[Info] Base Stats Table and Stats Calculation

Arrandale · 5-26-2015 18:09:01

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.

Level	DMG	CRIT	SPD	HP	DEF	EVA
1	58	4	4	351	25	8
2	58	4	4	366	26	9
3	60	5	5	390	26	10
4	61	6	6	424	27	12
5	63	7	7	468	29	14
6	66	8	8	522	31	17
7	69	10	10	585	33	20
8	73	12	12	658	35	24
9	77	14	14	741	38	28
10	82	16	16	834	41	33
11	87	19	19	936	45	38
12	92	22	22	1048	48	44
13	99	25	25	1170	52	50
14	105	28	28	1302	57	57
15	112	32	32	1443	61	64
16	120	36	36	1594	66	72
17	128	40	40	1755	72	80
18	136	44	44	1926	78	89
19	145	49	49	2106	84	98
20	155	54	54	2296	90	108
21	165	59	59	2496	97	118
22	175	64	64	2706	104	129
23	186	70	70	2925	111	140
24	198	76	76	3154	118	152
25	210	82	82	3393	126	164
26	222	88	88	3642	135	177
27	235	95	95	3900	143	190
28	248	102	102	4168	152	204
29	262	109	109	4446	162	218
30	277	116	116	4734	171	233
31	292	124	124	5031	181	248
32	307	132	132	5266	191	264
33	323	140	140	5504	202	280
34	339	148	148	5744	213	297
35	356	157	157	5987	224	314
36	373	166	166	6233	235	332
37	391	175	175	6482	247	350
38	409	184	184	6733	260	369
39	428	194	194	6986	272	388
40	447	204	204	7241	285	408
41	467	214	214	7498	298	428
42	487	224	224	7758	312	449
43	508	235	235	8020	325	470
44	529	246	246	8283	339	492
45	551	257	257	8548	354	514
46	573	268	268	8816	369	537
47	596	280	280	9084	384	560
48	619	292	292	9355	399	584
49	643	304	304	9627	415	608
50	667	316	316	9901	431	633
51	691	329	329	10176	448	658
52	716	342	342	10453	464	684
53	742	355	355	10731	481	710
54	768	368	368	11010	499	737
55	795	382	382	11291	516	764
56	822	396	396	11573	534	792
57	849	410	410	11856	553	820
58	877	424	424	12140	572	849
59	906	439	439	12426	591	878
60	935	454	454	12713	610	908
61	964	469	469	13000	630	938
62	994	484	484	13420	650	969
63	1025	500	500	13847	670	1000
64	1056	516	516	14280	690	1032
65	1087	532	532	14720	711	1064
66	1119	548	548	15167	733	1097
67	1152	565	565	15621	754	1130
68	1184	582	582	16082	776	1164
69	1218	599	599	16549	799	1198
70	1252	616	616	17024	821	1233
71	1286	634	634	17505	844	1268
72	1321	652	652	17993	867	1304
73	1356	670	670	18488	891	1340
74	1392	688	688	18989	915	1377
75	1428	707	707	19498	939	1414
76	1465	726	726	20013	963	1452
77	1503	745	745	20535	988	1490
78	1540	764	764	21064	1014	1529
79	1579	784	784	21600	1039	1568
80	1617	804	804	22142	1065	1608
81	1657	824	824	22692	1091	1648
82	1696	844	844	23248	1118	1689
83	1737	865	865	23811	1144	1730
84	1777	886	886	24381	1171	1772
85	1818	907	907	24958	1199	1814
86	1860	928	928	25541	1227	1857
87	1902	950	950	26132	1255	1900
88	1945	972	972	26729	1283	1944
89	1988	994	994	27333	1312	1988
90	2032	1016	1016	27944	1341	2033

*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:

Source	DMG Stats
Base DMG Stat at Lvl-72	1321
Zither of Gaia	22787+9343
Gaia Emblem	905
Maro's Thorny Feet	1390
Yimis's Inspiring Grip	1365
Jesper Energized Alloy Belt	871
Total	37982

Fixed DMG Stat Value Sources:

Source	DMG Stats
Digging Lvl-2	840
DMG Title Bonus	1775
Warm Heart Fishing Rod	1301
Golden Warrior Fishing Set	1860+2415
Summoned Aelius	0.1*26900
Total	10881

DMG % Sources:

Source	DMG %
DMG Stat Points	37*0.35%
Orange Divine Power Mastery	9%
Costume Enchantments	13%
Murfeo's Immortal Oath	1%
Total	35.95%

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

CRIT
(1/λ) = 260.7

Scalable CRIT Stat Value Sources:

Source	CRIT Stats
Base CRIT Stat at Lvl-72	652
Zither of Gaia	696-49
Forbidden Tome	675-75
Ruth's Charm Amulet	554
Murfeo's Immortal Oath	476
Total	2929

Fixed CRIT Stat Value Sources:

Source	CRIT Stats
Summoned Aelius	0.1*6228
CRIT Title Bonus	315
Total	937.8

Flat CRIT % Sources:

Source	CRIT %
Total	0%

CRIT % on CRIT Stat Value Sources:

Source	CRIT %
Costume Enchantments	5%
Total	5%

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

SPD
(1/λ) = 260.7

Scalable SPD Stat Value Sources:

Source	SPD Stats
Base SPD Stat at Lvl-72	652
Zither of Gaia	658
Murfeo's Immortal Oath	436
Rose's Fragrant Ring	349
Pyatic's Thorned Necklace	325
Ox King's Scarred Belt	222
Titan Warrior Headgear	519
Titan Warrior Battle Coat	585
Total	3746

Fixed SPD Stat Value Sources:

Source	SPD Stats
Summoned Aelius	0.1*8185
Murfeo's Immortal Oath	362
Ruth's Charm Amulet	477
Total	1657.5

Flat SPD % Sources:

Source	SPD %
SPD Stat Points	66*0.3%
Envoy Path	5.5%
Total	25.3%

SPD % on SPD Stat Value Sources:

Source	SPD %
Costume Enchantments	5%
Fortification effects of Forbidden Tome	1%
Total	6%

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

HP

Scalable HP Stat Sources:

Source	HP Stats
Base HP Stat at Lvl-72	17993
Zither of Gaia	2321+251
Forbidden Tome	1962+375
Gaia Emblem	2784
Ruth's Charm Amulet	2271
Rose's Fragrant Ring	1242+286
Pyatic's Thorned Necklace	1399+287
Ox King's Scarred Belt	1031+356
Maro's Thorny Feet	1780+107
Yimis's Inspiring Grip	1925+331
Jesper Energized Alloy Belt	981
Titan Warrior Headgear	2133
Titan Warrior Battle Coat	2384
Total	42181

HP % Sources:

Source	HP %
Envoy Path	12%+20%
Costume Enchantments	13%
Titan Warrior Headgear	1%
Titan Warrior Battle Coat	1%
Maro's Thorny Feet	2%
Yimis's Inspiring Grip	2%
Jesper Energized Alloy Belt	2%
Zither of Gaia	5%
Storm Song SS	8%+2%
Shadowbolt SS	8%+2%
Total	78%

Fixed HP Stat Value Sources:

Source	HP Stats
Fishing Lvl-2	549
Survive and Adapt Set HP Bonus	2847
HP Title Bonus	2427
Summoned Aelius	0.1*40626
Total	9885.6

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

DEF
(1/λ) = 260.7

Scalable DEF Stat Value Sources:

Source	DEF Stats
Base DEF Stat at Lvl-72	867
Maro's Thorny Feet	1424+584
Yimis's Inspiring Grip	1404+505
Jesper Energized Alloy Belt	1239+446
Titan Warrior Headgear	1745+489
Titan Warrior Battle Coat	1985+476
Total	11164

Fixed DEF Stat Value Sources:

Source	DEF Stats
Summoned Aelius	0.1*15044
Total	1504.4

Flat DEF % Sources:

Source	DEF %
DEF Stat Points	0.2*47
Total	9.4%

DEF % on DEF Stat Value Sources:

Source	DEF %
Costume Enchantments	5%
Murfeo's Immortal Oath	1%
Envoy Path	4%
Total	10%

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

EVA
(1/λ) = 260.7

Scalable EVA Stat Value Sources:

Source	EVA Stats
Base EVA Stat at Lvl-72	1304
Forbidden Tome	831
Ruth's Charm Amulet	964
Murfeo's Immortal Oath	746
Rose's Fragrant Ring	612
Pyatic's Thorned Necklace	542
Ox King's Scarred Belt	418
Maro's Thorny Feet	599
Yimis's Inspiring Grip	599
Jesper Energized Alloy Belt	401
Titan Warrior Headgear	751
Titan Warrior Battle Coat	815
Total	8582

Fixed EVA Stat Value Sources:

Source	EVA Stats
Summoned Aelius	0.1*7247
EVA Title Bonus	333
Charming Scent Set EVA Bonus	1043
Furious Titan Warrior Set EVA Bonus	493
Orange Capoeira Mastery	0.03*62517
Total	4469.21

Flat EVA % Sources:

Source	EVA %
Aelius 3-star Buffs	15%
Gaia Emblem	3%
5 EVA 2% SS	10%
Total	28%

EVA % on EVA Stat Value Sources:

Source	EVA %
Maro's Thorny Feet	2%
Yimis's Inspiring Grip	2%
Jesper Energized Alloy Belt	2%
Costume Enchantments	5%
Orange Extreme Speed	6%
Total	17%

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

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