 * (0.75 + 0.25 + 200 / 1,000)-------------------------------_1.2 * (1 + 50 / 100) * (1 + 160 / 200 * (0.75 + 200 / 1,000)
1.5 * 1.3 * (1 + 0.6 * 1.2)--------------------------------------------------------------------------------1.2 * 1.5 * (1 + 0.8 * 0.95)
1.95 * 1.72 = 3.354, or 335.4% damage on average--------------------------------------------------1.8 * 1.76 = 3.168, or 316.8% damage on average

If we then wanted to tailor this to some particular situation, we just multiply our Dmg by this amount and any relevant resistances; the order doesn't matter since it's all just multiplication, so I don't think an equation is necessary for that.

But of course, the damage inflicted on hits and crits is only part of the story; to find the real average damage we'd expect to do, we need to get into chance to hit. When determining chance to hit, there are 2 separate rolls involved; you roll a random number from 1-150 and add your Bonus to that number, and if it's higher than your enemy's MPM then you pass that roll and do the same thing again vs BPD if applicable. In order to get a full hit you have to pass both rolls, but failing one or both can lead to differing outcomes: The MPM roll takes precedence over the BPD roll, in that if you fail the MPM roll, then it stops there and you can't get a glancing blow, you get a full miss. Likewise, Direct Hit and Critical Miss are done on the MPM roll, and if Direct Hit activates you skip everything else and get an automatic hit while if Critical Miss activates you get an automatic full miss (do keep in mind though that, as noted in the Secondary Stats section, those do not activate unless your normal hit chance would fall outside of their bounds). And of course, Critical Hits can't be glancing blows, so those bypass the BPD roll as well. So with all that in mind:

Full hit chance = median(median(0, ((1 + Attacker's Luk / 25) / 150), 1), ((1 - median(0, ((Defender's Melee or Pierce or Magic - Attacker's Bonus) / 150), 1)) * (1 - median(0, ((Defender's Block or Parry or Dodge - Attacker's Bonus) / 150 * (1 - median(0, (Attacker's Crit / 200), 1))), 1))), 0.993)

So, say we've got an attacker with 60 Bonus, 120 Crit and 225 Luk going up against a defender who has 100 MPM and 130 BPD:

median(median(0, ((1 + 225 / 25) / 150), 1), ((1 - median(0, ((100 - 60) / 150), 1)) * (1 - median(0, ((130 - 60) / 150 * (1 - (0, (120 / 200), 1))), 1))), 0.993)
median(median(0, ((1 + 9) / 150), 1), ((1 - median(0, (40 / 150), 1)) * (1 - median(0, (70 / 150 * (1 - median(0, 0.6, 1))), 1))), 0.993)
median(median(0, (10 / 150), 1), ((1 - median(0, 0.267, 1)) * (1 - median(0, (0.467 * (1 - 0.6)), 1))), 0.993)
median(median(0, 0.067, 1), ((1 - 0.267) * (1 - median(0, (0.467 * 0.4), 1))), 0.993)
median(0.067, (0.733 * (1 - median(0, 0.187, 1))), 0.993)
median(0.067, (0.733 * (1 - 0.187)), 0.993)
median(0.067, (0.733 * 0.813), 0.993)
median(0.067, 0.596, 0.993) = 0.596, or a 59.6% chance to hit in total.

Alright, so we've got damage and we've got overall hit rate, but there's one last factor that needs to be considered; the previous formula tells us how many full hits we can expect to land, for inflicting effects that require such a thing for example, and we know that the only way to get a Glancing Blow is if a hit: is not a Miss; is not a Crit; is not a Direct Hit; is not a Critical Miss; has passed the MPM roll; and finally fails the BPD roll. That's a lot of restrictions to limit the significance of these pseudo-hits, however they're still an important factor especially when shield skills that buff BPD come into play, so we need to know how to find their chance. We've already gone over all the necessary information, so it's just a matter of doing the math; to get your Glancing Blow chance, you multiply your chance to fail the Glancing Blow roll by your chance to succeed at the MPM roll. To be sure of your results, your final Glancing Blow chance + your independent chance to fail the MPM roll + your full-hit chance will always equal 1, as being a probability the sum of all options has to equal 100%:

Note: "min(x,y)" and "max(x,y)" means to use whichever variable within the parentheses is the smallest (for min) or largest (for max). So, for example, min(0.2, 0.7) = 0.2, max(0.5, 0.6) = 0.6
Glancing blow chance = min(max((median(0, ((1 + Attacker's Luk / 25) / 150), 1)), (1 - median(0, ((Defender's MPM - Attacker's Bonus) / 150), 1))), 0.993) * median(0, ((Defender's BPD - Attacker's Bonus) / 150 * (1 - median(0, (Attacker's Crit / 200), 1))), 1)

So, using the same numbers as for the full hit-rate:

min(max((median(0, ((1 + 225 / 25) / 150), 1)), (1 - median(0, ((100 - 60) / 150), 1))), 0.993) * median(0, ((130 - 60) / 150 * (1 - median(0, (120 / 200), 1))), 1)
min(max((median(0, ((1 + 9) / 150), 1)), (1 - median(0, (40 / 150), 1))), 0.993) * median(0, (70 / 150 * (1 - median(0, 0.6, 1))), 1)
min(max((median(0, (10 / 150), 1)), (1 - median(0, 0.267, 1))), 0.993) * median(0, (0.467 * (1 - 0.6)), 1)
min(max((median(0, 0.067, 1)), (1 - 0.267)), 0.993) * median(0, (0.467 * 0.4), 1)
min(max(0.067, 0.733), 0.993) * median(0, 0.187, 1)
min(0.733, 0.993) * 0.187
0.733 * 0.187 = 0.137, or a 13.7% chance of a glancing blow.

So, now all that's left is to unify them to get a real expected damage value for any given situation. This is rarely - if ever - necessary, but it's fairly simple since we've already defined and solved almost all the necessary information - the only thing missing being the amount of damage the glancing blows will do, which as mentioned in the Secondary Stats section is 25% minus your Dex modifier. So with that in mind:

Real average damage = Average raw damage * Full hit chance + Base damage * (0.25 - Dex / 1,500) * Glancing blow chance

So, using all previous example numbers:

364.64-467.84 * 0.596 + 212-272 * (0.25 - 250 / 1,500) * 0.137
217.33-278.83 + 212-272 * (0.25 - 0.167) * 0.137
217.33-278.83 + 212-272 * 0.083 * 0.137
217.33-278.83 + 17.60-22.58 * 0.137
217.33-278.83 + 2.41-3.09 = 219.74-281.92

And that's it! You now know the rules and quirks to calculate any combat-related things you may desire. :)


Thanks to:

-- The DragonFable Encyclopedia and the contributors thereof for links and information.
-- Ashendal and Verlyrus for being awesome coders, giving the stats more meaning and being transparent in their exact effects.
-- dracojan, the previous owner.
-- All past, present and future DragonFable staff for creating this great game!
-- LouisCyphere and Solanaceae for helping me think through formulae


dracojan's credits
Thanks to the people who have helped on my guide:
Sakurai the Cursed, ClashOfTheTitans57, Elicius, Epsilon2012, gold, Baron Dante, Lord Vrael, Peachii, Mordred, nightslayer321, Therril Oreb, HellsWolf666, Wyker, Watashig, Ash and everybody on the forums.

< Message edited by Sakurai the Cursed -- 11/12/2018 9:59:11 >
AQ DF MQ AQW Epic  Post #: 2
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