Intro:
I've been interested in really nailing down an answer to the questions most shadow priests have of when to refresh dots. Here's my attempt to do so, and I'll do my best to explain what I've done. I welcome any discussion about my methods, as getting this information as accurate as possible is the goal! I am planning to expand this soon with more information on how the 2pc extensions affect these decisions, too.
So, let's just start off with the graphs. The reasoning and math behind them will follow. I've graphed when to refresh SWP and VT separately because they are quite a bit different, as you can see.

The Graphs:
(Click on a graph to enlarge it)
You need to know several things when considering when to refresh dots. One is how much time is left on your current dots. If they're about to expire, you refresh them right away, for instance. You also need to have an idea of how many ticks your new dots will last. You only spam SWP (i.e. it lasts 1 tick before it's refreshed again) as a last resort during movement, for instance. You also want to know your current damage increase/decrease compared to your state when the existing buffs were cast. I highly recommend checking out AffDotsSpriest (you'll also need Affdots for it to work). It displays information just like my graphs - if your current procs have increased your damage by 20%, you'll see a "120" on your dot trackers. Thank you very much for writing it, Alae and Ridcully!!

Let's choose an example where you have +30% damage from some int procs, are at +2 ticks from haste on your gear, and the current portion of your fight has very little movement, so you expect SWP and VT to last 8 and 7 ticks respectively. I find myself in this situation very frequently during a raid. Your current dots have 7 seconds left. What do you do? For SWP, the red line for 8 ticks shows that with 7 seconds left it's worth refreshing early when your buffs are at least 100% and have about 8.5 seconds left. You should refresh SWP here. For VT, the blue/gray line labeled 7 ticks shows that you should refresh it early when it has 7 seconds left if you're at around a 10% damage increase. You should refresh VT, too, because 30% > 10%.

One important aspect to look at is 10 second procs. In this case, if you're going to refresh immediately and then again right before the 10s proc fades, you're likely getting around 4 ticks of the dot before you recast it. For these situations, you should be looking at the purple 4 Ticks line. To simplify the LMG proc down to a +30% increase, for LMG procs (alone - no other procs up) you can safely refresh both dots immediately, regardless of their remaining duration.

The Math:
That's how it works. Now I'll explain how I came up with these. Here is where I would be particularly open to peer-reviewed criticism, so feel free!

What I did was figure out the damage you gain by refreshing dots and compare that to the damage you lose by spending that time refreshing dots instead of filling it with mind flay. Recasting one of the dots is half a mind flay channel, so I divided the mind flay damage by 2. Both SWP and VT would be ticking for damage even if you didn't refresh them early, so you need to subtract that out. You will need to spend that GCD refreshing the dot eventually, so refreshing it early is simply a fraction of that GCD. For instance: SWP lasts 18 seconds, so refreshing it with 6 seconds left means you're wasting 6/18ths of the GCD you could have spent casting MF by refreshing SWP early. Thus I also multiply MF by t/18 for SWP and t/15 for VT to get the fraction of MF time you lose by refreshing early. SWP has an initial tick component which is included. For the following formulas, d is your current damage increase from procs compared to what you had when the existing dots were cast. t = time left on the dots, M = MF damage for a full channel, S = the damage from 1 tick of SWP, V = the damage from 1 tick of VT, n = the number of ticks you expect the new dot to last.

For refreshing SWP: d*t*M/36 = dS + dnS - nS

Solved for d: d = 36nS/ (36S + 36nS - tM)

For refreshing VT: d*t*M/30 = dnV - nV

Solved for d: d = -30nV/(tM - 30nV)

This essentially gives us a formula for what we have if our spells are instant cast and we aim to refresh them as close to 0s left as possible. First, we aim to refresh them between the last two ticks, so I adjusted t by -1 for both dots. VT has a cast time, so I adjusted t by an additional -1 for VT because that's the time the dot will actually land, but we want to know when it's a good decision to start casting it or not based on the time it has left now. This seems right to me and led to what seems proper for VT on the graph. If any of you can think of a better way to adjust for these things, please let me know!

Conclusions (tl;dr):
Refreshing dots for procs can be very good. SWP is very forgiving when it comes to refreshing early. SWP's initial damage makes a big difference, and when you're expecting the dot to last its full normal duration, even a medium-sized buff, such as just a lone proc of my Megaera trinket makes it worthwhile to refresh very shortly (2-3 seconds) after it was just cast. VT is not quite as forgiving. However, with at least +20%, which most procs should give you, you can refresh it with 7 seconds left. I very frequently see over +30% when anything but small procs (jade spirit, etc.), which makes VT fine to refresh with 9-10 seconds left.

Some limitations:

1) The values used for the damges on MF, SWP and VT when making the graph are based on my character's stats, at 535 ilvl. If somebody would like to give me the formulas to include all stats, I can investigate the scaling a bit more. Some quick adjustments on my end showed similar enough numbers to what showed up on the graphs presented that they seem valid for anybody in t15-ish gear, though.
2) I did not factor in the type of buff. SWP clearly scales incredibly well with crit, especially with 2pc T15. Extra SA procs and dot extensions are not included. I did not factor in haste, either. While I included extra lines for increased numbers of ticks on the dots, I did not factor in the GCD cap of recasting these vs the higher GCD cap on MF.

Updated 10-8-2013:
- 5.4 changes to dots and a realization that the in-game tooltip accounts for 4 ticks of MF rather than 3 have hed to significant changes in the graphs.
- Removed the VED graphs and discussion, as it's not really relevant in T16.
Last edited by Sheitan on October 19th, 2013, 3:26 pm, edited 3 times in total.