Estimating the Value of Glyph of Starsurge

The value of Glyph of Starsurge is a common topic of discussion among Druids lately. Since its DPS contribution is nontrivial to estimate, I'll give a quick walkthrough of the basic calculation. For actual results and final DPS comparison, as always, look at my spreadsheet, but this post explains the way the spreadsheet models Glyph of Starsurge, and contains some general mathematical points that are useful for theorycrafting.

First, we need to know the frequency of Starsurge casts. In the absence of Shooting Stars, we'd get one Starsurge roughly every 17 seconds (15 seconds cooldown, plus the Starsurge cast time itself, plus around a GCD of fudge factor to account for the fact that you typically have to wait for a current cast to finish before you recast it). Call this T_CD. We also need know how often we get Shooting Stars procs. Assuming 100% IS and MF uptime (the sheet does something slight more complex than this, but since we generally maintain high DoT uptime the difference isn't important), the Shooting Stars mean proc time is given by:

,
Where T_IS and T_MF are the tick times of IS and MF. Currenly, both of those are equal to 2/(TotalHaste), ignoring the Sunfire tick time bug which should fixed at some point. On live right now with my total raid-buff haste of around 48% and NG uptime of around 75%, this is roughly 15s between Shooting Stars procs.

So how do we find our actual mean time between Starsurge casts? Remember we cannot use the same trick as above and say:
,
because ordinary Starsurge casts and Shooting Stars procs are not independent. Using a Shooting Stars proc resets the 15s cooldown for normal Starsurges. How do we deal with this?

First, assume that Shooting Stars procs obey a Poisson distribution - Wikipedia, the free encyclopedia . This is means that in a given time interval t, where the expected number of procs is t/T_SS, the chance of having 0 procs is:
. Specifically, if t = T_CD, this tells us the chance of a normal Starsurge cooldown going by without a proc.

This is what we need to know because it gives us the chance that, between two Shooting Stars procs, there will be enough time for a normal Starsurge. So we're going to start with the Shooting Stars proc only, and then add in the normal Starsurge casts that might occur in between. Before we finish however, we should consider the small chance of multiple normal Starsurge casts between procs. Each successive period of T_CD seconds brings an independent chance of proccing or not proccing another Shooting Stars. Therefore the actual expected number of normal Starsurges between procs is given by the sum of a geometric series:
.

We now finally have our final expected mean time between Starsurge casts given by:



With my values of around T_CD = 17s and T_SS = 15s, this gives a T_Total of around 10.3s.

But we still have to see how this affects Starfall cooldown. Call T_Total the final Starsurge proc time from above, and using 60s for the Starfall cooldown (can use the same equation for the 90s cooldown Starfall if you want). Be careful not to assume that the new cooldown is
.
This assumes that you get to apply 60 seconds' worth of Surges to each Starfall. Instead, we need to use:
.

Solving for T_SF:


And that's our final Starfall cooldown that we plug back into the rotation. If T_Total is around 10s, this gives a Starfall cooldown of just about 40 seconds.

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Brief postscript: To actually get a DPS value from this, you need to insert that cooldown into whatever rotation model you're using. Remember to account for the added cast time spend on Starfall in addition to the added damage done. In WrathCalcs, I find the damage value of this Glyph against a single target is less than that of Glyph of Wrath or Glyph of Moonfire. However, one possible scenario is that the Glyph will allow you to cast one Starfall every Lunar Eclipse where you otherwise couldn't. This would make the Glyph a DPS increase, but whether it happens or not depends on many details of the fight.