I guess the payoff for working out exacting models for Molten Core is that we can determine what behaviour we should be exhibiting when we recieve one. Is it better to instantly cast your 3 Incinerates and delay other abilities that may need refreshing until afterwards? Is there any advantage to saving a MC proc at 37% to use on Soulfires?

Your simplified model makes sense for understanding the underlying concerns, however in footnote 3 you talk about a simcraft constant you found based on that model (I think, maybe you found it based on "real" simulations, either way), you can't then use that constant when expanding to a more complex example, it will greatly depend on the exact priority list given. I'm not sure how you intend to calculate the constant but I think you may find it extremely difficult and it will depend very heavily on haste and the reaction time and latency of the player.

Perhaps it would be easier to start at the other end, the Soulfire Molten Core doesn't require the player to react, doesn't change cast time, it's just 18% damage and 15% crit, one is just scaling and the other will depend on your standard crit rate, which isn't used anywhere else and could be left as an unknown in any final solution.

The problem with your approach is mostly that it's not very mathy. There are *some* things that you can not calculate, for example player reactionspeed, this "variable" is going to be different depending on player skill aswell as the complexity of the encounter they're currently faced with.

Past reaction time however you can calculate the likelyhood that a new molten core proc would overlap an old one- the problem with calculating this is that it would be an incredibly large formula thats probably in parts still based on player/encounter specifics, haste values and other assumptions.

The alternative as you suggest is taking simulationcraft's results and feeding those into your spreadsheet. Frankly while I think it's a noble cause to want to create a spreadsheet- I'm not really sure if there's a real merit to having a spreadsheet based on results provided by a simulator.

Past that I'm not really sure what you're asking with this thread, are you asking wether or not you can trust the simulationcrafted results, or are you asking how to best calculate molten core clipping, or are you asking if your method of calculating the benefit from molten core is correct assuming that the number of molten core clipping is [x]%?

In attempt to make it simple, you can remove haste from the equation.
It affects how often Molten Core will procc, but just as much how fast it is consumed. Since the results from formula will be a percentage, haste wont affect it.
I also dont see a way formula can be created that would count in the immolate uptime, we need to ignore it or run simulation.

Asuming perfect play, MC can refresh after we used 2charges, or after we used all 3, not after 1. that makes couting much simplier. (for 3/3 and 2/3 only)
Uptime of 3/3 MC will be 21% (chance to procc for 3*incinerate cast time) * (1-0.12*1/3) (chance to lose 1procc)= 20,16%

(still asuming perfect usage of MC at cost of everything else)

79% of fillers will be Shadowbolt 20.16% incinerates. Thats constant independant of haste, if we use glyph of Quick Decay.
Now we need Damage for SB and Incinerate
20.16%*Incinerate+79%*SB for 3/3 and compare to 100% SB spam.
value of 3/3 MC will be the difference in DPS, counting 2/1 MC value can be simplified just count it as 15% 35% 100%

2/3 MC will have 33% less proccs, and incinerate will be 5% weaker AND 10% slower. at 1/3 incinerate wont even be worth casting over SB AND will have about 10% uptime, making it very poor talent (as its ^3 build).

Hope that helped.

However when MC procs you're probably doing something already, plus there's reaction time. You're looking at atleast an average extra ~1.25s before consuming all procs, besides as said above, both immolate and corruption take higher priority than incinerate, meaning that there's a ~6-7% chance that you should refresh immolate first after a proc, and a ~10% chance of having to refresh corruption first after a proc. Say 15% chance that you have to cast something else first.

In the real world you're going to clip molten core procs. In the real world it will happen atleast once or twice every fight. It has fairly little to do with player skill- and frankly the math to prove that it will happen is very simple. The math provided to show how much it happens is pretty poor.

2 formulas that at a very low level of accuracy could tell you something:
Likelyhood of molten core to proc again within [x]s with [y] haste rating

1-(0.88^([x]/(3/(1+[y]/3279))))
Example 0 haste, 3 seconds, 0 haste 6 seconds and 1083 haste and 8 seconds:
1-(0.88^(3/(3/(1+(0/3279))))=0.12 (12%)
1-(0.88^(6/(3/(1+(0/3279))))=0.2256 (23%)
1-(0.88^(8/(3/(1+(1083/3279))))=0.3646 (37%)

Technically you should account for raid haste buffs (5% and 3%) and it would look like:
1-(0.88^([x]/(3/(1+[y]/3279)/1.05/1.03)))

--

Calculating the average time to consume molten core:
Average time consumed by refreshing immolate during proc: 1.5/1.[haste]/24*(1.5/1.[haste])
Average chance that you'd have to refresh curse of doom: 1.5/1.[haste]/60*(1.5/1.[haste])
Average chance that you'd have to refresh corruption: 1.5/15 (haste can be ignored since it would show up equally on both sides)
I think it's reasonable to say that you don't need to refresh glyph of lifetap, you'll typically lifetap about 20 seconds before it expires and so long as you keep your mana above 50% you also shouldn't need to lifetap for mana reasons.
Average cast time of incinerate: 7.5*0.7/1.[haste]
Average time left on current cast will be a bit trickier, but 1s is probably a fair estimate.
Reaction time (if you want to factor it in) 0.5s

So @ 600 haste: 1+0.5+(7.5*0.7/1.2=4.375)+(1.5/1.2/24*(1.5/1.2)=0.065)+(1.5/1.2/60*(1.5/1.2)=0.026)+(1.5/15*1.5=0.15)=6.116

These are ballpark formulas, they dont account for having to refresh immolate/corruption after your first incinerate, and a bunch of other stuff, but you should be able to use them to gouge roughly how likely it is that procs will overlap.