Hey everyone,

recently on the discord there again was a dicussion if Undisputed is the best weapon for bleed damage. I decided to make some short evaluation and plots to show that a not-exalted Nagasa Symitar is better most of the time while providing another open suffix for utility.

# Undisputed

- 1.05 base attack rate
- Chance to bleed (implicit, 12 - 30%)
- Increased attack speed (20 - 27%)
- Up to 255% increase physical damage from buff effect

# Optimal Nagasa (T15 + X)

- 1.24 base attack rate
- Increased damage over time (implicit, 26 - 56%)
- Increased physical (70 - 105%)
- Increased attack speed (21 - 26%)
- Chance to Bleed on Hit (40 - 53%)
- Suffix of choice; possibly health on hit or ignite on hit

# Optimal case for Undisputed

- 51/4 hits per second → 255% increase from undisputed
- Requires an attack rate of 0.0784313725 in a single target fight
- Default attack rate: 0.68182
- Undisputed default attack rate (5% more attack speed, 27% increased attack speed): 0.511301087
- Solving 0.68182 / 1.05 / (1. + 0.27 + x) == 0.0784313725 yields x = 7.00924286 → 701% increased attack speed required to reach breakpoint
- Best case will rarely be achieved in a single target fight; even though most attacks are a little faster than default attack; doubled default attack rate (Warpath) still requires 350% increased attack speed

# Dual wielding: Undisputed + Nagasa → Two Nagasa

- 8.2% more hits (8.2% more damage) → 55/4 hits per second
- 255% - (56% + 105%) = 94% → -94% increased damage for bleeds
- +23% bleed on hit chance
- Increase attack speed difference at best 1% (not accounted for)

# Single weapon: Undisputed → Nagasa

- 18% more hits (18% more damage) → 60/4 hits per second
- 255% - (56% + 105%) = 94% → -94% increased damage for bleeds
- +23% bleed on hit chance
- Increase attack speed difference at best 1% (not accounted for)

# Numerics

- Dual Wielding assumes Nagasa in Offhand (1.24 default attack rate)
- Attack rate with Undisputed normalized to 1
- Bleed damage normalized to 1
- More multipliers and similar stats like bleed effect/duration can be neglected as they are multiplicative
- Simplified damage formula:

damage = (1. + increase_damage / 100) * (attack_rate) * (bleed_on_hit_chance / 100)- Undisputed: attack_rate = 1.
- Dual Wield Nagasa: attack_rate = 1.082
- Single Nagasa: attack_rate = 1.18

- Relative damage increase when replacing Undisputed with a T15 Nagasa (-94% increase, +23% chance to bleed, more attack speed):
- Dual Wield:

z = ((1. + x / 100 - 0.94) * 1.082 * (y / 100 + 0.23)) / ((1. + x / 100) * y / 100) - Sword and Board:

z = ((1. + x / 100 - 0.94) * 1.18 * (y / 100 + 0.23)) / ((1. + x / 100) * y / 100) - x = increases, y = bleed chance

- Dual Wield:

# Visualized

The following image show your relative damage increase when switching from an Undisputed to a T15 + X Nagasa like described above.

The values you have to look on the x and y axes are the stats you have while you have the Undisputed equipped. For x you must sum up all increases of the type generic, physical, damage over time and physical damage over time provided by gear and skills which apply the bleed (mostly attribute increases as the others generally provide more multipliers). Do not trust the character sheet since some increases are added to multiple rubrics.