# Melee – STR vs Attack

Melee Damage Formula:

Damage = (D + fSTR) * pDIF
D = Weapon Base Damage
fSTR
= number the represents our STR vs target VIT difference (note: there is lower and upper cap; see more info on fSTR here).

Values:
D = 75
fSTR = floor(STR – enemy VIT +4)/4
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 cRatio 0.5 < Ratio < 0.83 fMax(cRatio) = 1 0.83 < cRatio < 2 fMax(cRatio) = 1.2 x cRatio

pDIF min:

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

Damage range in terms with STR and Attack will be calculated by,
MaxD = [D + (STR – VIT +4)/4] * fMax[(Att /Def)- 0.050 x dlvl]

MinD = [D + (STR – VIT +4)/4] * fMin[(Att /Def)- 0.050 x dlvl]
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 + (STR – VIT +4)/4] and C = 0.050 x dlvl

 Ratio Range Function Value – MaxD 0 < cRatio < 0.5 B * [ 0.4 + 1.2 * [(Att /Def)- C] ] 0.5 < cRatio < 0.83 B *  0.83 < cRatio < 2 B * [ 1.2 * [(Att /Def)- C] ]

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

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

for MinD

 Ratio Range Function Value – MinD 0 < cRatio < 1.25 B * [ -0.5 + 1.2 * [(Att /Def)- C] ] 1.25 < cRatio < 1.5 B *  1.5 < cRatio < 2 B * [ -0.8 + 1.2 * [(Att /Def)- C] ]

find d(MinD)/d(Att)

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

We are usually most concerned with EXP monsters and high level monsters.

Merit Monster

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

For Hagun, Tarutaru, SAM/THF on lvl 82 Greater Colibri (TP gear shown here)
STR = 65 Base + 21 Gear +5 meat mithkabob + 10 Hasso = 101
B = 75 + (101 – 67 +4) / 4 = 84

Therefore,
B * 1.2 * (1/Def) = 84 * 1.2 (1/327) = 0.308..

I TP with 377 Attack, with meat mithkabob (+ 22% caps at 60, +5STR) with Hasso, which gives me 445 Attack with out Bard. My cRatio = 445 / 327 – 0.05 * 7 = 1.011..

cRatio = 1.011.. which is 0 < cRatio < 1.25 and 0.83 < cRatio < 2 will give me,

d(MaxD)/d(Att) = B * 1.2 * (1/Def) = 0.308..
d(MinD)/d(Att) = B * 1.2 * (1/Def) = 0.308..

In my worst situation without a BRD and Dia 2, I will be gaining 0.308 points of damage of max and min damage for every attack increase. Which means every 3.24 attack I increase I will gain 1 more point higher max and min damage.

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), it has more VIT than Greater Colibri (67 VIT) 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 = [D + (STR – VIT +4)/4] = 75 + fSTR
B[fSTR = -8] = 75 – 8 = 67
B[fSTR = 9] = 75 + 9 = 84 (assuming VIT is less than 67)
therefore B has the range of 67 to 84.

 Monster Defense High VIT B * 1.2 * (1/Def) Low VIT B * 1.2 * (1/Def) Attack needed to increase 1 Damage 500 67 * 1.2 * (1/500) = 0.161 84 * 1.2 * (1/500) = 0.202 5 to 6.2 600 67 * 1.2 * (1/600) = 0.134 84 * 1.2 * (1/600) = 0.168 6 to 7.5 700 67 * 1.2 * (1/700) = 0.115 84 * 1.2 * (1/700) = 0.144 6.9 to 8.7 800 67 * 1.2 * (1/800) = 0.101 84 * 1.2 * (1/800) = 0.126 7.9 to 10

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.

MaxD = [D + (STR – VIT +4)/4] * fMax[(Att /Def)- 0.050 x dlvl]
MinD = [D + (STR – VIT +4)/4] * fMin[(Att /Def)- 0.050 x dlvl]

d(MaxD) / d(STR) = 1/4 * fMax[(Att /Def)- 0.050 x dlvl]
d(MinD)
/ d(STR) = 1/4 * fMin[(Att /Def)- 0.050 x dlvl]

MaxD

 Ratio Range Function Value – d(MaxD)/d(STR) 0 < cRatio < 0.5 1/4 * [0.4 + 1.2 * [(Att /Def)- C]] 0.5 < cRatio < 0.83 1/4 *  0.83 < cRatio < 2 1/4 * [1.2 * [(Att /Def)- C] ]

MinD

 Ratio Range Function Value – d(MinD)/d(STR) 0 < cRatio < 1.25 1/4 * [ -0.5 + 1.2 * [(Att /Def)- C] ] 1.25 < cRatio < 1.5 1/4 *  1.5 < cRatio < 2 1/4 * [ -0.8 + 1.2 * [(Att /Def)- C] ]

Merit Monsters

Using the same example,

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

cRatio = 1.011.. calculated above

d(MaxD)/d(STR) = 1/4 * [ 1.2 * 1.011] = 0.303
d(MinD)/d(STR)
= 1/4 * [ -0.5 + 1.2 * 1.011] = 0.178

This means every STR increase will increase max by 0.303 damage and increase min by 0.178 damage. Which means it will take 3.3 STR to increase my max damage and 5.62 STR to increase my min damage. Do remember fSTR is floor, so it would take 4 STR to increase max and 8 STR to increase the min damage.

High Level Monster with High Defense

I will compare in similar fashion as Attack. Again we do not know their Defense or VIT.

Assumptions: Our attack < their defense (Att / Def < 1), it has more VIT than Greater Colibri (67 VIT) and their level is 85. cRatio = Att /Def -0.05 * dlvl = Att /Def -0.05 * 10 = Att /Def -0.5 , then cRatio < 0.5 ignoring the floor in fSTR, we know our, d(MaxD)/d(STR) = 1/4 * [0.4 + 1.2 * (Att/Def)]
d(MinD)/d(STR) = 1/4 * [-0.5 + 1.2 * (Att/Def)]
therefore B has the range of 67 to 82 (assuming VIT is less than 67)

 Monster Defense d(MaxD)/d(STR) = 1/4* [0.4 + 1.2 * (Att/Def) -0.5*dlvl] STR needed to increase 1 Damage 500 1/4* [0.4 + 1.2 * (445/500 – 0.5)] = 0.217 4.6 600 1/4* [0.4 + 1.2 * (445/600 – 0.5)] = 0.173 5.8 700 1/4* [0.4 + 1.2 * (445/700 – 0.5)] = 0.141 7.1 800 1/4* [0.4 + 1.2 * (445/800 – 0.5)] = 0.117 8.6

now for d(MinD)/d(STR)

 Monster Defense d(MaxD)/d(STR) = 1/4* [-0.5 + 1.2 * (Att/Def)] STR needed to increase 1 Damage 500 1/4* [-0.5 + 1.2 * (445/500 – 0.5)] = 0 N/A 600 1/4* [-0.5 + 1.2 * (445/600 – 0.5)] = 0 N/A 700 1/4* [-0.5 + 1.2 * (445/700 – 0.5)] = 0 N/A 800 1/4* [-0.5 + 1.2 * (445/800 – 0.5)] = 0 N/A

Conclusion

Merit Monster-
Attack is always better than STR for TP build, as it takes less attack to increase max damage and at the same time it will increase min damage for the same amount while it would take more STR to increase the same amount of min damage.

High level Monster-

I ignored the 2STR giving 1 Attack earlier. Now I add the extra attack given by the STR increase to the Attack side to give its equivalence. From example below, a 500 Defense monster, increasing 8 STR would be equivalent to increasing 5 – 6.2 Attack (depending on VIT) plus 4 attack (from 8STR) to increase the max damage by slightly over 1 point. Also adding the fact that fSTR only changes every 4 STR increase due the floor function means we need to add STR in multiple of 4.

 Defense STR (theory STR) Attack 500 8 (4.6) 9 – 10.2 600 8 (5.8) 10 – 11.5 700 8 (7.1) 10.9 – 12.7 800 12 (8.6) 13.9 – 16

The difference is not big but STR is usually more expensive than Attack gear.

STR increase in those defense range have no way to increase the lower range of your damage on these high defense monster. Increasing max by 1 point of damage would only increase your median by 0.5, while increasing max and min by 1 point would increase your median by 1 point. Again here attack is more beneficial where it can increase max and min damage at the same time.

Do note that attack doesn’t always increase minimal damage if the defense is too high you need to still be in range.

All these calculations are without buff and debuff and do not put critical hits into account as those are rare. This strictly for improving the worst case scenario for my SAM. Although the same logic applies to other jobs and weapons but the amount of STR and attack stated above is based on my stats and gear, which will differ with jobs, subjobs, race, and merits.

Attack is always better than STR for melee hits to increase both your MAX and MIN damage at the same time.