unborn aurora
TLDR:
- willful momentum good
- uptime has diminishing returns, on top of the score to percent DR and the percent to proc_chance DR
- At low values of spirit percent (less than 5%), uptime is linear:
uptime = 3 * spirit_percent - At 11% spirit (10% proc chance), uptime is 26%
- At 25% spirit percent (20% proc chance), uptime is 48%
This is valid for helena and elarion for which almost all GCDs are spent on abilities which can proc spirit.
For other chars, you have to determine which curve is the most appropriate depending on how frequent events which can do spirit procs are.
The plot shows uptime as a function of spirit proc chance.
The most important line is the middle line: n_casts = 3 which is typical of a finalized character.
For elarion, ult + grace puts us on n_casts = 4 or 5
The plot doesn't take into account the percent to proc chance DR:
proc_chance = spirit_percent / (1 + spirit_percent)
The math
uptime is surprisingly easy to compute: uptime = 1 (1 - spirit_proc_chance) ** n_casts where n_casts is the number of casts you get during the duration of the buff which can do a spirit proc
Proof:
- In order for the buff to be down, we need to have failed the procs of the last
n_casts = floor(wm_duration / gcd * (1 + haste_percent)casts - That probability is
(1 - proc_chance) ** n_casts - Thus:
uptime = 1 - (1 - proc_chance) ** n_casts - Linear approximation at 0:
approx = 0 + n_casts * proc_chance
broken orbit