Far too much guessing and too little excel, let's try again:

Average damages raidbuffed / debuffed mob, disregarding crit / hit etc with any given +dmg value with 0/21/40 build:

Shadow bolt:
(572+1.2*3/3.5*+dmg)*(1.1*1.15*1.05*1.1)=
(572+1.2*3/3.5*+dmg)*(1.461)

Incinerate:
(598.75+1.2*2.5/3.5*+dmg)*(1.1*1.15*1.1*1.15*1.05)=
(598.75+1.2*2.5/3.5*+dmg)*(1.680)


Thus, when does shadowbolt catch incinerate?:
(598.75+1.2*2.5/3.5*+dmg)*(1.680)=(572+1.2*3/3.5*+dmg)*(1.461) -->
(598.75+1.2*2.5/3.5*+dmg)*(1.680)/(1.461)=(572+1.2*3/3.5*+dmg) -->
688.5+0.9856*+dmg=572+1.2*3/3.5*+dmg -->
688.5-572=1.2*3/3.5*+dmg-0.9856*+dmg
116.5=0.04297*+dmg
+dmg = 116.5/0.04297 = 2711.1

Thus, Shadowbolt with no ISB proc is not going to catch Incinerates DPS with gear available in TBC unless maybe under very extreme proc conditions. (2/5 T4, Nightbane Robe, 2 proc trinkets, Hyjal exalted ring, etc. all procing at the same time.). Unless my equations are off. (Later part shouldn't, just plotting the first two equations in excel gives the same +dmg break even point)

Ok, now the real question. How's that with ISB? How much ISB uptime is needed for shadow bolt to deal more DPS than Incinerate with any given +dmg?

(598.75+itmod*+dmg)*(imod) = (572+stmod*+dmg)*(smod*ISB), where stmod = 1.2*3.0/3.5, smod = 1.1*1.15*1.05*1.1 and imod's in a similar way.
-->
(598.75+itmod*+dmg)*(imod)/(smod) = (572+stmod*+dmg) -->
(imod)/(smod*ISB)*598.75+(imod)/(smod*ISB)*itmod*+dmg = (572+stmod*+dmg) -->
(imod)/(smod*ISB)*598.75 - 572 = stmod*+dmg - (imod)/(smod*ISB)*itmod*+dmg
[(imod)/(smod*ISB)*598.75 - 572] / [stmod - (imod)/(smod*ISB)*itmod] = dmg


I made a graph. Read your +dmg from Y-axis, and check how much ISB uptime is required for shadow bolt to deal more DPS than incinerate. Or the opposite, choose your ISB uptime and check how much +dmg you need for shadowbolt to have more dps.

This assumes that you never have to lifetap, so it's not really practical, but this is the minimum ISB uptime needed to even get a close call. In real raiding situations uptime has to be much higher, because you'll lifetap 18% more with shadowbolt than incinerate. (Actually shadow bolt needs to do about 6% more DPS than Incinerate for not to loose due to increased lifetapping, assuming 0 manaregen while casting, with 50% ISB uptime that means about +dmg of 1175 to be on par...)

Which gives more raid-dps in different scenarios? Much harder question. Incinerate lock need less healing, but doesn't increase ISB uptime. Again, you are trading a HoT or two for increased shadow dps. Is it worth it? Most probably.

Interesting work, Zepi. My last calcuations showed a much lower number than what you have here (possibly because they were before the SW nerf, but they could also have just been wrong).

A more interesting question: is SnF additive or multiplicative? If it's additive, the answer is much worse that what Zepi's calculated, something over 20k +damage. Anyone have any data to prove one case or another? I'm flying to Dr. Boom to get some data right now.

I think the improved ISB uptime is a good argument, though, since with a 24% uptime you're breaking even again. You're also still improving the DPS of the other warlocks and shadow priests. However, with non-shadow gear, you can easily swap to fire-destro with 0/21/40 to be less of a healing burden.

Ok, I just killed Dr. Boom with nothing but SB, took a good few minutes. :-P For reference, I had 1284 shadow gear, capped hit (for Dr. Boom, anyway).

Throwing out bolts that had ISB up (which was quite a bit, sadly) and/or Lesser Spell Blasting, I got a total of 27 data points for SnF over the course of the fight. The average was 1935.

SnF, if additive, gives an expected value as follows:

572 + 1284 * (0.2 + 3/3.5) = 572 + 1284 * 1.05 ~= 1929

If SnF is multiplicative:

572 + 1284 * (1.2 * 3 / 3.5) = 572 + 1284 * 1.02 ~= 1893

Loosely, the variance in SB damage from the tooltip is 607 - 544 = 63, or +/- 31.5. So, this is far from definitive, but it still seems to support the additive theory more. If someone with more statistics background than I can help out in judging the accuracy of the data based on sample size, variance, etc., that would be helpful.

For the curious, the data set:

1949
1935
1942
1947
1930
1918
1928
1946
1904
1909
1927
1962
1948
1947
1963
1911
1957
1910
1958
1904
1959
1904
1923
1911
1956
1952
1954

I can provide the combat log if anyone wants to double check my work. Note that I was retarded and thought I could use SWS to do most of the recording, so I only turned the combat log on in the 60% range.

The easiest way to demonstrate the things is to go for the larges possible shadowbolt with the multiplicative model and if you get a Shadowbolt higher you can safely assume additive.

With a range of 607 - 544 thent he highest with multiplicative is 607 + 1284 * (1.2 * 3 / 3.5)= 1927.7 Which was clearly beaten many times the largest of which I have included above. Additive max is 607 + 1284 * (0.2 + 3/3.5)= 1964.3 which is what we have almost observed. So we can safely assume additive. You have to use the exact formulas not the 2 digit approximations to get these results.

Healing spells have also been demonstrated to be additive( I can't find a link >_<). Also improved corruption is definately 93%+ 36%= 129% not 0.93*1.36=126.5%. Finally the druid talent Wrath of Cenarious gives 20% to starfire but only 10% to wrath which doesn't make any sense for a multiplicative system but does for an additive system.

Reposted the graph with additive SnF coefficient. Now 30% ISB uptime means that shadow bolt scales over Incinerate at around 1200 damage.

There's a lot more numbers and theory crafting about raid ISB uptime here: [Warlock] UA vs. Ruin Overall Raid DPS Comparison

Basically, you will never have 100% ISB uptime on your own and affliction locks, even those with 15-20% crit, are more than likely adding to ISB uptime. Shadow priests are another matter but frankly the extra mana regen in worth a little ISB leeching.

Gaining the 20% on a Mind Blast is worth losing it for the few ticks of VT/SWP/MF. Mind Blast is a far superior DPS boost than 20% of those spells, and it would be an utter waste to not use it if mana allows. The extra 20% mana back for the party for this spell will cause more damage than the extra damage done by a warlock's shadowbolt taking it instead.

Regarding SB uptime, will start from simple scenario and then start working upwards to the more complicated:

Single warlock:
25% crit means chance for imp shadowbolt to NOT be up is 0.75^4 (4 last shadowbolts not critting), which leaves you with 69% of imp shadowbolt uptime.

As you add warlocks with equal crit, the imp shadowbolt uptime will be exactly the same (as been tested as well but can be seen very easily with the same mathematical model of a single warlock). Warlocks with less crit will then naturally lower it (but you will increase theirs), while warlocks with more crit will increase it (but you will decrease theirs). Overall the imp shadowbolt effect remains the same for the purpose of shadowbolts remains quite the same assuming you're not better or wosrse than the other warlocks - a difference of gear/skill will obviously make it so it's worthwhile to have the bad skilled warlocks not reduce imp shadowbolt uptime ;p but enough with discussing skill/gear issues, all your raid should be skilled and geared anyway.

The thing is, imp shadowbolt uptime doesn't only affect shadowbolt damage, which is the main error here when comparing imp shadowbolt to incinerate. You're missing on all the SW:P, mindflay, UA and corruption damage done during the time until the bolts are consumed.

For shadow priests that don't eat your imp SB, there's not much needed to be said. Add 20% X imp SB uptime to your own DPS when you calculate it. After all bosses don't really care who did damage to them other than aggro issues, which again I won't be going into here.

Where it really gets complicated is when shadow priests start eating your buffs, which they probably will as MB and SW:D are major DPS increases. However if a shadow priest ate your imp SB it just means his MB/SW:D did more damage, count that damage for yourself when calculating. However regarding wether SPs should or shouldn't eat your buffs is a lot more complicated. After all while a MB/SW:D will get the 20% damage bonus, it'll also mean 1 less shadowbolt will possibly not get 20% increase, while ALSO one of their mind flays may not get an increase. If they mindflay, not only it will get the 20% increase but also it means another shadowbolt will possibly get the 20% increase as well. Add to that the fact that SW:Ps and warlock dots will do more damage if the SP sticks to MF when imp SB is up and it gets really hard to tell if MB/SW:D should be used when imp SB is up.
The reason I say "possibly" is because the shadowbolt uptime formula for a single warlock was taking into account overlapping procs. However if shadow priests are eating your procs, the overlapping time will be reduced, thus even if you have a mind blast/SW:D casted for every shadowbolt that is casted (which is an extreme because it requires the SPs to outnumber the warlocks), your imp SB uptime will be MORE than 1/2 of what it would've been if you were in the single warlock scenario. If you want to get more accurate you have to know the SB to MB/SW:D ratio in your raid...

Most useful conclusions I can reach without going any deeper into numbers:
-Imp SB uptime is a lot more useful than what shown in the above posts. It is far more than an increase to SB DPS.
-Shadow priests really need to do a serious comparison of MF to MB/SW:D. First check if MF with 20% damage increase is more worthwhile than a MB with no damage increase. Then check if a MB with 20% damage increase + shadowbolt with no damage increase is actually better than a shadowbolt with 20% damage increase + mind flay with 20% damage increase (obviously checking the effect of the bonus on the single cast over long-term DPS and not just looking at the single cast, as cast times are different). Then if you still think you should mind blast, check how much imp SB time is lost by you mind blasting (as it WILL drop the imp SB uptime long-term), and calculate how much DoT damage is lost by the raid because of that.

My guestimations based on that (may be possible to prove otherwise if you do the numbers but I have serious doubts):
-Imp SB uptime is very important and one of the main reasons to consider a destro spec, ESPECIAlLLY on a SP heavy raid and even more with more affliction locks.
-SPs should probably save their MB/SW:D for when there is no imp SB up and with imp SB use MF so they don't eat up the imp SB and it stays up to give a greater benefit to the enitre raid's DoTs and MFs.

I did some testing with 2 of my locks on Dr. Boom. All tries were done up to when the shadow priest was OOM.

Try #1 affliction + affliction, drakana CoD, lane CoS:

http://www.lossendil.com/wws/?report=dy44wkxwkxmoq

Drakana: 973 dps, Lane: 925 dps, Disht 1036 dps: Total = 2934 dps


Try #2 affliction + affliction with some improvements in the dps cycles, drakana CoA, lane CoS:

http://www.lossendil.com/wws/?report=jxd5bqqrke1cm

Drakana: 882 dps, Lane 916 dps, Disht 985 dps: Total = 2783 dps


Try #3 affliction + demo, drakana CoA, lane CoS

http://www.lossendil.com/wws/?report=xitnkrrgyvyi1

Drakana: 871 dps, Lane 824 dps, Disht 899 dps: Total = 2594 dps


Try #4 affliction + demo, drakana CoA, lane CoS

http://www.lossendil.com/wws/?report=j3bjm66v2kmfs

Drakana: 937 dps, Lane 846 dps, Disht 941 dps: Total = 2724 dps


The results are a bit counter intuitive in terms of the Imp. SB debuff and the effects on the shadow casters. The lock that switched from affliction to demo gained 5% more crit (being at 30% crit on the test being specced demo). Even so that resulted in both the affliction lock and the shadowpriest to drop in dps.

My intuition says that given a non affliction lock the frequency of shadowbolts hitting the target is higher hence the average duration of a single Imp. SB debuff (all 4 charges) is lower. On the other hand you have more Imp. SB debuffs to start with with a demo lock. What happens though is that they do not compensate for the loss in DoT damage from the shorter Imp. SB debuff durations. I am going to try to get the combat logs for this and figure out if this is the case or not.

Definitely. They hardly make an exhaustive analysis. I will try when I have the time to take 2 shadow priests and 3 locks so that the shadow priests can go on for longer so that each run is longer so there is less variance between each test. One interesting thing to note about the above results is that the Demo lock didn't really know how to do dps rotations and he was refreshing dots before they expired (practically doing dot,dot,dot, sb, sb, sb, sb and repeat). This fact hints a bit towards me thinking that more crit but more sbs don't usually give you more raidwise dps.

Unfortunately I deleted the logs through the command line and I can't extract the information I want from them.

Another approach that I just thought about, would be to write up a script to simulate this with multiple locks + shadow priest casting everything in a perfect rotation and having the program roll for crits on each cast. That way you can simulate for long enough, for data to be meaningful and avoid shadow weaving build up time and human error on the cast rotations. WTB more free time please :-)