I am working with the R programming language. I have a dataset which contains a person's height and whether or not they play basketball.

**I want to see if on average, people over the 80th percentile (height wise) play basketball.**

To do this, I:

- I randomly break the data into a 70% group (train) and a 30% group (test)
- I calculate the 80th percentile of the train group: using this 80th percentile, I see how many people in the test group play basketball
- I calculate on average how accurate I was (on the test group)
- I repeat this procedure many times (e.g. 100) and calculate the total average.

Here is the R code that generates the data for this example:

```
set.seed(123)
height <- rnorm(1000,210,5)
status <- c("basketball", "not_basketball")
basketball_status <- as.character(sample(status, 1000, replace=TRUE, prob=c(0.80, 0.20)))
data_1 <- data.frame(height, basketball_status)
height <- rnorm(1000,190,1)
status <- c("basketball", "not_basketball")
basketball_status <- as.character(sample(status, 1000, replace=TRUE, prob=c(0.8, 0.2)))
data_2 <- data.frame(height, basketball_status)
height <- rnorm(1000,170,5)
status <- c("basketball", "not_basketball")
basketball_status <- as.character(sample(status, 1000, replace=TRUE, prob=c(0.20, 0.80)))
data_3 <- data.frame(height, basketball_status)
my_data <- rbind(data_1, data_2, data_3)
```

And here is the iterative process:

```
library(dplyr)
results <- list()
for (i in 1:100) {
train_i<-sample_frac(my_data, 0.7)
sid<-as.numeric(rownames(train_i))
test_i<-my_data[-sid,]
quantiles = data.frame( train_i %>% summarise (quant_1 = quantile(height, 0.80)))
test_i$basketball_pred = as.character(ifelse(test_i$height > quantiles_i$quant_1 , "basketball", "not_basketball" ))
test_i$accuracy = ifelse(test_i$basketball_pred == test_i$basketball_status, 1, 0)
results_tmp = data.frame(test_i %>%
dplyr::summarize(Mean = mean(accuracy, na.rm=TRUE)))
results_tmp$iteration = i
results_tmp$total_mean = mean(test_i$accuracy)
results[[i]] <- results_tmp
}
results
results_df <- do.call(rbind.data.frame, results)
```

But when I run the iterative process, all averages appear the same:

```
head(results_df)
Mean iteration total_mean
1 0.8344444 1 0.8344444
2 0.8344444 2 0.8344444
3 0.8344444 3 0.8344444
4 0.8344444 4 0.8344444
5 0.8344444 5 0.8344444
6 0.8344444 6 0.8344444
```

**Question:** Does anyone know why this is happening?

Thanks