 # Gaige Smaller, lighter, faster

Hey all, I’m back with another thread of questionable math and skill analysis, this time focusing on Electrical Burn, with a bit of Evil Enchantress later on. Anyway, I’m out of introductory buttcrap, so let’s get into it.

TL;DR? Just read the analysis section.

This thread is based on some of Adabiviak’s work, the important things to take away from this are as follows:

EB can proc on any tick of a given Shock DoT
EB can proc more than once on a given shock DoT
EB has an equal chance of procing on any given tick
When EB procs after the first proc, it cancles the previous fire DoT and starts fresh
EB is unaffected by DoT chance increasing effects

A little background from elsewhere:

the fire DoT’s damage from EB is based on the damage of the shock DoT
Evil Enchantress (and other DoT damage increases) apply to both the shock and fire DoTs
the previous 2 points result in the fire DoT being increased by the square of the buff
fire DoTs have 15 ticks
shock DoTs have 6 ticks
any other background will be provided in the the thread when it becomes relevant

This first graph has a lot of information in it, but hopefuly I can explain it well enough so that it makes sence.

Basicaly, both axes refer to time, denoted in DoT ticks, however, the Y-axis only refers to the first 6, each tick of the shock DoT, while the X-axis refers to possible ticks of fire DoTs (note that the first 6 ticks of the X-axis coinside with the ticks on the Y-axis).
The first row (row 2) refers to the fire DoT that could proc from the first tick of the shock DoT, which also starts on the first tick, and it has (in this case, with 5/5 EB) a 20% proc chance, so over a large number of trials the damage it puts out is equal to 20% of the shock DoT’s damage.
Since all ticks in a given DoT effect do (almost) the same damage, it follows that the next 14 ticks will also recive 20% damage from the shock tick.
From there, the next 5 rows function the same, starting on ticks 2-6 respectively.
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The “total” row is the composite of the damage delt in that given tick, given by this equasion:

C=1-(1-B)^n

Where:
C: the composite damage value for that tick
B: the proc chance for EB
n: the number of potential fire DoT ticks that tick

The “sum” value is simply the sum of all of the composites, and the “smpl” value is the overal equasion for determining the damage modifier for a single Shock DoT:

F=2*((6 – (((1-B)^1) + ((1-B)^2) + ((1-B)^3) + ((1-B)^4) + ((1-B)^5) + ((1-B)^6))) + 4*(1-(1-B)^6))

Where:
F: the overall multiplier for fire damage from EB, assuming no other damae bonuses, if you multiply the damage from a single shock DoT tick buy this number you will get the average amount of fire damage you should expect from any given shock DoT
B: the proc Chance from EB

###If anyone knows a simpler way to calculate this, I would appreciate if you let me know

Plotting the average overall damage and the chance for EB to proc at least once (refer to this thread for an explanation of where the true chance comes from) results in this sheet:
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The important part of this sheet is that it illustrates that EB continues adding damage, even after the chance to proc one fire DoT is very high and the chance per rank starts to diminish quite rapidly. I think what causes this is the chance for the second or third procs is still increasing strongly and extending the fire DoT duration.

[note to self: add analysis of higher proc counts]

Finally, this sheet lists the net overall modifiers based on ranks of both Electrical Burn and Evil Enchantress. the light gray area is only accessible with a L.Catalyst COM, and the dark gray is not possible.
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EE applies to both the shock and fire DoTs, and since the damage of the fire DoT is based on the shock DoT you can

This sheet can be used to compare the value of skillpoints for the distribution in a build.
I think it’s worth noting at this point that EB does not increase your maximum potential damage, it only shifts the average to be closer to that theoretical maximum, while EE will increase both the average and the maximum, by the same amount.

[note to self: make a graphic that more easiy demonstrates the weird trends in the modifier for this section]

###Analysis:
EB does a lot more than just give you a small chance to proc a fire DoT from a shock DoT, with the right setup, it can do quite a lot of damage, espicaly concidering the recent fix to Wires Don’t Talk.
The optimal point alocation, depends a lot on what COM you want to use, here are some quick guidelines:
[fill this in]

A few final notes:

Slag is applied to both the fire and shock DoTs, so to see how it effects the fire damage of EB, you have to square it (same as EE)
Elemental effect damage from BAR can just be added to the EE modifer and squared as normal, however, damage type specific Elemental effect damage (like the fire damage from the SoT COM) can only be added to the fire portion (this means you have to multiply the fire and shock modifiers, rather than just squaring)
Elemental damage (WDT or Bone of Ancients) should be multiplied in, if you have a shock bone and WDT, add the bonuses, if you have WDT and a fire bone, they act on different elements, so multiply them both in.

Anyway, thanks for reading this, I look forward to any feedback y’all have. 