# Diablo 3 Barbarian Mace vs Sword Calculation for Weapon Master passive [Math]

kenshin-
• Diablo 3 Barbarian Mace vs Sword Calculation for Weapon Master passive [Math] kenshin-

i need some help choosing my weapons in Diablo3 as a Barbarian.

Im trying to solve it mathematically and not just try-by-try or in Excel with long tables so maybe someone with more experience in using programs like Maple or Mathematica (Wolfram Alpha, yeah.. but it kinda didnt cut it) can help out. Probably i just need some help on some math syntax for any good math program to solve my problem with a plotted graph.

As a barbarian, the passive trait "Weapon master" offers either +15% Damage on swords and daggers or +10% critical hit chance on maces and axes.

So my average damage on a mace is something like this:

``````Mace: Damage+Damage*(CritChance%/100+0.1)*CritDamage%/100
``````

My average damage on a sword is something like this:

``````Sword: Damage*1.15+Damage*1.15*(CritChance%/100)*CritDamage%/100
``````

We assume that Damage is 1 for both weapons.

``````"Mace" 1+1*(CritChance%/100+0.1)*(CritDamage%/100)
"Sword" 1.15+1.15*(CritChance%/100)*(CritDamage%/100)

CritChance=x CritDamage=y
``````

A mace would do more damage per hit for "Mace/Sword">1 and for values <1 the sword does more damage.

``````(1+1*(x/100+0.1)*(y/100))/(1.15+1.15*(x/100)*(y/100))>=1
``````

We can safely limit "CritChance" to >=5<=60(the total max on gear was between 50 and 60 somewhere with perfect rolls, lets just limit to 60 because of skills - it also avoids the problem that x/100+0.1 for 100% critchance would reach 1,1 which of course does not make sense - a general solution to this would be welcome nontheless (maybe using x1 and x2 with different assumed limits?) and CritDamage to >=50<=650.

``````Assumptions:
x and y are rational and positive.
x>=5<=60
y>=5<=650
(1+1*(x/100+0.1)*(y/100))/(1.15+1.15*(x/100)*(y/100))>=1
``````

Can someone point me to the correct Maple/Mathematica syntax for making this a nice plot?

I want to see the answer to "For which range of critchance and critdamage does 10% critchance deal more damage than 15% damage?" in a plot. Ofc, damage, critrate and critdamage that are inserted are the same, only the result differs because of the modifiers in the formula.

Any help is really appreciated. Thanks in advance.

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