There's a big difference between playing perfectly and assuming uptimes/scenarios that even a computer player could never match. Frankly assuming such things makes the end result irrelevant in my eyes, as even perfect play would not match it. Anyway you should be able to calculate the overlap probability with the formula above.

I've been trying to understand the math behind Molten Core's dps increase to a player. The spreadsheet here has the old calculations of Molten Core which does not account for the changes. I'm thinking that you need to use a multi-formula equation. Any help on calculating this would be greatly appreciated. The tough part isn't the increase of duration to immolate, it's the 3 charges it yields.

You first need to know how fast your corruption will tick. This is based upon your Glyph (Quick Decay) and your Haste (18/(1+haste)).

Base: 6 ticks over 18 seconds. One tick every 3 seconds.
Haste = 25%: 18/(1+.25) = 6 ticks over 14.4 seconds. One tick every 2.4 seconds


Now, Molten Core tells us every 12%, corruption damage will proc Molten Core. This will buff your next 3 Incinerate or Soul Fire. Incinerate gains 18% damage and reduces the cast time by 30%. Soul Fire gains 18% damage and 15% crit.


So. How do we get those percentages applied to our damage?

The situation needs to be broken down into two parts first:

Damage done while the enemy is above 35%
Damage done while the enemy is at or below 35%

Lets look at Damage done while the enemy is above 35%. This means we would not be using Soul Fire, so we can ignore that completely. Focus just on the incinerate. Now lets just use a concrete example (theoretical numbers). Let's say you have 25% haste, so we use the 14.4 from before. We get that corruption will tick once every 2.4 seconds. For the sake of ease, lets say the fight (the portion above 35%) is 240 seconds long. This means you will now have 100 ticks over 240 seconds. Out of those 100 ticks, 12% will cause Molten Core. Very easily we can see that means Molten Core will occur 12 times.

BUT! The issue here is that there are multiple charges on Molten Core! This is where it gets tricky. Ideally you will consume your Molten Core by casting 3 times immediately. So if you get 100 shadow bolts off in those 240 seconds normally. Let's say shadow bolt is a 1s cast and incinerate is a 1s cast (Post 30% molten core increase). This makes them directly replaceable in our example. So now, back to the 18 Molten Core occurrences. Molten Core is a 3 charge ability, 3*12= 36 attacks. Ideally you will get 36 incinerates off. Since Shadow bolt and Incinerate have the same cast time (in this example) we can directly replace them¹. So 100 - 36 = 64 shadow bolts, 36 incinerates at an 18% increase in damage².

¹Of course the cast times are not going to match so there will be a bit of calculation to determine how many casts of shadowbolt you get against incinerate replacement with it's cast time. .9s incinerate, 36 times is only 32.4 seconds used. 240 - 32.4 = 207.6 . So, You have 207.6 seconds to deal out shadow bolts.

²Say for example in the absolute ideal scenario, using all of the charges it yields an extra 1,000 DPS (Value isn't actually calculated, just using fake numbers).

So far so good right? We can easily calculate our damage here with such ideal Molten Core usage. Well, what if corruption ticks, procs Molten Core and you cast Incinerate. This will consume 1 charge leaving you with 2 remaining. The problem occurs on corruption's next tick. If Molten Core procs again, your stack will be reset to 3, thus losing 2 charges you could have potentially used. Right? So, from our example above we had 12 procs of Molten Core, lets say you only were able to use 30 of the 36 charges, this means only 83.33% were beneficial³. From footnote two, I speculated the DPS increase was 1,000. Using the new number of beneficial charges with our DPS value, we can calculate the actual DPS given. In this example we take 1,000 * .8333, giving us 833.33. So, our actual DPS yield is 833.33, ideal scenario is 1,000.

³This value needs actual calculation, I think the 10,000 iteration tests by SimulationCraft give it a benefit of about 87%. Would this be the proper constant to use in the calculation?

So far so good? Is this method of calculation correct so far? What's wrong? Please provide any feedback you have here. I won't continue with the Soul Fire calculations since they will follow suite.

Can you merge this thread with the Warlock Spreadsheet 3.3.0 now that it's started?

Haste is entirely factored out for this calculation, and latency / remaining cast time aren't entirely factored in, which screws with equation 2. I think it's a good start, however.

1. Average number of MC procs per cast of Corruption:
sum{from n=0, to n=6} of {0.88^6-n*n *0.12^n}

e: I tried putting this term together with Latex but couldn't figure it out. I'll clean it up later and hope it makes sense.
I think this figures to 0.085 procs per cast.

2. Average number of casts benefitting from each Core proc, mostly discounting latency and remaining cast time:

0.88^2*3+0.88*0.12*1+0.12*0=2.429

3. DPS benefit per use = DPS benefit * duration
Numbers pulled from Simcraft SampleOutputT9T10

35%+: (incinerate_dps-shadowbolt_dps) * incinerate_cast_time = (7898-5796) * 1.923 =4038D
35%-: (MC_Soul_Fire_dps - Soul_Fire_dps) * soul_fire_cast_time = (5435) * 5435.04D
(I don't think the Simcraft sample does casts Corruption when the target is below 35% HP, which would skew Soul Fire's damage upward a little bit. I'm not sure.)

Damage benefit over a Corruption from Molten Core:

procs_per_cast * benefits_per_proc * damage_per_benefit

35%+: 832.8D
35%-: 1120.85D

No need to split out the binomial in step 1. Mean procs per Corruption cast is 6*0.12 = 0.72.

(Also, your sum is wrong--you need to include the binomial coefficent 6Cn. And multiply by the number of procs n in each case. The correct sum is:
, which equals 0.72)

Anyway, on to the problem from the OP. Best I can tell (I don't really know anything about Warlocks), Incinerate cast time before haste is 2.5/1.3 = 1.92s. Corruption tick time is 3s before haste. Both decrease equally with haste, so that ratio shouldn't change.

Simplified outlook to start: all cast time is spent on either Shadow Bolt or Incinerate.

At any given moment, Molten Core will be up if it has procced within the amount of time it takes to cast 3 Incinerates. Given a bit of reaction time, etc., let's say that there always 2 Corruption ticks in the time it takes to chaincast 3 Incinerates. In other words, if at time T, one of your last two Corruption ticks has procced MC, you'll still be casting Incinerate. Otherwise, you'll be casting SB (since two Corruption ticks is the time it takes to use up your 3 MC charges).

One of your two Corruption ticks will have procced MC with probability (1-0.88^2)= 22.6%. So a good first-order estimate is that you'll be casting Incinerate 22.6% of the time, and Shadow Bolt the rest of the time. Curiously, this is constant with respect to haste, which may be counterintuitive at first but makes sense when you think about it.

Note that 22.6 is very close to Mahida's above empirical estimate of 27%*82%.

-------

The big wrench in the works is all the execution time spent on things other then Incinerate or SB (including Corruption itself). I think the best way to deal with this is to average in the cast time spent on anything other than nukes in the form of added Corruption ticks (since, from the perspective of the Immolate/SB question, the time spent casting other stuff only matters insofar as it provides extra time during which Corruption may have ticked). Essentially if you spend a fraction X of your time casting things other than SB/Incinerate, perform the same computation I did above, but imagine that Corruption ticks 1/(1-X) times more quickly.

So, above, I assumed that the ratio of Incinerate cast time to Corruption tick time (call this R) is 2/3. Here let's start with the real value of R=C/3 (where C is the pre-haste cast time of a buffed Incinerate, 25/13). And, using the approximation from the last paragraph, we'll instead model the ratio as R=C/(3*(1-X)).

Now basically repeat what I did in the top half of the post. Since Corruption will tick R times during one Incinerate cast, it will tick 3R times during 3 Incinerate casts. So, at any time, you'll find yourself casting Incinerate instead of SB if any of the last 3R Corruption ticks have procced MC. This leads to a time spent casting Incinerate (as a fraction of total time spent casting nukes) of:

, or

, where C = 25/13 (pre-haste cast time of Incinerate).

Hey there - first of all may I say very well done and I comment you for your hard work and effort!

However, when I try loading my character from the armory into the spreadsheet it says:

" 48667 is not a supported Back please use Custom Gear for it "

Why is this error message being displayed (maybe I just don't understand what it's asking me to do) and how do I fix it?

Many thanks
Vidiz

Base damage range for normal Nibelung is 1591-1785. It's affected by level-based partial resists, and by caster debuffs on the target (Earth and Moon, Imp. Scorch, Totem of Wrath). 50% crit bonus, 0% base crit rate, 0% miss. Casts on average 17 Smites per proc if it stays still. 1% proc rate, but a bunch of weird talents and things proc it; you'll have to experiment some yourself.

I get the same error for a couple of my armor pieces.

My main concern is I'm getting a ton of #N/A errors in cells where there's supposed to be DPS/Damage numbers. Anyone else having this issue?

Here's a picture of the spreadsheet after I import my armory to avoid confusion:

You're getting those errors because you have 2 items that aren't in the spreadsheet's database. Also ran into a bunch of bugs with loading a character...Ill try and fix all this by tomorrow.

That's what I figured - just wanted to report in case it was something else.

The two items for me were: Bindings of Dark Essence - wrists from ToC 25 and the Icehowl Cinch from ToGC 10.