Code Block 1. Simulating H.T.’s training and performance data using the fitness-fatigue model from Physiology.

cumulative-impact-part-ii-catching-up.R

train_df <- data.frame(day = 1:259, day_of_week = 0:258 %% 7)                   
train_df$period <- ifelse(train_df$day <= 147, "build-up", "competition")       
train_df$w <- with(train_df, w <-                                               
  -24 * (day_of_week == 0) +                                                    
   12 * (day_of_week == 1) +                                                    
    8 * (day_of_week == 2) +                                                    
    0 * (day_of_week == 3) +                                                    
    6 * (day_of_week == 4) +                                                    
   -8 * (day_of_week == 5) +                                                    
    6 * (day_of_week == 6))                                                     

set.seed(1523)
train_df$w <- rpois(nrow(train_df),                                             
                    train_df$w + ifelse(train_df$period == "build-up", 34, 24)) 
                                                                                
exp_decay <- function(t, tau) {                                                 
  exp(-t / tau)                                                                 
}                                                                               
                                                                                
convolve_training <- function(training, n, tau) {                               
  sum(training[1:(n - 1)] * exp_decay((n - 1):1, tau))                          
}                                                                               
                                                                                
fitness <- sapply(1:nrow(train_df),                                             
                  function(n) convolve_training(train_df$w, n, 60))             
                                                                                
fatigue <- sapply(1:nrow(train_df),                                             
                  function(n) convolve_training(train_df$w, n, 13))             
                                                                                
E_perf <- 496 + .07 * fitness - .27 * fatigue
                  
set.seed(45345)                                                                         
train_df$perf <- E_perf + 7.0 * rnorm(nrow(train_df))