I saw this report as an opportunity to prove the R skills that I
picked up this semester and expand upon them. I chose an optimization
problem because I thought that I would come to a satisfying conclusion
after learning how to build a model in R. I picked this dataset and
question because Elden Ring is one of my favorite games of all time. It
is notoriously hard and I felt that if I could come to an answer that
could make the game easier, it would be worth my time.
Given the Ultimate Elden Ring dataset, I wanted to figure out the
best possible armor combinations against each of the different damage
types. I also wanted to see how these armor combinations changed when
you changed the player’s weight and roll speed.This was an optimization
problem where I was putting together the best combination of armor
pieces to minimize damage taken.
The data that I am using for this project can be accessed from Kaggle : Ultimate Elden Ring with Shadow of the Erdtree
The first thing that I did was call in the packages I may need while wrangling this data
library(dplyr)
library(tidyr)Then I unzip the file in my Google Drive and bring in the two datasets I needed from the zip: the armor set and the weapons set. I will be performing my optimization based on the armor csv and the weapon csv is needed to add weapon weight into my calculations
# project_files <- unzip('G:/My Drive/MSBA/MSBR 70280/archive.zip')
armors <- read.csv('C:/Users/liams/OneDrive/Documents/R Practice/er-optimizer/data/armors.csv')
weapons <- read.csv('C:/Users/liams/OneDrive/Documents/R Practice/er-optimizer/data/weapons.csv')For the most part the data was clean, but there was some funky stuff going on in the damage negation column. Inside of each row, all of the 8 different damage types were held in this column. Before I could do anything, I needed to break this apart. I put the damage types into a blank data frame, then binded the damage data frame to the original armor one.
armors$damage.negation <- gsub("\\[|\\]|\\{|\\}|'", "", armors$damage.negation)
init_split <- strsplit(armors$damage.negation, ",")
blank_matrix <- matrix(NA, ncol = 8, nrow = length(init_split))
for(i in 1:length(init_split)) {
blank_matrix[i, ] <- init_split[[i]]
}
blank_matrix <- as.data.frame(blank_matrix)
new_names <- c("phy", "vs_str", "vs_sla", "vs_pie",
"mag", "fir", "lit", "hol")
colnames(blank_matrix) <- new_names
blank_matrix[, new_names] <- lapply(new_names, function(x) {
gsub("^.*: ", "", blank_matrix[, x])
})
armors <- cbind(armors, blank_matrix)Next I do some work in the armor data frame to make it easier to work with. I converted all of the damage resistances to numeric. I had to clean up the DLC column into being binary, as before it either had a 0, 1, or it read “Base Game”. Finally, I selected the columns I needed for analysis.
armors <- armors %>%
mutate(phy = as.numeric(phy),
vs_str = as.numeric(vs_str),
vs_sla = as.numeric(vs_sla),
vs_pie = as.numeric(vs_pie),
mag = as.numeric(mag),
fir = as.numeric(fir),
lit = as.numeric(lit),
hol = as.numeric(hol)) %>%
mutate(dlc = case_when(dlc == 'Base Game' ~ 0,
dlc == 0 ~ 0,
TRUE ~ 1)) %>%
select(1, 2, 5, 8, 12:20)In order to make the optimization run smoother, I created dummy variables for each different armor piece. This allowed me to keep everything in one dataframe, as opposed to breaking it out by armor type.
library(fastDummies)
armors <- dummy_cols(armors, select_columns = 'type')
names(armors)[names(armors) == 'type_chest armor'] <- 'type_chest'
names(armors)[names(armors) == 'type_leg armor'] <- 'type_leg'The last “wrangling” I need to do is creating some objects that hold important numbers to my optimization. This means different potential player weights and our base weapon weight. I chose the base equip load based on a normal end game endurance level. I chose the weapon that I did because it was around the average weight of all weapons and it is something that you would probably be carrying around the end of the game. I also made the three different equip loads for each different roll type. Note: this weight does not include any talismans you may be wearing, just armor and the Rivers of Blood katana.
base_EL <- 84.1
weapon_weight <- weapons$weight[weapons$weapon_id == 154]
light_EL <- (0.299 * base_EL) - weapon_weight
med_EL <- (0.699 * base_EL) - weapon_weight
heavy_EL <- (0.99 * base_EL) - weapon_weight
This armor optimization is a bin packing problem. I have what I
want to maximize, damage negation, and I have a few constraints that my
result set needs to follow. One constraint is that total weight needs to
be less than the max weight that I set. Another is that there can only
be at most one armor piece per piece type. This is because you cannot
wear two chest pieces or two gauntlets at a time. I also create two
optimization models, one of which has a constraint for only pulling
items from the base game and one that includes items from the DLC.
First, I pull in the packages I need to optimize.
library(ompr)
library(ompr.roi)
library(ROI.plugin.glpk)
library(magrittr)Next, I create the different variables I need for my optimization function and for my mapply.
armor_row <- nrow(armors)
obj_vars <- colnames(armors)[6:13]
el_vars <- c(light_EL, med_EL, heavy_EL)
obj_vars <- colnames(armors)[6:13]
option_combos <- expand.grid(obj_vars = obj_vars,
el_vars = el_vars)
option_combos$obj_vars <- as.character(option_combos$obj_vars)Here is my optimization function with the base game constraint. This is what I will run through my mapply. This creates a function based on the restraints I talked about earlier. It then solves the function and brings it back to the complete data data frame.
optim_function_base <- function(obj_vars, el_vars) {
obj_var_loop <- armors[, obj_vars]
full_model <- MIPModel() %>%
add_variable(x[i], i = 1:armor_row, type = 'binary') %>%
set_objective(sum_expr(x[i] * obj_var_loop[i], i = 1:armor_row), sense = 'max') %>%
add_constraint(sum_expr(armors$weight[i] * x[i], i = 1:armor_row) <= el_vars) %>%
add_constraint(sum_expr(armors$type_helm[i] * x[i], i = 1:armor_row) <= 1) %>%
add_constraint(sum_expr(armors$type_chest[i] * x[i], i = 1:armor_row) <= 1) %>%
add_constraint(sum_expr(armors$type_gauntlets[i] * x[i], i = 1:armor_row) <= 1) %>%
add_constraint(sum_expr(armors$type_leg[i] * x[i], i = 1:armor_row) <= 1) %>%
add_constraint(sum_expr(armors$dlc[i] * x[i], i = 1:armor_row) == 0)
model_solve <- solve_model(full_model, with_ROI('glpk'))
model_solution <- get_solution(model_solve, x[i])
complete_data <- cbind(armors, model_solution)
output <- complete_data[complete_data$value > 0, ]
output$obj_var <- obj_vars
output$el_vars <- el_vars
output
}Next I put this into an mapply. The mapply runs through all the different possible damage resistances and equip loads and gives me a nice data frame with all the optimal combinations.
all_combo_optim_base <- mapply(
optim_function_base,
option_combos$obj_vars[1:24],
option_combos$el_vars[1:24],
SIMPLIFY = FALSE
)
all_combo_optim_base <- do.call(rbind, all_combo_optim_base)I then repeat this process without the base game constraint just to personally see what DLC items can be valuable.
optim_function_full <- function(obj_vars, el_vars) {
obj_var_loop <- armors[, obj_vars]
full_model <- MIPModel() %>%
add_variable(x[i], i = 1:armor_row, type = 'binary') %>%
set_objective(sum_expr(x[i] * obj_var_loop[i], i = 1:armor_row), sense = 'max') %>%
add_constraint(sum_expr(armors$weight[i] * x[i], i = 1:armor_row) <= el_vars) %>%
add_constraint(sum_expr(armors$type_helm[i] * x[i], i = 1:armor_row) <= 1) %>%
add_constraint(sum_expr(armors$type_chest[i] * x[i], i = 1:armor_row) <= 1) %>%
add_constraint(sum_expr(armors$type_gauntlets[i] * x[i], i = 1:armor_row) <= 1) %>%
add_constraint(sum_expr(armors$type_leg[i] * x[i], i = 1:armor_row) <= 1)
model_solve <- solve_model(full_model, with_ROI('glpk'))
model_solution <- get_solution(model_solve, x[i])
complete_data <- cbind(armors, model_solution)
output <- complete_data[complete_data$value > 0, ]
output$obj_var <- obj_vars
output$el_vars <- el_vars
output
}
all_combo_optim_full <- mapply(
optim_function_full,
option_combos$obj_vars[1:24],
option_combos$el_vars[1:24],
SIMPLIFY = FALSE
)
all_combo_optim_full <- do.call(rbind, all_combo_optim_full)
I do not have any visualizations, but I do have two data frames
each consisting of 24 different armor combinations. There is a
combination for each damage type (8) and for each equip load (3). While
this was not a statistics problem, I know that my model provided me with
the best possible armor combination to negate a certain type of damage.
The data frames are all_combo_optim_base and all_combo_optim_full.
The second to last column in the data frames tells you which damage type
it is optimizing based on, and the last column gives you the equip load
constraint that it followed. If you were looking to stop physical damage
at a medium equip load while playing the base game, you would wear the
Bull-Goat Helm, Radahn’s Lion Armor, Banished Knight Gauntlets, and
Bull-Goat Greaves. If you include the DLC, you actually change your helm
and leg armor, instead equipping the GreatJar and the Verdigris Greaves.
Follwoing are the main damage types and equip loads I focused on for my
report. I will show how you can easily find them and what they look like
in game.
This is the armor set for light rolling against slashing
damage.
lr_vs_slash <- all_combo_optim_base %>%
filter(obj_var == 'vs_sla',
el_vars == light_EL) %>%
select(name, type, weight, vs_sla)
lr_vs_slash name type weight vs_sla
vs_sla.143 Land of Reeds Helm helm 3.6 4.8
vs_sla.344 Marionette Soldier Armor chest armor 8.8 13.5
vs_sla.573 Sorcerer Manchettes gauntlets 1.1 1.3
vs_sla.683 Zamor Legwraps leg armor 5.1 6.8
Here is the armor set for medium rolling against magic damage.
mr_vs_mag <- all_combo_optim_base %>%
filter(obj_var == 'mag',
el_vars == med_EL) %>%
select(name, type, weight, mag)
mr_vs_mag name type weight mag
mag.1631 Nox Mirrorhelm helm 7.5 6.7
mag.2621 Azur's Glintstone Robe chest armor 7.1 15.4
mag.561 Preceptor's Gloves gauntlets 2.1 3.6
mag.663 Preceptor's Trousers leg armor 3.9 8.3
And here is the armor set for heavy rolling against holy damage,
allowing items from the DLC.
hr_vs_hol <- all_combo_optim_full %>%
filter(obj_var == 'hol',
el_vars == heavy_EL) %>%
select(name, type, weight, hol)
hr_vs_hol name type weight hol
hol.1182 Greathood helm 5.1 6.2
hol.2831 Crucible Tree Armor chest armor 15.5 14.5
hol.5302 Godskin Apostle Bracelets gauntlets 2.1 3.6
hol.5872 Dryleaf Cuissardes leg armor 3.1 8.1
When playing a video game that takes some over 100 hours to
complete in full, there are plenty of decisions to be made. If you are
making these decisions without any guidance, the choices you make may
make your life a lot harder. I think that my findings are interesting
and significant because they can be applied to pretty much any situation
the game puts you in to. As long as you are able to find the armor it
recommends, you can set yourself up to dominate any encounter if you
know what type of damage type you will be facing.