interface procs Interface Damage over Time (DoT) Procs: How to quantify their effects

[Bopper]

Interface Damage over Time (DoT) Procs

How to Quantify Their Effects

by Bopper

Written: 14 February 2020

Last updated: N/A

 

Some quick news. The bug causing Interface DoT procs to under-perform has been found and a fix should be easy enough to implement and hopefully will go live soon. With that being said, I wanted to put together a quick guide (or crib sheet, really) that details how you should quantify the effects of the Interface DoTs (once the bug is fixed, that is). This should help you decide if/which Interface DoT is right for your build. 

How do the Interface DoT procs work?

The description of the Interfaces will read as “Adds… a Minor/Moderate DoT (X% chance) to most damaging attacks”. This phrasing causes some confusion as most assume this to mean there is an X% chance that each of your attacks will add 5 ticks of Damage over Time. In actuality, the Interface procs are mechanized such that each of the DoT ticks will have an X% chance to proc; however, once a tick misses all remaining DoT ticks are cancelled. This is what’s referred to as “Cancel-On-Miss”.

How much damage do Interface DoT procs do?

There are 5 Interfaces that offer a DoT proc: Cognitive (Minor Psionic), Degenerative (Minor Toxic), Reactive (Moderate Fire), Preemptive (Moderate Energy), and Spectral (Moderate Negative Energy). The Minor damage DoTs do up to 5 ticks of 10.71 damage each, and the Moderate damage DoTs do up to 5 ticks of 13.39 damage each (25% stronger than minor damage). Those numbers assume same level enemies (refer to Purple Patch mechanics if you’re considering fighting weaker/stronger enemies).

What can I expect from a 25% DoT proc?

This is the lowest performer of the bunch as it is very likely to miss on an early damage tick, resulting in all subsequent ticks to be cancelled. That being said, what is the expected performance?

Probability and Expectation of Exactly X Ticks Proc'ing (25% DoT)

X	Prob(X)	E[X] =X*Prob(X)
0	75.00%	0
1	18.75%	0.1875
2	4.69%	0.09375
3	1.17%	0.035156
4	0.29%	0.011719
5	0.10%	0.004883
Total	100%	0.333008

These numbers tell us that on average, each attack will do 0.333 ticks of damage. Given that a Minor DoT does 10.71 damage (Major DoT does 13.39 damage), this equates to averaging only 3.57 more damage per hit (or +4.46 damage, for Major DoT).

What can I expect from a 50% DoT proc?

This is the middle performer of the bunch and is only available as a Tier 3 Interface Proc. Below is its expected performance.

Probability and Expectation of Exactly X Ticks Proc'ing (50% DoT)

X	Prob(X)	E[X] =X*Prob(X)
0	50.00%	0
1	25.00%	0.2500
2	12.50%	0.2500
3	6.25%	0.1875
4	3.125%	0.1250
5	3.125%	0.15625
Total	100%	0.96875

These numbers tell us that on average, each attack will do 0.96875 ticks of damage, which equates to averaging +10.375 and +12.969 more damage for the Minor and Major DoTs, respectively. In this case, doubling our Proc probability nearly tripled out added damage performance.

 

What can I expect from a 75% DoT proc?

This is the top performer of the bunch and is only available as a Tier 3+ Interface Proc. Below is its expected performance.

Probability and Expectation of Exactly X Ticks Proc'ing (75% DoT)

X	Prob(X)	E[X] =X*Prob(X)
0	25.00%	0
1	18.75%	0.1875
2	14.06%	0.28125
3	10.55%	0.316406
4	7.91%	0.316406
5	23.73%	1.186523
Total	100%	2.288086

These numbers tell us that on average, each attack will do 2.288 ticks of damage, which equates to averaging +24.505 and +30.632 more damage for the Minor and Major DoTs, respectively. In this case, using a 75% DoT proc instead of a 25% DoT proc has increased the average DoT output by 587% (so nearly 7x damage). Using a 75% DoT proc instead of a 50% DoT proc increased the average DoT output by 136% (more than 2x damage).

 

Can you show your work?

Spoiler

Gotcha! I will show my math later if folks really don't want to believe the numbers I just gave. Until then, be patient and I'll add numbers and formulas if you really need it.

 

Edited February 14, 2020 by Bopper

[Generator]

If the damage ticks pull their cancel-on-miss tricks, will that impact any debuffs that are applied?  Like, if Reactive stops ticking its Fire DOT, will that stop the -Res from applying?

 

Thanks very much for doing the math on this.

[Bopper]

Just now, Generator said:

If the damage ticks pull their cancel-on-miss tricks, will that impact any debuffs that are applied?  Like, if Reactive stops ticking its Fire DOT, will that stop the -Res from applying?

 

Thanks very much for doing the math on this.

The debuff is unaffected and its roll is independent of the DoT roll. I havent necessarily tested to monitor this, but when I was testing the 50% DoT proc, it had a 10% immobilize debuff proc too. Out of the 2,096 samples, I believe the immobilize proc'd about 9.6% of the time. So no impact.

[Generator]

18 minutes ago, Bopper said:

The debuff is unaffected and its roll is independent of the DoT roll. I havent necessarily tested to monitor this, but when I was testing the 50% DoT proc, it had a 10% immobilize debuff proc too. Out of the 2,096 samples, I believe the immobilize proc'd about 9.6% of the time. So no impact.

Great, thanks!

[Underfyre]

So some quick and dirty testing (as most of my "testing" is) is telling me that each ability (it does say "most damaging attacks") has a chance to independently trigger a proc, essentially adding a flat (2.288086 * 10.71 or 13.39) damage to each ability, which obviously favors low recharge abilities more than high recharge abilities.

[Bopper]

On 7/29/2020 at 1:55 PM, underfyre said:

So some quick and dirty testing (as most of my "testing" is) is telling me that each ability (it does say "most damaging attacks") has a chance to independently trigger a proc, essentially adding a flat (2.288086 * 10.71 or 13.39) damage to each ability, which obviously favors low recharge abilities more than high recharge abilities.

It does. If you have a very fast set, something like Katana, you could leverage those fast attacks for heavy DoT stacking (I think up to 8 stacks, but seeing as how the DoTs only last about 4-5 seconds you wouldn't be hitting that anyways).  Anyways, not only do you get a ton of DoTs, it also gives you more opportunity to apply debuffs as well. Debuffs last for 8.3s, so if you only have 25% chance to apply the debuff, you can likely keep a couple of debuff stacks (max 4 stacks) through the fast attacks applying more opportunities.

[Enots]

Was the bug ever fixed?

[Bopper]

6 minutes ago, Enots said:

Was the bug ever fixed?

I think so

[tripthicket]

Reading over this, I'm still a bit fuzzy, so I may be asking a question you've already answered. I vaguely recall reading that, with Reactive Radial Interface, if the 25% chance of defense debuff doesn't go off, the DOT will never even get checked. Thus, I've been telling a folk or three to choose Core instead. This would seem to be a misinterpretation of the inner mechanics as you described them above.

 

My new understanding: Reactive Radial/Core will do their percentage checks independently for the debuff and the DOT, and their own percentage chances will determine how effective they each are. One does not affect the other.

 

Have I gotten that right?

Edited July 16, 2022 by tripthicket

[Bopper]

18 minutes ago, tripthicket said:

Reading over this, I'm still a bit fuzzy, so I may be asking a question you've already answered. I vaguely recall reading that, with Reactive Radial Interface, if the 25% chance of defense debuff doesn't go off, the DOT will never even get checked. Thus, I've been telling a folk or three to choose Core instead. This would seem to be a misinterpretation of the inner mechanics as you described them above.

 

My new understanding: Reactive Radial/Core will do their percentage checks independently for the debuff and the DOT, and their own percentage chances will determine how effective they each are. One does not affect the other.

 

Have I gotten that right?

The checks are independent. So let's say you pick an incarnate where the debuff is 25% and the DoT is 75%, you effectively get two independent procs. 25% chance for debuff and a DoT that has a 75% chance of doing damage on each tick. This DoT is cancel on miss, so as soon as one tick misses no more ticks of damage can go off.

[tripthicket]

Thanks for your swift reply. I'm calling my prior advice a result of my poor understanding of the issue, and will now make efforts to spread the correct word.

[Galactiman]

I noticed Bopper never came back and explained the math, so maybe I can help with that.

 

First, you need to know how to calculate an expected value. I found a pretty easy to understand explanation here:

https://www.varsitytutors.com/hotmath/hotmath_help/topics/expected-value#:~:text=In a probability distribution %2C the,represented by E(x) .

 

This tells us we need the sum of the products of the probability of each potential outcome and its value. In this case, the potential outcome and its value are the same (i.e., 1 tick = 1, 2 ticks = 2, etc.)

 

To calculate the probability of each outcome, we multiply the chance of the previous tick occurring, the chance of the current tick occurring, and the chance of the next tick not occurring.

 

Example using the 25% chance proc:

The chance of the first tick occurring is 25% and the 2nd tick not occurring is 75%, so:

0.25 * 0.75 = 0.1875

 

This means the chance of getting exactly one tick is 18.75%.

 

Chance of getting exactly 2 ticks:

Chance of the first tick occurring is 25%, chance of the 2nd tick occurring is 25%, and chance of the 3rd tick not occurring is 75%, so:

0.25 * 0.25 * 0.75 = 0.046875

 

You'll quickly notice we can simplify this calculation to:

0.25x * 0.75

where x is the number of ticks.

 

The exception being the last tick because if it has occurred then we're done, so it is simply:

0.25x

 

Now to put it all together (factoring out 0.75 for brevity):

0.75(0.251(1) + 0.252(2) + 0.253(3) + 0.254(4)) + 0.255(5) = 0.3330078125

 

As you can see, that matches up with Bopper's results.

 

For nerds:

Spoiler

Edited July 22, 2022 by Galactiman

[Bopper]

10 minutes ago, Galactiman said:

I noticed Bopper never came back and explained the math, so maybe I can help with that

Haha, thanks. 2.5 years later and I never remembered to come back to this.

 

Your numbers are right. And if anyone wants a calculator that does this math, I have one available in the tools section. Just look for the sheet called cancel-on-miss and it will show your average performance and probability of getting exactly X ticks, using a DoT with any probability and any number of ticks.