The idea here is to create a line-up optimizer for Fantasy Premier League.
I draw on existing fantasy optimizer repositories, especially dfs-with-r's 'coach' package: https://github.com/dfs-with-r/coach.
In particular, we use the follow R packages:
'ompr' # this is the basic MILP - Mixed Integer Linear Programming - package in R that we use to 'solve' our basic optimization equation 'ompr.roi' # this additional solver package helps us utilise the R Optimization Infrastructure (ROI) with ompr 'ROI.plugin.glpk' # this additional package supplies the freely available 'GLPK' solver that we'll use with OMPR and ROI. 'dplyr' # data wrangling and manipulation package to transform our data along the way
I use the example of FPL Review's projections for FPL DGW32. Here I've simply grabbed the table manually and put it in a CSV titled 'fplreview.csv'. There are alternative projections available out there from Fantasy Football Fix, Fantasy Overlord, Foomni Analytics, etc. - you can test these out as well.
First we load the data and add the 'player_id' column in order to be able to identify each player using a unique number. We also add a variable 'n' specifying the total number of players - this will come in handy for our functions below.
Importantly, we also transform the 'team' column to integers, for the optimizer to handle. For the FPL Review data, the 'team' column is already integer, but for other sources this might not be the case, so we include the step.
library(dplyr)
data <- read.csv("data/fplreview.csv",sep=";") %>% tibble::rownames_to_column("player_id")
data$team <- as.integer(data$team)
head(data)
## player_id pos name cost xpts team
## 1 1 G Cech 4.8 0.00 1
## 2 2 G Leno 4.8 4.38 1
## 3 3 D Koscielny 5.4 4.04 1
## 4 4 D Bellerín 5.4 0.00 1
## 5 5 D Monreal 5.4 3.81 1
## 6 6 D Holding 4.3 0.00 1
n <- nrow(data)
Next we add a host of 'helper functions' that will support the optimizer modelling below.
library(ompr)
# this defines how the constraint function (below) will identify the player costs in the data
cost <- function(i) data[["cost"]][i]
# this adds the constraint to our optimizer model that the total cost of our selected players (expressed in the variable 'x'), out of the total number of players ('n'), cannot exceed the budget (a variable we specify in the model function further below)
add_budget_contraint <- function(model, n, cost, budget) {
add_constraint(model, sum_expr(colwise(cost(i)) * x[i], i = 1:n) <= budget)
}
# this adds the constraint to our optimizer model that the total number of selected players (x) cannot exceed the teamsize (a variable we specify in the model function further below, but that will default to '11')
add_teamsize_constraint <- function(model, n, teamsize) {
add_constraint(model, sum_expr(x[i], i = 1:n) == teamsize)
}
# this adds the constraint to our optimizer model that the unique identifier (player_id) can only feature once in the modelled solution
add_unique_id_constraint <- function(model, data) {
n <- nrow(data)
ids <- unique(data[["player_id"]])
has_id <- function(i, id) as.integer(data[["player_id"]][i] == id)
# only need to apply this constraint to players that appear more than once
multi_players <- names(which(table(data[["player_id"]]) > 1))
for (id in multi_players) {
model <- add_constraint(model, sum_expr(colwise(has_id(i, id)) * x[i], i = 1:n) <= 1)
}
model
}
# this sets the basic objective of the optimizer model - that we have to maximize the expected points (xpts)
set_generic_objective <- function(model, n, xpts) {
set_objective(model, sum_expr(colwise(xpts(i)) * x[i], i = 1:n))
}
# this functions defines how the constraint function (below) will identify the player teams in the data
is_team <- function(j, i) as.integer(data$team[i] == j)
# this adds the constraint to our optimizer model that the total number of selected players from a given team cannot exceed the max_from_team variable (a variable we specify in the model function further below, but that will default to '3')
add_max_from_team_constraint <- function(model, n, max_from_team, is_team) {
for (j in 1:length(unique(data$team))) {
model <- add_constraint(model, sum_expr(colwise(is_team(j, i))*x[i], i = 1:n) <= max_from_team)
}
model
}
# these three first functions specify constraints for our optimizer model that the number of goalkeepers in the solution have to be a) the exact number we specify, b) at least 1, c) no more than 2. In the model function further below, we'll specify that unless we manually supply a desired number in our solution (a), the model will apply constraints (b) and (c). The fourth function defines how the constraint functions will identify the goalkeepers in the data.
add_gk_constraint <- function(model, n, gk, is_gk){
model <- add_constraint(model, sum_expr(colwise(is_gk(i)) * x[i], i = 1:n) == gk)
model
}
add_min_gk_constraint <- function(model, n, is_gk){
model <- add_constraint(model, sum_expr(colwise(is_gk(i)) * x[i], i = 1:n) >= 1)
model
}
add_max_gk_constraint <- function(model, n, is_gk){
model <- add_constraint(model, sum_expr(colwise(is_gk(i)) * x[i], i = 1:n) <= 2)
model
}
is_gk <- function(i) as.integer(data$pos[i] == "G")
# these three first functions specify constraints for our optimizer model that the number of defenders in the solution have to be a) the exact number we specify, b) at least 3, c) no more than 5. In the model function further below, we'll specify that unless we manually supply a desired number in our solution (a), the model will apply constraints (b) and (c). The fourth function defines how the constraint functions will identify the defenders in the data.
add_def_constraint <- function(model, n, def, is_def){
model <- add_constraint(model, sum_expr(colwise(is_def(i)) * x[i], i = 1:n) == def)
model
}
add_min_def_constraint <- function(model, n, is_def){
model <- add_constraint(model, sum_expr(colwise(is_def(i)) * x[i], i = 1:n) >= 3)
model
}
add_max_def_constraint <- function(model, n, is_def){
model <- add_constraint(model, sum_expr(colwise(is_def(i)) * x[i], i = 1:n) <= 5)
model
}
is_def <- function(i) as.integer(data$pos[i] == "D")
# these three first functions specify constraints for our optimizer model that the number of midfielders in the solution have to be a) the exact number we specify, b) at least 2, c) no more than 5. In the model function further below, we'll specify that unless we manually supply a desired number in our solution (a), the model will apply constraints (b) and (c). The fourth function defines how the constraint functions will identify the midfielders in the data.
add_mid_constraint <- function(model, n, mid, is_mid){
model <- add_constraint(model, sum_expr(colwise(is_mid(i)) * x[i], i = 1:n) == mid)
model
}
add_min_mid_constraint <- function(model, n, is_mid){
model <- add_constraint(model, sum_expr(colwise(is_mid(i)) * x[i], i = 1:n) >= 2)
model
}
add_max_mid_constraint <- function(model, n, is_mid){
model <- add_constraint(model, sum_expr(colwise(is_mid(i)) * x[i], i = 1:n) <= 5)
model
}
is_mid <- function(i) as.integer(data$pos[i] == "M")
# these three first functions specify constraints for our optimizer model that the number of forwards in the solution have to be a) the exact number we specify, b) at least 1, c) no more than 3. In the model function further below, we'll specify that unless we manually supply a desired number in our solution (a), the model will apply constraints (b) and (c). The fourth function defines how the constraint functions will identify the forwards in the data.
add_fwd_constraint <- function(model, n, fwd, is_fwd){
model <- add_constraint(model, sum_expr(colwise(is_fwd(i)) * x[i], i = 1:n) == fwd)
model
}
add_min_fwd_constraint <- function(model, n, is_fwd){
model <- add_constraint(model, sum_expr(colwise(is_fwd(i)) * x[i], i = 1:n) >= 1)
model
}
add_max_fwd_constraint <- function(model, n, is_fwd){
model <- add_constraint(model, sum_expr(colwise(is_fwd(i)) * x[i], i = 1:n) <= 3)
model
}
is_fwd <- function(i) as.integer(data$pos[i] == "F")
# the first function specifies the constraint that a 'must'-have player, to be specified in the model function below, HAS to be part of the solution. The second function defines how the constraint functions will identify the 'must' player in the data.
add_must_constraint <- function(model, n, must, is_must){
model <- add_constraint(model, sum_expr(colwise(is_must(i, must)) * x[i], i = 1:n) == length(must))
model
}
is_must <- function(i, must) as.integer(data$name[i] %in% must)
# the first function specifies the constraint that a 'nope' player, to be specified in the model function below, WILL NOT be part of the solution. The second function defines how the constraint functions will identify the 'nope' player in the data.
add_nope_constraint <- function(model, n, nope, is_nope){
model <- add_constraint(model, sum_expr(colwise(is_nope(i, nope)) * x[i], i = 1:n) == 0)
model
}
is_nope <- function(i, nope) as.integer(data$name[i] %in% nope)
Next we create the simple MILP model function to optimize our line-up, using the constraints defined above.
# first we define the function, specifying the variables to be supplied (per above helper functions) and their default values:
model_fpl <- function(data, budget, teamsize = 11, max_from_team = 3, gk = NULL, def = NULL, mid = NULL, fwd = NULL, must = NULL, nope = NULL, type = "binary"){
# first we define the base model, applying the constraints that HAVE to be a part of the solution:
my_model <- MILPModel() %>%
add_variable(x[i], i = 1:n, type = "binary") %>%
add_budget_contraint(n, cost, budget) %>%
add_teamsize_constraint(n,teamsize) %>%
add_max_from_team_constraint(n, max_from_team, is_team) %>%
add_max_gk_constraint(n, is_gk) %>%
add_max_def_constraint(n, is_def) %>%
add_max_mid_constraint(n, is_mid) %>%
add_max_fwd_constraint(n, is_fwd)
# next we apply the position-specific constraints that depend on whether we've supplied the function with targeted numbers of GK/DEF/MID/FWD players and MUSTs/NOPEs for our solution.
ifelse(is.null(gk),
my_model <- my_model %>% add_min_gk_constraint(n, is_gk),
my_model <- my_model %>% add_gk_constraint(n, gk, is_gk))
ifelse(is.null(def),
my_model <- my_model %>% add_min_def_constraint(n, is_def),
my_model <- my_model %>% add_def_constraint(n, def, is_def))
ifelse(is.null(mid),
my_model <- my_model %>% add_min_mid_constraint(n, is_mid),
my_model <- my_model %>% add_mid_constraint(n, mid, is_mid))
ifelse(is.null(fwd),
my_model <- my_model %>% add_min_fwd_constraint(n, is_fwd),
my_model <- my_model %>% add_fwd_constraint(n, fwd, is_fwd))
ifelse(is.null(must),"",
my_model <- my_model %>% add_must_constraint(n, must, is_must))
ifelse(is.null(nope),"",
my_model <- my_model %>% add_nope_constraint(n, nope, is_nope))
# finally we add the 'unique id' constraint
my_model %>% add_unique_id_constraint(data)
}
Next we create the optimizer function, which will take the constraints model set out above and 'solve' the optimization equation to produce the optimal FPL line-up:
library(ompr.roi)
library(ROI.plugin.glpk)
# first we define the function and its basic properties, incl. the data, model and a selection of 'solvers'
optimize_fpl <- function(data, model, solver = c("glpk","symphony","cbc")){
# defining helpers for the solver to identify in the data
n <- nrow(data)
xpts <- function(i) data[["xpts"]][i]
# using our 'generic objective' function above to set the optimizer objective
model <- set_generic_objective(model, n, xpts)
# drawing out the selected 'solver'
solver <- match.arg(solver)
# developing the model solution using our solver
result <- solve_model(model, with_ROI(solver=solver))
# grabbing the result solution for our variable 'x' (the players)
solution <- get_solution(result, x[i])
# filtering out or final line-up (those player with 'x' marked in the solution)
matches <- (solution %>% filter(value==1))$i
# structuring the line-up output nicely
lineup <- data
lineup$x <- solution$value
return(lineup %>% filter(x==1) %>% select(player_id,pos,name,cost,xpts,team) %>% arrange(factor(pos,levels=c("G","D","M","F")),-desc(name),-desc(xpts)))
}
Finally, we test out the model, saying we have a budget for 11 players of around 85m:
model <- model_fpl(data, budget = 85, teamsize = 11, gk = 1)
my_lineup <- optimize_fpl(data,model)
my_lineup
## player_id pos name cost xpts team
## 1 62 G Ryan 4.4 7.48 3
## 2 154 D Azpilicueta 6.3 9.09 6
## 3 372 D Laporte 5.9 9.95 13
## 4 159 D Rüdiger 5.9 7.80 6
## 5 187 D Schlupp 4.5 7.69 7
## 6 375 M David Silva 8.5 10.25 13
## 7 498 M Eriksen 9.2 9.02 17
## 8 163 M Hazard 10.9 11.66 6
## 9 408 M Pogba 8.9 10.03 14
## 10 501 M Son 8.6 9.18 17
## 11 384 F Agüero 11.8 13.15 13