## weapon damage modeling and comparisons

A guildie once asked me how to compare the damage rate for 2 weapons that incorporates the use of special attacks. Here's a simple technique to do so:

Routine A:
Simulate the damage done from a normal hit by rolling 1-20 each 1 time, and then averaging by dividing by 20. There are plenty of posts on how to do this so I'm not going to dwell on it here, but this is where you will take into account base damage, critical profile, enhancement bonus, weapon effects, damage bonus from attributes, feats, enhancements, gear, and destinies, damage mitigation, fortification, and confirm critical rolls (if you choose). This produces an average damage per hit result indicated by variable D0. Then we multiply by the rate of attack 1/T0, which has contributions from BAB, haste, boosts, etc. This will produce an average DPS result that we can call x0 = D0/T0.

Routine B:
Simulate the damage done from special attacks by running routine A (rolling dice 1-20 but with special bonuses) with each special attack such as cleave, producing the value D1. By using a special attack, you are giving up the time required to produce normal attacks, For cleave, it's approximately 1 normal attack or so, but for momentum swing it's about 2. Let's represent the time taken for this attack by T1, which are tabulated in the forums somewhere. The additional DPS contribution from using a special attack is then (D1 - x0*T1)/T1 = D1/T1 - x0. However, this only works if the ability has no cooldown. If the cooldown time of the ability is C1, then the final additive DPS bonus for using cleave is then x1 = (D1 - x0*T1)/C1.

Routine C:
Repeat routine B with each special attack to generate additive DPS bonuses x2, x3, and so on. Some, such as lay waste, are triggered off cooldown by other abilities. If momentum swing goes off cooldown with 35% chance on cleaves and great cleaves, but itself has a natural cooldown of 60s, then its average cooldown is calculated like this: every 6 seconds (cleave cooldown) there are 2 chances, each with 35% probability, for the cooldown to be reset, so let's just assume you alternate cleave and great cleave so that every 3 seconds there is a 35% chance to reset the cooldown. Thus the cooldown would be equal to the time it took you to reset it. The probability of a 3s cooldown is .35. The probability of a 6s cooldown is .65 * .35. The probability of a 3*n second cooldown would be .35 * .65^(n-1), up to n=19 (57s, since 60s is just guaranteed). The probability of the 60s cooldown would finally be just .65^19. The average cooldown of momentum swing is then C2 = Sum( 3n*.35*.65^(n-1), n = integers 1 to 19 inclusive ) + 60*.65^19 seconds. You can then use this average cooldown to figure out using the same process, the average cooldown of lay waste.

Result:
The average DPS of the weapon would be x0 + x1 + ...
Then repeat the routines for the second weapon that you want to compare to.