SA + Weapon Skill – STR vs Attack

Weapon Skill Damage Formula:

 

Damage = [( D + fSTR + WSC) * fTP] * (PDIF +1)

D = Weapon Damage
fSTR = number the represents our STR vs target VIT difference (note: there is lower and upper cap; see more info on fSTR here).
WSC = Secondary Attribute (see more info on WSC here)
fTP = multiplier for weapon skill (usually dependent on TP, see more info on fTP here)
pDIF = uses your attack and enemy defense to determine your damage lower and upper range. (see more info on pDIF here)

The weapon skill we will look at is Yukikaze, Gekko, Kasha which have the same fTP and WSC.

 

Values:
fSTR = (STR – enemy VIT +4)/4

α = variable to scale down your WSC when you level up (α = 0.83 for lvl 75)
WSC = floor( floor((STR * 75%)) * α )

fTP = 1.5, 2.0, 2.5 for 100%TP, 200%TP, 300%TP respectively.

Ratio = Attack /Defense
dlvl = Enemy level – your level (if you are higher level dlvl = 0)
cRatio = Ratio – 0.050 x dlvl

pDIF max:

Ratio Range	Function Value
0 < Ratio < 0.5	fMax(cRatio) = 0.4 + 1.2 x Ratio + 1
0.5 < Ratio < 0.83	fMax(cRatio) = 1 + 1
0.83 < Ratio < 2	fMax(cRatio) = 1.2 x Ratio + 1

pDIF min:

Ratio Range	Function Value
0 < Ratio < 1.25	fMin(cRatio) = -0.5 + 1.2 x cRatio + 1 if fMin < 0 < fMin = 0
1.25 < Ratio < 1.5	fMin(cRatio) = 1 + 1
1.5 < Ratio < 2	fMin(cRatio) = -0.8 + 1.2 x cRatio + 1

We compare weapon skill at 100% TP with Hagun, fTP = 2.0.

Effect of Attack on Damage

if we derive the damage w.r.t. attack we can see the effect of attack on damage,

for simplicity,

let B = [D + fSTR +WSC] * fTP and C = 0.050 x dlvl

Ratio Range	Function Value – MaxD
0 < Ratio < 0.5	B * [ 1.4 + 1.2 * [(Att /Def)- C] ]
0.5 < Ratio < 0.83	B * [2]
0.83 < Ratio < 2	B * [ 1.2 * [(Att /Def)- C] +1]

now lets find d(MaxD)/d(Att)

Ratio Range	Function Value – d(MaxD)/d(Att)
0 < Ratio < 0.5	B * 1.2 * (1/Def)
0.5 < Ratio < 0.83	0
0.83 < Ratio < 2	B * 1.2 * (1/Def)

for MinD

Ratio Range	Function Value – MinD
0 < Ratio < 1.25	B * [ 0.5 + 1.2 * [(Att /Def)- C] ]
1.25 < Ratio < 1.5	B * [2]
1.5 < Ratio < 2	B * [ 0.2 + 1.2 * [(Att /Def)- C] ]

find d(MinD)/d(Att)

Ratio Range	Function Value – d(MinD)/d(Att)
0 < Ratio < 1.25	B * 1.2 * (1/Def)
1.25 < Ratio < 1.5	0
1.5 < Ratio < 2	B * 1.2 * (1/Def)

As you can see the derivative is the same as non SA WS which means Attack affects max and min damage in the same way.

Merit Monster

Greater Colibri Level 82 Def 327 VIT 67 AGI 67 Evasion 341

For Hagun, Tarutaru, SAM/THF on lvl 82 Greater Colibri (WS w/ SA gear shown here)
STR = 65 Base + 55 Gear +5 meat mithkabob + 10 Hasso = 135
fSTR = (135 – 67 +4) / 4 = 16 (capped)
WSC = floor( floor((135 * 75%)) * 0.83 ) = 83
fTP (100) = with Hagun and weapon skill gorget 2.1
B = [D + fSTR +WSC] * fTP = (75 + 16 + 83) * 2.1 = 365.4

Therefore,
B * 1.2 * (1/Def) = 365 *1.2 * (1/327) = 1.339..

I weapon skill in 382 Attack, with meat mithkabob (+ 22% caps at 60, +5STR) with Hasso, which gives me 450 Attack with out Bard. My cRatio = 457 / 327 – 0.05 * 7 = 1.026..

cRatio = 1.026.. which is 0 < Ratio < 1.25 and 0.83 < Ratio < 2 will give me,
d(MaxD)/d(Att) = B * 1.2 * (1/Def) = 1.026..
d(MinD)/d(Att) = B * 1.2 * (1/Def) = 1.026..
In my worst situation without a BRD and Dia 2, I will be gaining 1.339 points of damage of max and min damage for every attack increase. That’s 1 more weapon skill damage every attack I add into my setup.

High Level Monster with High Defense

Since we do not know the Higher level monster’s VIT and their defense. We will just have to make assumptions and guess to generalize things.

Assumptions: Our attack < their defense (Att / Def < 1) and their level is 85. cRatio = Att /Def -0.05 * dlvl = Att /Def -0.05 * 10 = Att /Def -0.5 , then cRatio < 0.5 so we know our, d(MaxD)/d(Att) = B * 1.2 * (1/Def)
d(MinD)/d(Att) = B * 1.2 * (1/Def)
Since they are the same we know it takes the same amount of attack to raise the min and max damage.

Hagun’s weapon rank = floor (75 / 9 ) = 8
which means the fSTR range is -8 to 16. (see more weapon rank info here)
since B = [75 + fSTR + WSC] * fTP
B [fSTR= -8] = [75 + -8 + 83] * 2.1 = 315
B [fSTR= 16] = [75 + 16 + 83] * 2.1 = 365
therefore B has the range of 315 to 365.

Monster Defense	High VIT B * 1.2 * (1/Def)	Low VIT B * 1.2 * (1/Def)	Attack needed to increase 1 Damage
500	315 *1.2 *(1/500) = 0.756	365 *1.2 *(1/500) = 0.876	1.1 to 1.3
600	315 *1.2 *(1/600) = 0.63	365 *1.2 *(1/600) = 0.73	1.3 to 1.5
700	315 *1.2 *(1/700) = 0.54	365 *1.2 *(1/700) = 0.625	1.5 to 1.8
800	315 *1.2 *(1/800) = 0.472	365 *1.2 *(1/800) = 0.547	1.8 to 2.1

Effect of STR on Damage

Now we need to look at STR’s effect on Damage by deriving it w.r.t. STR. Since Attack is also a function of STR we will keep things simple here and keep Attack constant.

Damage = ( D + fSTR[STR] + WSC[STR]) * fTP * PDIF

let E = fTP * PDIF
Damage = (D + floor((STR -VIT +4)/4) + floor(floor(STR * 75%)*0.83)) *E
d(Damage)/d(STR) = E*floor'(STR/4) + E*floor'(floor'(3/4STR) *0.83)

Merit Monsters

Using the same example,

Greater Colibri Level 82 Def 327 VIT 67 AGI 67 Evasion 341

fTP = 2.1
cRatio = 1.026..
PDIF min = -0.5 + 1.2 * 1.026.. + 1= 1.731..
PDIF max = 1.2 * 1.026.. + 1= 2.231..

E min = 0.758.. * 2.1 = 3.635..
E max = 1.258.. * 2.1 = 4.685..

Weapon Rank = floor ( D /9 ) = 8
fSTR max = 2 * Weapon Rank = 16
fSTR min = -1 * Weapon Rank = -8

fSTR = (135 – 67 +4) / 4 = 16 (capped)135
therefore increasing anymore STR in this case will not increase fSTR

d(maxD)/d(STR) = 3.635.. *floor'(floor'(3/4STR) *0.83)
d(minD)/d(STR) = 4.685.. *floor'(floor'(3/4STR) *0.83)

Since we cannot derive the floor function I will list the effect per STR increase.

STR increase (total STR)	min increase	max increase	min increase per STR	max increase per STR
1 (136)	5	6	5	6
2 (137)	5	6	2.5	3
3 (138)	10	12	3.33	4
4 (139)	12	14	3	3.5
5 (140)	16	20	3.2	4
6 (141)	16	20	2.66	3.33
7 (142)	21	26	3	3.71
8 (143)	25	30	3.12	3.75
9 (144)	28	34	3.11	3.77
10 (145)	28	34	2.8	3.4
11(146)	33	40	3	3.63
12 (147)	36	44	3	3.67
Average :			2.97	3.61

The average min damage increase per STR in these last 11 STR increase is 2.97 damage and max damage increase per STR in these 12 STR increase is 3.61.

500
High Level Monster with High Defense

Since we do not know the Higher level monster’s VIT and their defense. We will just have to make assumptions and guess to generalize things.

Assumptions: Our attack < their defense (Att / Def < 1) and their level is 85. cRatio = Att /Def -0.05 * dlvl = Att /Def -0.05 * 10 = Att /Def -0.5 , then cRatio < 0.5 Defense: 500

STR increase (total STR)	min increase	max increase	min increase per STR	max increase per STR
1 (136)	5	8	5	8
2 (137)	5	8	2.5	4
3 (138)	8	13	2.66	4.33
4 (139)	9	15	2.25	3.75
5 (140)	14	23	2.8	4.6
6 (141)	14	23	2.33	3.83
7 (142)	17	28	2.42	4
8 (143)	19	32	2.37	4
9 (144)	20	35	2.22	3.88
10 (145)	20	35	2	3.5
11(146)	23	39	2.09	3.54
12 (147)	25	43	2.08	3.58
Average :			2.33	3.90

Defense: 600

STR increase (total STR)	min increase	max increase	min increase per STR	max increase per STR
1 (136)	4	7	4	7
2 (137)	4	7	2	3.5
3 (138)	6	12	2	4
4 (139)	7	13	1.75	3.25
5 (140)	11	21	2.2	4.2
6 (141)	11	21	1.83	3.5
7 (142)	14	25	2	3.57
8 (143)	15	28	1.87	3.5
9 (144)	17	31	1.88	3.44
10 (145)	17	31	1.7	3.1
11(146)	19	35	1.72	3.18
12 (147)	21	38	1.75	3.16
Average :			1.88	3.49

Defense: 700

STR increase (total STR)	min increase	max increase	min increase per STR	max increase per STR
1 (136)	3	7	3	7
2 (137)	3	7	1.5	3.5
3 (138)	5	11	1.66	3.66
4 (139)	6	13	1.5	3.25
5 (140)	9	20	1.8	4
6 (141)	9	20	1.5	3.33
7 (142)	11	23	1.57	3.28
8 (143)	12	27	1.5	3.37
9 (144)	14	29	1.55	3.22
10 (145)	14	29	1.4	2.9
11(146)	16	33	1.45	3
12 (147)	17	36	1.41	3
Average :			1.53	3.31

Defense: 800

STR increase (total STR)	min increase	max increase	min increase per STR	max increase per STR
1 (136)	2	7	2	7
2 (137)	2	7	1	3.5
3 (138)	4	10	1.33	3.33
4 (139)	5	12	1.25	3
5 (140)	8	16	1.6	3.2
6 (141)	8	16	1.33	2.66
7 (142)	9	22	1.28	3.14
8 (143)	11	25	1.37	3.12
9 (144)	12	27	1.33	3
10 (145)	12	27	1.2	2.7
11(146)	13	30	1.18	2.72
12 (147)	15	33	1.25	2.75
Average :			1.28	3.01

ConclusionMerit Monster-

Each STR will increase an average of 2.97 point of min damage and 3.61 max damage increase while every point of attack will give you 1.339 point of min and max damage increase therefore STR is a lot better than attack for this situation.

High level Monster-

As shown above, for monster with defense of 500-800 it takes 1 to 2 attack to increase max and min damage by 1 point while 1 STR can increase 1.28 to 2.33 points of min damage and 3.01 to 3.9 points of max damage. Again STR is a lot better than attack for this situation.

STR is always better than Attack for SA + Weapon Skill.