Supplementary Figure S7

library(tidyverse)

df <-
  tibble(n_matches = seq(30)) %>%
  mutate(n_cpds = ceiling((1 / (n_matches * 1.5) * 100)))

df

df %>%
  ggplot(aes(n_matches, n_cpds)) +
  geom_point()

generate_unif_corr <-
  function(n_matches, n_cpds) {
    seq(n_cpds) %>%
      map_dbl(~ mean(runif(n_matches)**2))
  }

sd(generate_unif_corr(1, 1000))

[1] 0.3020492

sd(generate_unif_corr(100, 1000))

[1] 0.03106674

df1 <- 
  df %>% 
  rowwise() %>% 
  mutate(avg_corr = list(corr = generate_unif_corr(n_matches, n_cpds)))

df2 <- 
  df1 %>%
  unnest(avg_corr)

df2 %>% 
  ggplot(aes(avg_corr, n_matches)) + 
  geom_point() +
  ggtitle("Random data")