On Sharpcast Usage
by Fürst Blumier
Introduction
This document aims to answer the question whether it is better to use Sharpcast for Thunder or for Fire in an ideal setting. Basis for the calculations provided in this document is the model DialaceStarvy employs in his own Thunder calculations.
We will clarify some abbreviations and terminology that will be used. “Thunder III” and “Thundercloud proc” will be abbreviated by “T3” and “T3P” respectively. “Fire III” and “Firestarter proc” will be abbreviated by “F3” and “F3P” respectively. A “hard refresh cycle” (HRC) refers to the chain of procs a single hard refresh produces (at least the procs which actually get used). It also includes all Thunder ticks produced by said hard refresh and chain of procs.
Sharp Fire
We begin with the usage of Sharpcast for F3. This changes nothing about the HRC so we can just use the normal equations given for the delayed proc usage. The average number of ticks per HRC is given by
with
which results in
The average number of refreshes avgrefresh is independent of proc usage and a result of the limit of the geometric series. Thus the average number of ticks is given by
with avgrefresh = 2.32. Now the average potency of a standard HRC results in
with s denoting the spellspeed scalar.
Sharp Thunder
Now to the usage of Sharpcast for T3. DialaceStarvy already did all the necessary calculations in his Document and we will use the results. The average number of ticks is
with
This gives us
After the guaranteed proc from the Sharpcast is used, the situation is the same as with a normal HRC. Thus the potency a Sharpcast used on T3 results in
over the standard HRC. Or
Here s denotes the spellspeed scalar.
Comparison between Sharp Thunder and Sharp Fire
The duration of a HRC is given by
Now we let g be the time of a base 2.5s cast, performing an HRC takes g avgrefresh seconds on average. We remember that avgrefresh is independent of usage and equals the limit of the geometric series. P denotes the average potency per second outside of thunder, without taking raid buffs or Enochian into account. With that our potency per second equals
This equation holds true for both sharp Thunder and sharp Fire. What differs is the avgpot in both cases and the average potency per second P outside of thunder. In the following part we will denote all variables in respect to thunder with a prime if it’s applicable. The gain of sharp Thunder over sharp Fire is
P is being calculated using 6 standard rotations to gain a timeframe of 3 minutes which is the same as the cooldown time of Convert, our longest CD. For P 3 sharped Fires are used and the other F3P combinations are weighted by its probability to occur. For P’ all combinations of F3Ps are weighted by its probability to occur. The results are calculated here and presented in the following graph:
and
This graph assumes optimal play though. In reality ticks are gonna be cut short and F4s have to be skipped or downgraded in Convert phases. Assuming every Thunder refresh being cut short by 2 ticks and 1 downgraded F4 every 3 minutes the results looks like this:
and
Conclusion
As expected sharp Thunder is a slight potency gain of about 1.5 pps or about 3.75 potency per GCD or 900 potency in a 10 min fight assuming optimal play. The downside of sharping Thunder is less safety in your Fire phase since you are lacking the F3P. The calculations also assume perfect Thunder usage without cutting a T3 short which is in reality most of the time not the case. This means with perfect play sharp Thunder is a gain, while sharp Fire is a safer and nearly equal alternative.
