Loading Packages and Simulating Data<\/strong><\/span><\/p>\n Aside from loading {tidyverse<\/strong>} we will also load the {zoo<\/strong>} package, which is a common package used for constructing rolling window functions (this is useful as it prevents us from having to write our own custom function).<\/p>\n We will start with a simple data set of just 10 training load observations.<\/p>\n <\/p>\n Calculate the z-score with the mean and standard deviation of all data that came before it<\/strong><\/span><\/p>\n To do this we use the rollapplyr()<\/strong> function from the {zoo<\/strong>} package. If we want to include the most recent observation in the mean and standard deviation we can run the function as is. However, because we want the mean and standard deviation of all data previous to, but not including, the most recent observation we wrap this entire function in the lag<\/strong>()<\/strong> function, which will take the data in the row directly above the recent observation. The width<\/strong> argument indicates the width of the window we want to calculate the function over. In this case, since we have a day<\/strong> variable we can use that number as our window width to ensure we are getting all observed data prior to the most recent observation.<\/p>\n <\/p>\n This looks correct. As a sanity check, let’s calculate the mean and standard deviation of the first 4 rows of training load observations and see if those values correspond to what is in the lag_mean<\/strong> and lag_sd<\/strong> columns at row 5.<\/p>\n It worked!<\/p>\n A more complicated example<\/strong><\/span><\/p>\n Okay, that was an easy one. We had one athlete and we had a training day column, which we could use for the window with, already built for us. What if we have a data set with multiple athletes and only training dates, representing the day that training happened?<\/p>\n To make this work we will group_by()<\/strong> the athlete, and use the row_number()<\/strong> function to calculate a training day variable that represents our window width. Then, we simply use the same code above.<\/p>\n Let’s simulate some data.<\/p>\n Now we run all of our functions for each athlete.<\/p>\n\r\n## Load Libraries\r\nlibrary(tidyverse)\r\nlibrary(zoo)\r\n\r\n## Simulate Data\r\nset.seed(45)\r\nd <- tibble(\r\n day = 1:10,\r\n training_load = round(rnorm(n = 10, min = 250, max = 350), 0)\r\n)\r\n\r\nd\r\n<\/pre>\n
![\"\"](\"https:\/\/optimumsportsperformance.com\/blog\/wp-content\/uploads\/2023\/04\/Screenshot-2023-04-04-at-7.09.30-PM.png\")
<\/a><\/p>\n\r\nd <- d %>%\r\n mutate(lag_mean = lag(rollapplyr(data = training_load, width = day, FUN = mean, fill = NA)),\r\n lag_sd = lag(rollapplyr(data = training_load, width = day, FUN = sd, fill = NA)),\r\n z_score = (training_load - lag_mean) \/ lag_sd)\r\n\r\nd\r\n<\/pre>\n
![\"\"](\"https:\/\/optimumsportsperformance.com\/blog\/wp-content\/uploads\/2023\/04\/Screenshot-2023-04-04-at-7.14.20-PM.png\")
<\/a><\/p>\n\r\nfirst_four <- d %>%\r\n slice(1:4) %>%\r\n pull(training_load)\r\n\r\nmean(first_four)\r\nsd(first_four)\r\n<\/pre>\n
![\"\"](\"https:\/\/optimumsportsperformance.com\/blog\/wp-content\/uploads\/2023\/04\/Screenshot-2023-04-04-at-7.15.01-PM.png\")
<\/a><\/p>\n\r\nset.seed(67)\r\nd <- tibble(\r\n training_date = rep(seq(as.Date("2023-01-01"),as.Date("2023-01-05"), by = 1), times = 3),\r\n athlete = rep(c("Karl", "Bonnie", "Thomas"), each = 5),\r\n training_load = round(runif(n = 15, min = 250, max = 350), 0)\r\n)\r\n\r\nd\r\n<\/pre>\n![\"\"](\"https:\/\/optimumsportsperformance.com\/blog\/wp-content\/uploads\/2023\/04\/Screenshot-2023-04-04-at-7.25.47-PM.png\")
<\/a><\/p>\n\r\nd <- d %>%\r\n group_by(athlete) %>%\r\n mutate(training_day = row_number(), \r\n lag_mean = lag(rollapplyr(data = training_load, width = training_day, FUN = mean, fill = NA)),\r\n lag_sd = lag(rollapplyr(data = training_load, width = training_day, FUN = sd, fill = NA)),\r\n z_score = (training_load - lag_mean) \/ lag_sd)\r\n\r\n\r\nd\r\n<\/pre>\n
![\"\"](\"https:\/\/optimumsportsperformance.com\/blog\/wp-content\/uploads\/2023\/04\/Screenshot-2023-04-04-at-7.27.50-PM-1024x610.png\")
<\/a><\/p>\n