# [Guide] Electrical Burn and its contribution to damage output

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.

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:

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.

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.

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Thanks for taking the time to do all this math, even if I don’t understand a lick of it lol.

^.^ tell me about it. It’s a bit rough, I’ll come back and make it more reader friendly eventually, but for now y’all’r just gunna have to deal with my awkwardness for now. I’ll try to fix it up faster than my last few threads though.

Why do you have a collumn for damage in the EB table ?

EB’S damage is based on the shock DoT damage, it doesn’t go up with ranks in the skill.
Is it an average damage taking into consideration the odds of EB proccing or not ?

A note to add: You should mention that Slag applies twice, just like EE and WDT

And finally: great work Wings!

the EB damge bit is one if the things I really need to fix. For now, this will have to do:

If you look at the first table, basicaly, the more ranks you have in EB, the higher your median damage is, because you have a higher likelyhood of procing a Fire DoT and a higher likelyhood of having that fire DoT up for longer.
The “damage” I refer to in this thread is the average amout of fire DoT damage you get from a very large sample of shock DoTs.

Good point about the slag, I totaly forgot about that with all of the DoT stuff, Thanks.

Thanks! I apreciate that!

Regarding the multiple procs:
(@Chuck80, Ping!)

The multiple procs thing is based on a few of the things Ada said in the EB chance thread, specificaly:

and

He decribes the observed behavior much better than I would have, so here’s his discription:

(this part is partialy a note-to-self)
However, there was a bunch of stuff in there that I havn’t dealt with (yet), including the following:

and

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Ok that makes sense, thanks

Higher proc chance mean more chance to apply, and more chance that EB procs sooner in the Shock dot’s life (making the process of re-applying faster, resulting in higher damage over a long period of time)

But Burn DoTs are always 5 seconds
…Or I misunderstood you somewhere

Bookmarking to see what you guys reason out. Wonderful job, Wings.

It’s way too late in this timezone for me to think straight, but is there a clear formula for the synergy with anarchy and its boost to WDT?

I was on Discord earlier with a random question about it now that the electrocute damage of WDT is (supposedly) fixed, but that probably made little sense…

As will this if I keep it up. G’night.

Anarchy doesn’t affect DoTs (except when using the Storm) so the fix brings nothing new to Anarchy-focused builds.

The thing that bothers me is that when you have EB active, there is an EB icon that appears above the xp bar, suggesting a limit on it. (though it doesn’t necessarily mean anything)

I have tested EB a lot and have never seen a dual proc on one target…

That sounds like EB can proc again on a target that already has it, but they don’t stack…it simply resets the timer (and the icon’s duration)

As for the last part, it’s pretty strange… almost as if EB will not stack with any burn DoTs…even those from other sources. Maybe it’s in the way it was coded, so as not to be abusable…but it just applies to all burn DoTs.

I interpreted the multipule procing as a timer reset as well, and I’m fairly certain that the way I moddled the EB damage allows for the extension fof DoTs, but not stacking. However I’m not 100% sure, I was messing around with a few different models, including one where, in this sheet:

on the bottom row, instead of just adding up the column above it, I multiplied them together using the %chance stacking formula (1-(1-0.2)^n). My first instinct was that it worked like this, but I couldn’t find a way to work that by adding up each row first, so i decided I must have been doing something wrong and went with the adding method I have now.

I would apreciate a second on that actually, the more I think about it, I think i might have been right in the first place.

I’m pretty sure you were right the first time: chances can get asymptotically close to 100% but they will never reach it.

@Adabiviak, we need you in here

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I mentioned I was tired, right? Sorry if that made no sense.
Anarchy affects splash a very great deal, which ties into the above about reapplying DOTs where applicable and resetting the timer.
I clearly need to re-read Ab’s post to make sure I understand the process he describes of burn damage ticks being lower than the shock ones, since I’ve frequently seen the opposite.
That probably means there’s context I’m missing since I doubt I’ve been as thorough.

I’m pretty sure you are as well.

Now I really will be quiet and go to bed.

Awesome, glad to see that I wasn’t crazy at first, I’ll be updating the OP in a bit.

Also I highly recomend checking out ada’s posts in the other EB thread, it’s some good stuff.

You really are tired
Splash damage may increase from Anarchy, but DoT, even proccing from splash, will not change.

I too see the opposite, but that’s probably because the targets are flesh and/or we have DoT boost.
The base value however may be lower.

For example, let’s say that EB damage is …60% of the base shock damage…for example, and that our source creates 100dmg DoTs

100 dmg shock
Gets boosted through catalyst COM to 150 (so it displays 150 dmg)
EB procs, creates a 150 * 0.6 = 90 dmg fire DoT
which recieves the catalyst bonus too (so it’s now 135)
and then it gets the fire-on-flesh multiplier 135 * 1.75 = 236
So it displays 236 fire damage for 150 shock damage

At 68% or more, you would get higher fire damage even on a target that isn’t weak to fire, just based on the DoT boost from the Catalyst com… let alone other boosts.

Another factor is shield:

Create a shock DoT
It gets boosted by *2.5 (because shock on shield)
EB procs, based on that value
Shield is now depleted
EB’s damage is based on the shock on shield value…but is now fire on flesh, compounding both matching element bonus.

Add in a few other bonus from a Bones, WDT (now) and Slag and you can truly transform a small number into a big one.

I’ve got the new screenshots up, I haven’t fixed the text yet, but that should be reletively straight forward.

Also, here’s a link to the google doc, feel free to mess around with it a bit if you want, I have a local copy.

Hey everyone… just got off work and am getting settled in. I’m not sure what the current question is?

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Less a question, more of a rewording of your findings so we’re all on the same page.

What percentage of the shock dot is the burn one based on ?
You said it was lower than 100%

Ok (clears throat for a heck of a Scooter impersonation)

Let me throw some numbers at you! 5! 26! 812!

Seriously though, this should be easy to approximate? The variable to account for will be the difference in elemental damage against a fleshy target (since we’re all going to be lighting up the target dummy, I imagine) between fire and shock.

Assuming (grain of salt here, but I think the numbers for this are correct) the wiki is corect, shock has a multiplier of 1 against flesh (no alteration), where fire has a 1.75 multiplier against flesh. If I hit the target dummy for 100 shock damage, and the fire from Electrical Burn is hitting for 175, we would know that the fire is hitting for 100% of the value of the shock damage (and getting the buff due to the target’s health type). We could confirm against the stationary turret in Opportunity to observe a burn damage of 40 against the armored target.

Let me re-run some tests here.

edit - short version, I think the fire damage is one third of the shock damage that spawned it. If I go to Normal mode, burn damage is about half the electrocute damage that triggers it. Because the target is flesh, the fire damage gets a “free” 1.5 multiplier; if I back that out to derive the value of the original fire damage value, I get a value that’s about a third of the electrocute damage.

If I bring this to Ultimate mode, the fire damage is lower at like 26% of the electrocute damage, which I’m guessing is from the damage scaling (I’m at OP3). I’m not sure how to factor that in. Also, in UVHM, Electrical Burn against armored targets is super low… I was hoping to use this to check my method here, but 51103 electrocute damage was triggering 330 fire damage. Anyway, does that seem like a sound way to calculate this?

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