During my final semester at Miami University, I had the opportunity to work with the Senior Synchronized Skating Team, analyzing past competition data to identify ways to optimize their performance. My goal was to help the team focus on specific skating elements (or moves) that could maximize their overall score in competitions.
In synchronized skating, teams are judged using the International Judging System (IJS), where the combined score from both the Short Program and Long Program can reach a maximum of 190 points. To assist the team in strategic planning, I developed an R script that simulates a competition scenario based on IJS scoring protocols.
This script allows for:
The input of specific skating elements to calculate their potential contribution to the total score.
The generation of realistic scores using predefined Grade of Execution (GOE) values and component scores.
The identification of score targets for each element, helping the team understand which moves they should emphasize in practice.
By running thousands of simulations, this analysis helps pinpoint optimal scoring strategies and provides actionable insights on which elements the team should refine to achieve a score close to 190.
if (!require(tidyverse)) install.packages("tidyverse")## Loading required package: tidyverse## Warning: package 'ggplot2' was built under R version 4.3.2## Warning: package 'tidyr' was built under R version 4.3.2## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
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## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errorsif (!require(readxl)) install.packages("readxl")## Loading required package: readxllibrary(tidyverse)
library(readxl)file_path <- "Copy of 24-25 IJS Protocol Testing.xlsx"
sov <- read_excel(file_path, sheet = "Scale of Value")
# Remove the first row (column headers) and convert BASE to numeric
sov <- sov[-1, ]
sov$BASE <- as.numeric(sov$BASE)
# Rename columns for consistency
colnames(sov) <- c("Element", "BASE", "-5", "-4", "-3", "-2", "-1", "0", "1", "2", "3", "4", "5")short_program <- tibble(
Element = c("SySp4", "I4+pi4", "TrE4", "NHEb+s4", "ME4"),
Base_Value = c(6.50, 7.50, 5.00, 5.00, 6.50)
)
long_program <- tibble(
Element = c("Pa4", "PB4", "GL4", "I4+pi4", "TwE4", "ME4", "Cr1", "I4+piB", "NHE4+sB", "AC2"),
Base_Value = c(6.50, 6.50, 7.50, 7.00, 6.50, 6.50, 4.00, 4.25, 4.00, 4.00)
)# Function to generate GOE scores between 1 and 3
generate_goe <- function(num_elements) {
sample(1:3, num_elements, replace = TRUE)
}
# Function to generate component scores
generate_component_scores <- function() {
runif(3, 7.00, 9.75) # Generate 3 scores between 7.00 and 9.75
}
calculate_goe_value <- function(element, base_value, goe) {
goe_value <- sov[[as.character(goe)]][sov$Element == element]
if (is.na(goe_value) || length(goe_value) == 0) {
goe_value <- base_value * (goe / 10)
}
as.numeric(goe_value)
}calculate_program_score <- function(program, goe_scores, component_scores, is_short_program) {
technical_score <- program %>%
mutate(
GOE = goe_scores,
GOE_Value = mapply(calculate_goe_value, Element, Base_Value, GOE),
Total = Base_Value + GOE_Value
)
component_factor <- if(is_short_program) 1.33 else 2.67
component_score <- sum(component_scores) * component_factor
list(
technical_details = technical_score,
component_scores = component_scores,
technical_score = sum(technical_score$Total),
component_score = component_score,
total_score = sum(technical_score$Total) + component_score
)
}simulate_competition <- function() {
sp_goe <- generate_goe(nrow(short_program))
lp_goe <- generate_goe(nrow(long_program))
sp_components <- generate_component_scores()
lp_components <- generate_component_scores()
sp_details <- calculate_program_score(short_program, sp_goe, sp_components, TRUE)
lp_details <- calculate_program_score(long_program, lp_goe, lp_components, FALSE)
total_score <- sp_details$total_score + lp_details$total_score
list(
SP = sp_details,
LP = lp_details,
Total = total_score
)
}
# Run simulations
num_simulations <- 10000
results <- replicate(num_simulations, simulate_competition(), simplify = FALSE)
# Find best combination
best_simulation <- which.min(abs(sapply(results, function(x) x$Total) - 190))
best_result <- results[[best_simulation]]
cat("\nBest combination for score close to 190:\n")##
## Best combination for score close to 190:cat("\nShort Program:\n")##
## Short Program:print(best_result$SP$technical_details)## # A tibble: 5 × 5
## Element Base_Value GOE GOE_Value Total
## <chr> <dbl> <int> <dbl> <dbl>
## 1 SySp4 6.5 1 0.65 7.15
## 2 I4+pi4 7.5 2 1.5 9
## 3 TrE4 5 2 1 6
## 4 NHEb+s4 5 1 0.5 5.5
## 5 ME4 6.5 1 0.65 7.15cat("Component Scores:", best_result$SP$component_scores, "\n")## Component Scores: 7.422705 7.528882 8.332669cat("Total Short Program Score:", best_result$SP$total_score, "\n")## Total Short Program Score: 65.76806cat("\nLong Program:\n")##
## Long Program:print(best_result$LP$technical_details)## # A tibble: 10 × 5
## Element Base_Value GOE GOE_Value Total
## <chr> <dbl> <int> <dbl> <dbl>
## 1 Pa4 6.5 2 1.3 7.8
## 2 PB4 6.5 1 0.65 7.15
## 3 GL4 7.5 2 1.5 9
## 4 I4+pi4 7 1 0.75 7.75
## 5 TwE4 6.5 1 0.65 7.15
## 6 ME4 6.5 1 0.65 7.15
## 7 Cr1 4 2 0.8 4.8
## 8 I4+piB 4.25 3 1.27 5.52
## 9 NHE4+sB 4 1 0.4 4.4
## 10 AC2 4 1 0.4 4.4cat("Component Scores:", best_result$LP$component_scores, "\n")## Component Scores: 7.19239 7.039825 8.075722cat("Total Long Program Score:", best_result$LP$total_score, "\n")## Total Long Program Score: 124.6872cat("\nTotal Combined Score:", best_result$Total, "\n")##
## Total Combined Score: 190.4553