Talk:Improved Shadow Bolt
ISB/Shadow Mastery vs Mage/Improved Scorch and DPS
Citation needed in "Notes" section regarding the question of optimizing DPS, when both a warlock with 5/5 Improved Shadow Bolt and a Mage with 3/3 in 
[Improved Scorch] + Glyph of Improved Scorch are in the same raid/group. Presumably it's a greater DPS loss for the mage to include Scorch in their fire rotation when a Warlock with the talent is in the same group, since ISB can be part of the standard warlock rotation with less of a DPS loss (or no DPS loss at all?). Also presumably, it would be a DPS increase for the Mage to NOT have to waste a Glyph slot on Glyph of Improved Scorch if there is a guarantee that a warlock with the talent will be present. Conclusion: a warlock with ISB should always be the preference to keeping up the crit debuff, and would be of greater benefit to the raid/group, over having the mage cast scorch, when both are in the same raid/group and both have their "improved" talent filled. --Maverick (talk) 00:58, 29 July 2009 (UTC)
Mathematics
I'm not very good at stochastics, but don't you need to count in the probability of having multiple consecutive crits, which would lower the damage increase by this talent. If you had two crits, and then eight normal hits, it would still reflect a crit chance of 20%, but not all of them would be improved by this talent. Hence the current calculation seems to be a best case scenario. Though I may be mistaken. Can anyone confirm whether this is true or not? --bfx 02:14, 3 November 2006 (EST)
- You are right, but this was already taken into account in the article. You do that by calculating the chance that there is NO critical hit in the previous 4 hits, and so calculating the chance for any Shadow Bolt to NOT have improved damage. From that, it is simple to calculate the chance to HAVE improved damage. --LarsPensjo 05:15, 9 January 2007 (EST)
Question of conclusion
The article concludes that this talent is better than Nightfall. Is it really that easy? Take PvP for example, where you can hardly count on being able to send 4 Shadow Bolts at a target after a crit. Another example is PvE solo grinding, where the mob usually will be dead before you succeed in sending 4 more bolts. The only good example that remains would be boss killing in raids?
- --LarsPensjo 04:53, 9 January 2007 (EST)
More Mathematics
I've done some calculations as well and thanks to some help from the mathematics community on livejournal, I've come up with some interesting formulas for percentages of different kinds of Shadow Bolts, there are 4 kinds:
1)non-imp crit
2)non-imp norm
3)imp crit
4)imp norm
Depending on chance to crit, the following formulas apply (roughly, this doesn't take things like LifeTap, Timeout, Bane, etc, into consideration)
If you had an infinite amount of mana and could cast an infinite amount of Shadow Bolts and always managed to cast 4 Shadow Bolts before the timer expired, the percentages would converge to the following:
| non-imp crit | p*a | |
| non-imp norm | (1-p)*a | |
| imp crit | 4*p*p*a | |
| imp norm | 4*p*(1-p)*a |
where
a=1/(1+4*p)
So, for the following crit rates I get:
| crit-rate | non-imp-crit | non-imp-norm | imp-crit | imp-norm |
|---|---|---|---|---|
| 5.0% | 4.2% | 79.2% | 0.8% | 15.8% |
| 10% | 8.1% | 59.5% | 3.9% | 28.5% |
| 15% | 9.4% | 53.1% | 5.6% | 31.9% |
| 20% | 11.1% | 44.4% | 8.9% | 35.6% |
| 25% | 12.5% | 37.5% | 12.5% | 37.5% |
| 30% | 13.6% | 31.8% | 16.4% | 38.2% |
The point here, which has impressed me, is that with Imp SB, the higher the crit rating, the more SB's will be affected by Imp SB, which can lead to an overall increase in damage depending on the chance to crit.
Here are a couple of simple, rough calculations:
with ruin, I get:
a*(p+1)*(4*p*w+1)
without ruin, I get:
a*[1+.5*p+2*p*w*(p+2)] where w=1.2
So for the following crit rates I get
| crit rate | w ruin | w/o ruin |
|---|---|---|
| 5% | 108.5% | 106.0% |
| 10% | 116.2% | 111.0% |
| 15% | 126.5% | 117.3% |
| 20% | 133.4% | 122.4% |
| 25% | 140.2% | 125.3% |
| 30% | 146.8% | 129.0% |
So Imp SB with Ruin seems to work very well together, getting an extra 30% or more damage with 20% or better crit rate, which is a realistic goal.
I wrote a C program which comes up with similar numbers, which simulates things like SB Timer expiration, and mana recovery downtime (LifeTapping).
So, the other point here would be that Shadow Bolt should scale very nicely with levels and gear if Imp SB and Ruin are taken.
Also, after about a 20% crit rate is attained, the returns on crit rate seem to be diminishing with respect to Imp SB, but OTOH it looks like Ruin makes up for this according to the damage table.
--Rhennig 17:49, 12 January 2007 (EST)
I copied your text, edited it slightly (no data changed), and saved it as article [Formulas:Shadow Bolt]. --LarsPensjo 09:43, 15 January 2007 (EST)
Archive from Formulas:Shadow Bolt
I think it is a good idea to keep mathematics saved in special articles, and let the main articles just use the conclusions. That way, the "proof" is available if you doubt the conclusion, but you still don't have to read through it all. That's why I created this article. --LarsPensjo 09:41, 15 January 2007 (EST)
One way to verify this data is to try what happens for the extreme cases, like 0% crit and 100% crit. In this case, it seems the result from 100% crit is wrong, as all hits should be of improved crit, not 80%. Is the mathematics wrong? --LarsPensjo 09:59, 15 January 2007 (EST)
The original author did not comment on the contradiction in results, so I made new calculations instead. --LarsPensjo 06:41, 14 February 2007 (EST)
Ah, the first Shadow Bolt is never imp crit and Imp SB only lasts for the next 4 SBs.
--Rhennig 04:08, 10 July 2007 (UTC)
Was checking again. I thought that the Imp SB counter did not renew until 4 SBs had been cast. That is the formulas were the way they were. Thanks for fixing. Hmmm, maybe a derivation and a graph? I could add a simple derivation and a graph from Excel.
--Rhennig 21:29, 31 July 2007 (UTC)