Improved Shadow Bolt

Note that Improved Shadow Bolt affects all shadow damage, including damage over time effects. It is a common misconception that it just affects non-DoTs like Shadow Bolt and Mind Blast. The section seems to assume it does.

In reality it boosts all shadow damage by 20% until 4 non-DoT spells have landed or 12 seconds. Needless to say, boosting all shadow damage by 20% in a raid, even for short duration, is a significant amount of damage. Improved Shadow Bolt is therefore highly recommended for raiding warlocks.

The following section therefore just calculates the effect your shadowbolt crits will have on your own shadowbolts, not what it does for a raid.

Mathematics

Let I be the number of point in the talent Improved Shadow Bolt. Let C be the probability of having a critical strike with Shadow Bolts.

To Figure out how often it is up on average is a bit tricky, but if we calculate the average number charges that get wasted then we could figure out how often it is up.

C stands for your Crit rate as a number between 1 and 0

The chance that three charges is wasted is $C$.

The chance that two charges is wasted is $C(1-C)$.

The chance that one charges is wasted is $C(1-C)^{2}$.

So the average number of wasted charges is $C(1-C)^{2}+2C(1-C)+3C$.

$4-(C(1-C)^{2}+2C(1-C)+3C)$ is the average number of charges per shadow bolt crit.

And thus $C(4-(C(1-C)^{2}+2C(1-C)+3C))$ is the percentage of the time imp shadow bolt is up.

Simplify $C(4-(C(1-C)^{2}+2C(1-C)+3C))$ $=C(4-(C(1-2C+C^{2})+2C-2C^{2}+3C))$ $=C(4-(C-2C^{2}+C^{3}+2C-2C^{2}+3C))$ $=C(4-(C^{3}-4C^{2}+6C))$ $=C(4-C^{3}+4C^{2}-6C)$ $=-C^{4}+4C^{3}-6C^{2}+4C$

Multipy this by 1+.04/.08/.12/.16/.20 (based on talent rank) to get the average % increase in shadow damage.

note: this assumes 0% miss rate because .01 error will have a negligible impact on the over-all equation and assuming 0% miss make the whole system much easier to handle.

For affliction warlocks however choosing exclusively this talent will result in less profitable returns if he fails to get Bane and Devastation, when the bonus will fall to 7.72% for a warlock similar to the prior example. Also, at higher levels, some destruction warlocks might prefer to use Fire spells and benefit from Emberstorm, sticking with Immolate/Incinerate/Conflagrate, in which case Improved Shadow Bolt could be replaced with Cataclysm.

note: this assumes 0% miss rate because .01 error will have a negligible impact on the over-all equation and assuming 0% miss make the whole system much easier to handle.

One other note: since most solo fights end in less than 20 seconds this benefit is subject to some statistical variations and could be considered unreliable for regular grind and leveling. For longer fights however, longer than 90 seconds, this deviation can be disregarded.

Distribution

So, for the following rates you get the following distribution between the different kinds of hits (based on the above formulas):

crit-rate	% increase From ISB!
0.0%	0.0%
5.0%	3%
10%	6%
15%	9%
20%	11%
25%	14%
30%	15%
100%	20%