Improved Shadow Bolt uptime estimates

isb_sim.R

library("tidyverse")
library("tidylog")

### Mechanic explantion

# When your SB crits, a debuff (shadow vulnerability=SV) is placed on your 
# target. That debuff increases ALL shadow damage taken by 20% and can last 
# up to 12 seconds. So SV will actually increase the damage:
#    
#    - your shadow dots tick for,
# - of your next SB,
# - of your drain life,
# - of another warlock's SB and shadow dots and drain life,
# - of the spells of a shadow priest,
# - of a shadow dmg wand
# - etc..etc..
# 
# Now, SV has 4 charges hence the number "4" on the icon on your target. That 
# means that the debuff will stay on the target until 4 NON-PERIODIC shadow dmg
# sources are applied. So dots do NOT consume the charges of SV debuff. Direct 
# shadow damage will though. So a shadow bolt, a shadow burn, a shadow wand or 
# a mind blast will consume 1 charge.
# 
# When all 4 charges are consumed by direct shadow damage or 12 seconds pass 
# without all 4 charges having been consumed, SV ends.
# 
# If the target is hit by a new shadow bolt crit while under the influence of 
# the debuff, the charges become again 4 and the 12 sec timer is reset and 
# starts ticking for another 12 seconds.


isb <- 0
simulations <- 1000000
isbuptime <- 0
crit <- 0.15
hit <- 0.83
bolt <- 1054.74
casttime <- 2.5
isbtimeleft <- 0
counter <- 0

for ( i in seq(1:simulations)) {
   counter = counter + 1
   if (isb > 0) { isbtimeleft = isbtimeleft - casttime }
   if (isbtimeleft < 0) { isb = 0 }
   if (isb > 0) { isbuptime = isbuptime + casttime }
   if (runif(1) > hit) { next }
   if (runif(1) <= crit) {
      if (runif(1) <= hit) {
         isb = 4
         isbtimeleft = 12
      }
      else {
         if (isb > 0) { isb = isb - 1 }
         }
   } else {
      if (isb > 0) { isb = isb - 1 }
   }
}

sim_isbuptime <- isbuptime / (simulations * casttime)
sim_isbuptime
# 0.35
1 - (1- crit * hit) ^ 4
# 0.41