Comparing Warrior Rifle and Ranger Shortbow
Since both Bleeding Shot and Crossfire are skills with similar effects, I decided to make a comparison of them. My aim is to show how coefficients can help determining optimal builds. Numbers on this page apply to character that is level 80 using exotic-grade weapons.
Bleeding Shot deals 155 damage and 255 bleeding damage over 6 seconds. It has attack speed of approximately 0.96 attacks per second. It means that over long period of time we can expect it to deal (155+255)/0.96 = 427 damage per second with standard values.
Crossfire deals 134 damage and 128 bleeding damage over 3 seconds. It has attack speed of approximately 0.50 attacks per second. Over long period of time we can expect it to deal (134+128)/0.5 = 524 damage per second with standard values.
Next we can find out coefficients for Bleeding and power. Coefficient is part of a formula that tells us how skill scales with power. For power the coefficient is derived from this formula (courtesy of user Capric): damage = (skill-specific coefficient) * (average weapon damage) * power / (2600). In other form: coefficient = damage * 2600 / ((average weapon damage) * power). Bleeding Shot has coefficient 155 * 2600 / (1095.5 * 916) = 0.40. Crossfire has coefficient of 134 * 2600 / (952.5 * 916) = 0.40. Coincidentally the coefficients are exactly the same, since shortbows have lower average damage than rifles.
Important note to make is that power-based attacks are reductible by armor, while Condition Damage is non-reductible.
Skill coefficient is an essential part of the formula, but as I tested it doesn't answer the important question: "How much damage do I get on this skill if I increase my Power by some number X?". To find out how much each point in Power adds to damage, we have to use the formula (average weapon damage) * (skill specific coefficient) / 2600. For Bleeding Shot that number is 1095.5 * 0.40 / 2600 = 0.169 "base". For Crossfire that number is 952.5 * 0.4 / 2600 = 0.147 "base" . Note that these numbers are what skill tooltips say. They are automatically compared against target with 2600 armor. This armor value is quite high. A "glass cannon" Ranger with no increased toughness has 1980 armor in PvP, making attacker's power-to-damage coefficients for Bleeding Shot and Crossfire 0.22 and 0.19 respectively.
Since direct damage attacks can hit critically and Critical Damage can also be increased, we have to increase this coefficient. Since attacks can either crit or not crit but not both, we're dealing with discrete problem here. Expected damage = damage * (1.00 - critical chance) + damage * critical chance * (1.50 + 0.01 * Critical Damage). Default critical chance is 4% and critical damage increase 0, making the formula above Expected damage = 0.96*damage + 0.06*damage = 1.02*damage. 1.02 is the number we can use to multiply our Power-to-damage coefficient for default case. Bleeding Shot: 0.172 "default", Crossfire: 0.150 "default"
Condition Damage to Bleeding damage coefficient
Bleeding coefficient is simply 0.05 times duration of condition in seconds (only full seconds count). For Bleeding Shot that number is 0.30 and Crossfire that number is 0.15. Assumption we're making here is that conditions are allowed to run their whole course. While power-to-damage coefficient can be increased by Precision, critical chance and critical damage modifiers, the only thing increasing Condition Damage coefficient are modifiers increasing condition duration. Since all conditions tick their damage once per second, there exists breakpoints where full seconds are rounded.
All of this comes down to a simple comparison. Which number is bigger: Condition damage coefficient or Power-to-Damage coefficient? We don't know the armor our enemies are going to have, so the default (2600) is a reasonable assumption. Every character creation begins with a build. That is, selecting the trait slots that give unique benefits that are difficult to measure. Once traits and weapon has been selected, it's time to compare coefficients on our most frequently used skills.
Let's do this. Level 80 Warrior. I'll be using a Rifle and expecting to spam Bleeding Shot quite a bit. Default comparison is 0.172 to 0.30 Power vs. Condition Damage. I'll go with the default Knight's set of insignias (+50 power). I want Death from Above to prevent death when jumping from cliffs. I take Deep Cuts, Crack Shot and Furious in Arms tree. I finish by taking Leg Specialist in Tactics and Heightened Focus and Sweet Revenge in Discipline tree. This gives us base stats 100 power, 300 Condition Damage. Critical damage is increased to 20 and critical chance to 18%, or rather 27% with 3rd level of Heightened focus. One of our traits also gives +10% damage against bleeding foes, so that final power coefficient becomes 0.20 from base value. Deep Cuts increases our bleeding duration from 6 seconds to 9 and coefficient to 0.45.
The answer is clear: if I'm to deal maximum damage with rifle autoattacks as Warrior, I'm going to take Condition Damage as first priority in equipment. If I slot PvP Carrion Amulet with Carrior jewel, it gives me 923 Condition Damage, or as the Condition Damage coefficient tells us 923 * 0.45 = 415 Bleeding damage. Traits and runes in this build I've selected give me 150 * 0.20 + 300 * 0.45 = 165 damage for autoattack.