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[Data] [Info] Base Stats Table and Stats Calculation

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5-26-2015 18:09:01 | Show all posts |Reader
Edited by Arrandale at 7-8-2015 12:59

Base Stats Table

The following table shows the base stat values for each level. This is useful as the stats as shown in the character window are derived from these values.
LevelDMGCRITSPDHPDEFEVA
15844351258
25844366269
360553902610
461664242712
563774682914
666885223117
76910105853320
87312126583524
97714147413828
108216168344133
118719199364538
1292222210484844
1399252511705250
14105282813025757
15112323214436164
16120363615946672
17128404017557280
18136444419267889
19145494921068498
201555454229690108
211655959249697118
2217564642706104129
2318670702925111140
2419876763154118152
2521082823393126164
2622288883642135177
2723595953900143190
282481021024168152204
292621091094446162218
302771161164734171233
312921241245031181248
323071321325266191264
333231401405504202280
343391481485744213297
353561571575987224314
363731661666233235332
373911751756482247350
384091841846733260369
394281941946986272388
404472042047241285408
414672142147498298428
424872242247758312449
435082352358020325470
445292462468283339492
455512572578548354514
465732682688816369537
475962802809084384560
486192922929355399584
496433043049627415608
506673163169901431633
5169132932910176448658
5271634234210453464684
5374235535510731481710
5476836836811010499737
5579538238211291516764
5682239639611573534792
5784941041011856553820
5887742442412140572849
5990643943912426591878
6093545445412713610908
6196446946913000630938
6299448448413420650969
631025500500138476701000
641056516516142806901032
651087532532147207111064
661119548548151677331097
671152565565156217541130
681184582582160827761164
691218599599165497991198
701252616616170248211233
711286634634175058441268
721321652652179938671304
731356670670184888911340
741392688688189899151377
751428707707194989391414
761465726726200139631452
771503745745205359881490
7815407647642106410141529
7915797847842160010391568
8016178048042214210651608
8116578248242269210911648
8216968448442324811181689
8317378658652381111441730
8417778868862438111711772
8518189079072495811991814
8618609289282554112271857
8719029509502613212551900
8819459729722672912831944
8919889949942733313121988
902032101610162794413412033

*The data was extracted and parsed from the unpacked pkg files of the game.

Stats Equations

Equation for DMG

DMG = (Base DMG Stat + Gear DMG Stat)*(100% + DMG% from Gears + DMG% from Envoy Path + <DMG Stat Points>*0.35% + DMG% from Masteries) + DMG from Title Bonuses + DMG from Fishing Equipments + DMG from Profession (Fishing/Digging Achievements etc.) + DMG from Gear Set Bonuses + Contribution from Eidolon's Stats

Contribution from Eidolon Stats here refers to the fraction of stat values obtained when an Eidolon is summoned. It depends on the star-evolution of the Eidolon. 1-star gives 3%, 2-star gives 7% while 3-star provides 10% of the Eidolon's stat values. For example, if a 3-star evolved Aelius has a DMG stat of 26900, the Contribution from Eidolon Stats value would be 2690 and it will be added to the overall DMG without any scaling.

Equation for CRIT

CRIT (%) = Flat CRIT Increment (%) + (<CRIT Stat Points>*0.25%) + λ*[(CRIT Stat Increment (%)*(Base CRIT Stat + Gear CRIT Stat) + CRIT from Title Bonuses + Contribution from Eidolon's Stats]

where
  • Flat CRIT Increment (%): CRIT (%) from Secret Stones, Eidolon Star Buffs (Zaahir and Bel's +15% CRIT), Envoy Path, CRIT stat etc.
  • λ: Constant of proportionality relating the conversion from stat value to stat percentage (%). It varies with the character level and it is defined as follows:
    λ=[0.05*Lvl(Lvl+1) + (1.5-(Lvlx0.05))]^(-1)

    The value of (1/λ) quantifies the amount of stat value needed to maintain a 1% increase in CRIT. For example, if you're a level 70 character, (1/λ) has a value of 246.7, which means every increment of 246.7 in stat value will increase CRIT by 1%. As you can see, the value of (1/λ) increases as you level. Therefore, you would need gears with higher stats (higher-level gears etc.) to compensate for this. Note that the Flat CRIT Increment (%) and (<CRIT Stat Points>*0.25%) terms aren't affected by (1/λ), which is why they are highly-regarded in the game. It should also be noted that the expression for λ isn't limited to the calculation of CRIT. In fact, the same expression is used for the calculation of SPD, DEF and EVA.



Equation for SPD

SPD (%) = Flat SPD Increment (%) + (<SPD Stat Points>*0.3%) + λ*[(SPD Stat Increment (%)*(Base SPD Stat + Gear SPD Stat) + SPD from Title Bonuses + Contribution from Eidolon's Stats]

where
  • Flat SPD Increment (%): From Envoy Path, SPD stat.
  • λ: Same as defined in the equation for CRIT.


Equation for HP

HP = (Base HP Stat + Gear HP Stat)*(100% + %HP)*(100% + <HP Stat Points>*0.58%) + HP From Title Bonuses + Contribution from Eidolon's Stats + HP from Gear Set Bonuses

where
  • %HP: %HP from Gears, Secret Stones, Costume Enchantments, Envoy Path, lvl-70 Enchantment Cards, Masteries etc.


Equation for DEF

DEF (%) = Flat DEF Increment (%) + (<DEF Stat Points>*0.2%) + λ*[(DEF Stat Increment (%)*(Base DEF Stat + Gear DEF Stat) + DEF from Title Bonuses + Contribution from Eidolon's Stats + DEF from Gear Set Bonuses]

where
  • Flat DEF Increment (%): Don't know of any sources of this at this point in time apart from the contribution from DEF stat.
  • λ: Same as defined in the equation for CRIT.


Equation for EVA

EVA (%) = Flat EVA Increment (%) + (<EVA Stat Points>*0.35%) + λ*[(EVA Stat Increment (%)*(Base EVA Stat + Gear EVA Stat) + EVA from Title Bonuses + Contribution from Eidolon's Stats + EVA from Gear Set Bonuses]

where
  • Flat EVA Increment (%): From Eidolon Star Buffs, Secret Stones, Gaia Emblem, EVA stat etc.
  • λ: Same as defined in the equation for CRIT.


Calculation Example


I will be using my lvl-72 bard alt as an example to demonstrate the use of the aforementioned equations. First off, here are the stats as shown in the character window:

The goal here is to get those values from manual calculations. Although manual calculations may seem pointless, the verification of the equations as stipulated in the previous section can be a stepping stone to creating an AK character simulator and also, it provides us with a better understanding on how stats are being calculated in the game. Plus, with the equations at hand, mathematical constrained optimization can be performed. For example,

        maximize f(DMGStatPoints,CRITStatPoints,SPDStatPoints)
        
        subject to the contraints:
            DMGStatPoints + CRITStatPoints + SPDStatPoints = TotalATKPoints
        etc.
        


This is just a crude example but it will useful when we are considering trade-offs between various factors and we would like to answer a common question on whether a given gear should be upgraded and how beneficial would that upgrade be. Of course, that would require a more elaborate formulation of the objective function f(.).

Having said that, we shall now look at the gears that I had equipped at that time, title bonuses and the stats of my Eidolon, before going into the calculation of each stats.

Weapons


Armors








Costumes






Eidolon Stats




Title Bonuses




Calculations
DMG
Shown on the character window: 62517
NOTE: Only calculations pertaining to the primary weapon damage is shown. It is straightforward to do the same calculation for the secondary weapon damage.

Scalable DMG Stat Value Sources:
SourceDMG Stats
Base DMG Stat at Lvl-721321
Zither of Gaia22787+9343
Gaia Emblem905
Maro's Thorny Feet1390
Yimis's Inspiring Grip1365
Jesper Energized Alloy Belt871
Total37982

Fixed DMG Stat Value Sources:
SourceDMG Stats
Digging Lvl-2840
DMG Title Bonus1775
Warm Heart Fishing Rod1301
Golden Warrior Fishing Set1860+2415
Summoned Aelius0.1*26900
Total10881

DMG % Sources:
SourceDMG %
DMG Stat Points37*0.35%
Orange Divine Power Mastery9%
Costume Enchantments13%
Murfeo's Immortal Oath1%
Total35.95%


DMG = 37982*(1+0.3595)+10881 = 62517.529 (Verified)


CRIT
(1/λ) = 260.7

Scalable CRIT Stat Value Sources:
SourceCRIT Stats
Base CRIT Stat at Lvl-72652
Zither of Gaia696-49
Forbidden Tome675-75
Ruth's Charm Amulet554
Murfeo's Immortal Oath476
Total2929

Fixed CRIT Stat Value Sources:
SourceCRIT Stats
Summoned Aelius0.1*6228
CRIT Title Bonus315
Total937.8

Flat CRIT % Sources:
SourceCRIT %
Total0%

CRIT % on CRIT Stat Value Sources:
SourceCRIT %
Costume Enchantments5%
Total5%


CRIT = 0+0*0.25+λ*(1.05*2929+937.8) = 15.394% (Verified)


SPD
(1/λ) = 260.7

Scalable SPD Stat Value Sources:
SourceSPD Stats
Base SPD Stat at Lvl-72652
Zither of Gaia658
Murfeo's Immortal Oath436
Rose's Fragrant Ring349
Pyatic's Thorned Necklace325
Ox King's Scarred Belt222
Titan Warrior Headgear519
Titan Warrior Battle Coat585
Total3746

Fixed SPD Stat Value Sources:
SourceSPD Stats
Summoned Aelius0.1*8185
Murfeo's Immortal Oath362
Ruth's Charm Amulet477
Total1657.5

Flat SPD % Sources:
SourceSPD %
SPD Stat Points66*0.3%
Envoy Path5.5%
Total25.3%

SPD % on SPD Stat Value Sources:
SourceSPD %
Costume Enchantments5%
Fortification effects of Forbidden Tome1%
Total6%


SPD = 25.3+λ*(1.06*3746+1657.5) = 46.889% (Verified)


HP

Scalable HP Stat Sources:
SourceHP Stats
Base HP Stat at Lvl-7217993
Zither of Gaia2321+251
Forbidden Tome1962+375
Gaia Emblem2784
Ruth's Charm Amulet2271
Rose's Fragrant Ring1242+286
Pyatic's Thorned Necklace1399+287
Ox King's Scarred Belt1031+356
Maro's Thorny Feet1780+107
Yimis's Inspiring Grip1925+331
Jesper Energized Alloy Belt981
Titan Warrior Headgear2133
Titan Warrior Battle Coat2384
Total42181

HP % Sources:
SourceHP %
Envoy Path12%+20%
Costume Enchantments13%
Titan Warrior Headgear1%
Titan Warrior Battle Coat1%
Maro's Thorny Feet2%
Yimis's Inspiring Grip2%
Jesper Energized Alloy Belt2%
Zither of Gaia5%
Storm Song SS8%+2%
Shadowbolt SS8%+2%
Total78%

Fixed HP Stat Value Sources:
SourceHP Stats
Fishing Lvl-2549
Survive and Adapt Set HP Bonus2847
HP Title Bonus2427
Summoned Aelius0.1*40626
Total9885.6


HP = 42181*1.78*(1+0.0058*55)+9885.6 = 108918.995 (Verified)


DEF
(1/λ) = 260.7

Scalable DEF Stat Value Sources:
SourceDEF Stats
Base DEF Stat at Lvl-72867
Maro's Thorny Feet1424+584
Yimis's Inspiring Grip1404+505
Jesper Energized Alloy Belt1239+446
Titan Warrior Headgear1745+489
Titan Warrior Battle Coat1985+476
Total11164

Fixed DEF Stat Value Sources:
SourceDEF Stats
Summoned Aelius0.1*15044
Total1504.4

Flat DEF % Sources:
SourceDEF %
DEF Stat Points0.2*47
Total9.4%

DEF % on DEF Stat Value Sources:
SourceDEF %
Costume Enchantments5%
Murfeo's Immortal Oath1%
Envoy Path4%
Total10%


DEF = 9.4+λ*(1.10*11164+1504.4) = 62.276% (Verified)


EVA
(1/λ) = 260.7

Scalable EVA Stat Value Sources:
SourceEVA Stats
Base EVA Stat at Lvl-721304
Forbidden Tome831
Ruth's Charm Amulet964
Murfeo's Immortal Oath746
Rose's Fragrant Ring612
Pyatic's Thorned Necklace542
Ox King's Scarred Belt418
Maro's Thorny Feet599
Yimis's Inspiring Grip599
Jesper Energized Alloy Belt401
Titan Warrior Headgear751
Titan Warrior Battle Coat815
Total8582

Fixed EVA Stat Value Sources:
SourceEVA Stats
Summoned Aelius0.1*7247
EVA Title Bonus333
Charming Scent Set EVA Bonus1043
Furious Titan Warrior Set EVA Bonus493
Orange Capoeira Mastery0.03*62517
Total4469.21

Flat EVA % Sources:
SourceEVA %
Aelius 3-star Buffs15%
Gaia Emblem3%
5 EVA 2% SS10%
Total28%

EVA % on EVA Stat Value Sources:
SourceEVA %
Maro's Thorny Feet2%
Yimis's Inspiring Grip2%
Jesper Energized Alloy Belt2%
Costume Enchantments5%
Orange Extreme Speed6%
Total17%


EVA = 28+λ*(1.17*8582+4469.21) = 83.658% (Verified)
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