Below are the calculations to determine the effective increase to the power strike of a character using an heirloom weapon in place of the normal version of the same weapon.
From the mechanics megathread:Damage = BWD * (PS * 0.08 + 1) * Held Weapon Damage Bonus * WPF Damage Bonus + Strength Bonus Damage
Where:
Damage is the damage dealt prior to modifications for armor and speed bonus.
BWD is the base weapon damage for the normal version of the weapon.
PS is power strike ranks of the characters.
Held Weapon Damage Bonus is a modifier based on the time the attack is held before release.
WPF Damage Bonus is a modifier that takes into account WPF in the weapon type.
Strength Bonus Damage is a modifier that takes into account the character strength.
Heirloom Bonus Damage (HBD from here on) and Bonus Power Strike (BPS from here on) can be added such that:
Damage1 = (BWD +
HBD) * (PS * 0.08 + 1) * Held Weapon Damage Bonus * WPF Damage Bonus + Strength Bonus Damage
Damage2 = BWD * ((PS +
BPS) * 0.08 + 1) * Held Weapon Damage Bonus * WPF Damage Bonus + Strength Bonus Damage
Where both Damage1 and Damage 2 represent the increase damage due to using an heirloom weapon in place of the normal version. Damage1 is written such that the increase damage is done by increasing the weapon damage through the addition of the bonus damage of heirlooms (this is how the system actually works,) but Damage2 can also be written such that the heirloom provides the same increase to damage by adding power strike ranks. For a fair comparison, BWD, PS, Held Weapon Damage Bonus, WPF Damage Bonus, and Strength Bonus Damage are all held as constants. To determine how many ranks of power strike heirlooms effectively add, Damage1 and Damage2 can be made equal such that:
Damage1 = Damage2
(BWD + HBD) * (PS * 0.08 + 1) = BWD * ((PS + BPS) * 0.08 + 1)
The above equation can be rearranged and simplified to:
HBD/BWD = (BPS * 0.08) / (PS * 0.08 + 1)
And further rearranged to:
BPS = (HBD * (PS * 0.08 + 1)) / (0.08 * BWD)
From this equation the equivalent bonus to power strike from an heirloom can be determined as a function of the actual power strike ranks, the base damage of the weapon, and the bonus damage added by the heirloom ranks. Below is a plot showing the equivalent bonus to power strike as a function of base weapon damage for a character with 6 ranks of power strike.
Increasing the actual power strike ranks of a character increases the equivalent bonus to power strike from an heirloom while decreasing the actual power strike ranks of a character decrease the equivalent bonus to power strike from an heirloom. The differences are less than 1 equivalent bonus rank to power strike for most weapons (damages greater than 25) and the most typical amounts of power strike (3-9).
The effective WPF increase for using an heirloom weapon with increased speed can be determined in a similar fashion.
Also from the mechanics mega thread:Time per attack with a weapon at 1 WPF:
T0 = 2.47 sec 0.014 sec * Spd
where Spd is the speed rating of the weapon. Time per attack as a function of T0 and WPF:
T = T0(Spd) * (100 0.065 * WPF)
For a change in time per attack for an increase T0 from T0(Spd1) to T0(Spd2):
deltaT0 = T0(Spd2) * (100 0.065 * WPF) - T0(Spd1) * (100 0.065 * WPF)
deltaT0 = (T0(Spd2) - T0(Spd1)) * (100 0.065 * WPF)
For a change in time per attack for an increase in WPF from WPF1 to WPF2
deltaT = T0 * (100 0.065 * WPF2) T0 * (100 0.065 * WPF1)
deltaT = -0.065 * T0 * (WPF2 - WPF1)
deltaT = -0.065 * T0 * deltaWPF
The change in time per attack from increasing weapon speed is equal to the change in time per attack from increasing WPF (that is deltaWPF) is when:
deltaT0 = deltaT
(T0(Spd2) - T0(Spd1)) * (100 0.065 * WPF) = -0.065 * T0(Spd1) * deltaWPF
deltaWPF = ((T0(Spd2) - T0(Spd1)) * (100 0.065 * WPF)) / (-0.065 * T0(Spd1))
From this equation the equivalent bonus to WPF for time per attack from an heirloom can be determined as a function of the base WPF of the character, the base speed of the weapon, and the heirloom bonus to speed. The plot below shows the equivalent bonus to WPF for time per attack from an heirloom granting +1 speed as a function of the base WPF of the character and the base weapon speed.
From this plot if can been seen that the equivalent bonus to WPF for time per attack from an heirloom is around 15 to 20 WPF for typical weapon speeds and base WPF values. This amounts to multiple ranks worth of weapon master for a level 30 character placing the majority of their proficiency skill points into a single weapon type.
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