Shadow Vulnerability simulation

sv_sim_grid_expand.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.
# 
# I really hope I helped some warlocks figuring how this talent really works.
# Source: https://blue.mmo-champion.com/topic/18196-improved-shadow-bolt-explained/

# Original sim code here (by Guybrush?): http://jsfiddle.net/turinpt/rgfdxyr4/

# Player stats
crit_hit_expand <- expand.grid(crit = seq(1:50) / 100, hit = c(83:99) / 100)
crit <- crit_hit_expand %>% pull(crit)
hit <- crit_hit_expand %>% pull(hit)
# Shadow Vulnerability counters
sv_charges <- 0
sv_uptime <- 0
sv_timeleft <- 0
# Metrics
counter <- 0
lock_missed <- 0
is_crit <- 0

sim <- function(crit, hit) {
   
   simulations <- 100000
   #Player Constants
   bolt <- 1054.74
   sb_casttime <- 2.5
   
   for ( i in seq(1:simulations)) {
      counter = counter + 1
      if (sv_charges > 0) { sv_timeleft = sv_timeleft - sb_casttime }
      if (sv_timeleft < 0) { sv_charges = 0 }
      if (sv_charges > 0) { sv_uptime = sv_uptime + sb_casttime }
      if (runif(1) > hit) { 
         lock_missed = lock_missed + 1
         next }
      if (runif(1) <= crit) {
         is_crit  = is_crit + 1
         if (runif(1) <= hit) {
            sv_charges = 4
            sv_timeleft = 12
         }
         else {
            if (sv_charges > 0) { sv_charges = sv_charges - 1 }
         }
      } else {
         if (sv_charges > 0) { sv_charges = sv_charges - 1 }
      }
   }
   
   # ISB Uptime. Assume constant, uninterrupted casting and no lag
   sim_sv_uptime <- sv_uptime / (simulations * sb_casttime)
   # Simulated crit rate
   sim_crit <- round(is_crit / simulations, 3)
   # True crit rate
   true_crit <- round(crit * hit, 3)
   # Roll up metrics for each run of the simulation into a list.
   sim_vars <- list(sim_sv_uptime = sim_sv_uptime, hit = hit, crit = crit,
                    sim_crit = sim_crit, true_crit = true_crit)
}

# Map each of the 850 hit and crit values to the sim function
sim_results <- pmap(list(crit, hit), sim) %>%
   map_df(as_tibble) %>%
   mutate(sim_sv_uptime = round(sim_sv_uptime, 3),
          quartic_predict = 1 - (1 - crit * hit) ^ 4)

# Create a polynomial model to fit our simulation results.
model <- lm(data = sim_results, sim_sv_uptime ~ poly(crit * hit, 2, raw = TRUE))
summary(model)
confint(model, level=0.95)
# Add the model predict to the dataframe for plotting
sim_results$predict <-  round(predict(model, newdata = sim_results), 3)

# Plot 1
sim_results %>%
   ggplot(aes(x = true_crit, y = predict)) +
   geom_point(color = "red") +
   geom_point(aes(x = true_crit, y = quartic_predict)) +
   theme_minimal() +
   scale_y_continuous(limits = c(0,1), labels = scales::percent) +
   scale_x_continuous(limits = c(0,0.5), labels = scales::percent) +
   labs(x = "True Crit (Hit chance * Critical hit chance)", y = "Estimated Shadow Vulnerability uptime %",
        title = "Simulations predict lower uptime vs. quartic equation",
        subtitle = "Formula: 1 - (1 - crit * hit) ^ 4")

# Plot 2
sim_results %>%
   ggplot(aes(x = crit, y = sim_sv_uptime, group = hit, color = as.factor(hit))) +
   geom_smooth() +
   theme_minimal() +
   scale_y_continuous(limits = c(0,1), labels = scales::percent) +
   scale_x_continuous(limits = c(0,0.5), labels = scales::percent) +
   labs(x = "Critical hit chance", y = "Shadow Vulnerability uptime %",
        title = "Shadow Vulnerability uptime by critical hit chance.", subtitle = "Each curve is the simulated SV uptime by crit for a given hit chance.", color = "Hit chance")