Introduction:So as not to be outdone by Skittles, I’ve decided to write up a guide concerning a question that was posed a few nights ago in guild chat. The question regarded which “DPS” sigil (Fire, Strength, Force, Night) was most optimal to run for a particular build, and the answers that were given were quite varied. Since there was some opinion as to which was best I decided to do some math on the matter.
The most important thing to note about this is
different builds will yield different results with the exception of Night being superior to Force when conditions for the Night sigil are met. This means you’ll have to do math if you really care to optimize sigils for any particular build. There are a lot of variables associated this, but the math is very straightforward and I’ve done all the work is determining which equations to use for what.
DPS Sigil Spreadsheet  You still need to calculate Skill Specific Coefficient yourself. See that section for details.
Things you need to know about your build in order for this to work:1.)
Power – The number next to power in the hero panel. This is not the same as Attack.
2.)
Precision – The number next to Precision in the hero panel.
3.)
Critical Damage – The number next to Critical Damage in the hero panel. This does not include the base 50%, but the formula in this guide does. Just plug in the hero panel’s number.
4.)
Base Damage Modifiers – Any traits that give +X% damage. (Not Critical damage) Do not include modifiers from Force or Night sigils in this number.
5.)
Weapon Strength – This is the average damage of your weapon(s). For example, on my axe the range is 900 to 1100, so the average is 1000. Weapon strength is also equal to the difference between the values of Attack and Power in the hero panel.
6.)
Skill Rotation Time and strikes per rotation – Time will be in seconds. For example, one rotation of Axe auto attack on Warrior is 3.6 seconds with 6 strikes. If you auto attack a lot you can use that, but if you hardly auto attack you’ll want to use your other skills.
7.)
Skill Specific Coefficient – This one is a little trickier. I’ll have a section on how to calculate this.
8.)
Bonuses – This includes any bonuses to Power, Precision, Crit Chance, Critical Damage, potential Might stacks (not including Sigil of Superior Strength), Fury, etc. that are not included in the numbers on the hero panel. For example if there aren’t any banners down you won’t get a boost for it even if it is on your bar. Heightened Focus, a warrior trait in the Discipline line provides a 15% boost to Crit Chance that will not show up on the hero panel. The best way to be sure if you have a trait like this is to swap out the trait and see if a number changes. If it does not change you’ll have to add it manually.
Some other useful information to you:1.)
Might – Each stack of might provides 35 Power.
2.)
Superior Sigil of Fire – The Skill Specific Coefficient for this skill is 1.0. 30% chance to trigger on crit, 5 second cool down.
3.)
Sigil of Superior Strength – 30% chance on crit to gain might for 10 seconds. It has a 1 second cool down. Because it has a cool down of 1 second and the might lasts for 10 seconds, the maximum might stacks you can get from this is 5. This equates to a maximum of 175 power.
Formulas and other mumbojumbo:This section is going to detail how to calculate the effectiveness of these sigils using my Warrior build as an example. It’s helpful to write out your variables beforehand, so for my Warrior’s build the variables are:

Power:
2879 (Base + 3xMight from FGJ + Banner of Str + Empower Allies)

Crit Damage:
143% = 1.43 (Base + Sweet and Spicy Butternut Squash Soup)

Precision:
2250 (Base + 25 Perception stacks + Banner of Disc + Signet of Fury)

Base Damage Modifiers:
30% = .3 (Strength traits V and XI, Scholar Runes)

Additional Crit Chance:
35% = .35 (Fury, Heightened Focus)

Weapon Strength:
1080 (Ascended Axe, Ascended Mace)

Skill Specific Coefficient:
1.2 (I’ll show calculations for this in a later section)

Rotation (Strikes/seconds):
6 Strikes, 3.6 Seconds (Axe Auto Attack chain)
Crit Chance: Spoiler:

You may have noticed a distinct lack of crit chance in the above sections. This is because crit chance is calculated based on Precision. If you stack Precision with a Sigil of Perception and do not have the stacks when you write down your crit chance you’ll have to add it in manually anyway. This just makes things a little bit simpler.
*This number is then rounded down.*
Warrior Example:Crit Chance caps at 100%, so this value is actually 100%, or 1.
Skill Specific Coefficients: Spoiler:

This is the fun bit. The equation you use to calculate this is:
Variables:Damage is equal to the combined total of the damage listed in the tooltip of the skills in the rotation being used divided by the number of times you’re attacking. It is just the average damage of the attacks in your chain. It should be noted, however, that some of the damage information in the tooltips do not include Weapon Damage in their calculation so look on wiki before you add them up.
Warrior Example:Target Armor is the same for all skills in this section. The game uses an armor value of 2600 to calculate the damage tooltip, so we use an armor value of 2600 to find the SSC.
Warrior Example:Power is equal to your power while you’re noting your skill damage. It doesn’t matter if you have buffs, but make sure you are consistent. It’s easier to just use base power with no might stacks because the numbers won’t change while you’re recording them.
Warrior Example: Note that this power is different from the power listed earlier. This is base power for the build, so it doesn’t include any buffs.
Weapon Damage is the same as it is in the sections above.
Warrior Example: SSC is our unknown. We are solving for this.
Calculating SSC in the Warrior Example:So, the average SSC for the skill rotation I’m using for Warrior is 1.2, and this is the value that will be used in the equations.
PROC of Sigil of Fire, Sigil of Strength: Spoiler:

The effectiveness of these sigils is based on how often they can activate, which is affected by their internal cool down, your crit chance, and your attack speed. To calculate the efficiency of these sigils with your build you’ll need to know the rate at which they will need to PROC (programmed random occurrence) to be maximally efficient. You’ll need your crit chance, your attacks per second, and the internal cool down of the sigils.
To calculate the percentage of your attacks that PROC:
Warrior Example:To calculate the percentage of your attacks that need to PROC for Superior Sigil of Fire to be maximally efficient, where n is the number of foes hit per attack:
Warrior Example:This means that for Sigil of Fire to PROC every 5 seconds against 1 foe, a PROC rate of 0.12 is needed. You’ll notice that the rate for this build is .3 PROCs per Attack, which is higher than the threshold number. This means that the build can PROC the Superior Sigil of Fire’s flame burst every 5 seconds. For thresholds where n>1, the required PROCs per attack will decrease in size so if Threshold
_{1} is less than your PROC percentage on hit you will not need to calculate anything else.
For the final equation you will also need the number of time the Superior Sigil of Fire will PROC during your chain. This is obtained my dividing the chain’s time (3.6 seconds in this example) by the cool down of the sigil (5 seconds). For the warrior example it is 0.72.
To calculate the percentage of your attacks that need to PROC for Sigil of Superior Strength to be maximally efficient, where n is the number of foes hit per attack:
Warrior Example:No cleave:Unlike the Superior Sigil of Fire, the Threshold
_{1} for this sigil to be maximally efficient is much higher than the PROC on hit rate for my warrior build. This means that the maximum amount of Might stacks obtained from PROCing the Sigil of Superior strength is a ratio of the PROC on hit rate to this threshold multiplied by the maximum possible Might stacks from the sigil. For this example the equation will look like:
Cleaving n:This means in order for my warrior build’s PROC on hit to meet the threshold and provide 10 stacks of might, you must be attacking at least 2 enemies. This information will be useful later for when cleave damage and single target damage calculations are performed later.
Damage of Superior Sigil of Fire: Spoiler:

The formula for this is the same as damage. The SSC is 1, so the formula looks like:
Warrior Example:This number will get rounded down to the nearest whole number.
The Big Equation: Spoiler:

At this point all of the information needed to calculate the effectiveness of the different sigils is available. The Formula used is a combination of two formulas used to calculate Base Damage and Average Damage in regards to critical hits. The damage formula is the same one used in calculating the SSC, except damage becomes the unknown and SSC is a defined variable. Together the two formulas look like this:
Variables:

BDM: Base Damage Modifiers (+X% damage buffs, not including crit damage buffs)

CC: Crit Chance (range of 0 – 1)

CD: Crit Damage

M_{n}: Maximum number of might stacks gained from the sigil when hitting n enemies

Fire: Damage inflicted by Flame Burst

x: Number of foes being hit by Flame Burst (range 15)

n: Number of foes being cleaved

PPC: PROCS per Chain (Chain time divided by 5 seconds)
Now that you see this, you’ll notice that the outcome changes depending on how many foes you hit with your attacks. Because of this, we’ll have to perform the operations a total of 3 times for each sigil, and a total of 5 times for Fire because the flame blast hits 5 enemies.
For the five calculations for the fire sigil, n will remain at 3 for when x is 4 and 5.
If you’re still reading this it means you either like math or you’re good at it. If that’s the case I’m going to assume you can finish this on your own, and I’m just going to make a spreadsheet for everyone else. I’m tired of typing out equations…