Completion Rate Intuition

The median difference between n=5 & n=20 is 10%

The median difference between n=5 & the actual completion rate at N=10,000 is 11.0059%

Here is a graph from 1000 iterations showing the absolute error at a sample size of 5. The median error at n=5 is 11%, meaning 50% of the time the completion rate will change by less than 11%. 75% of the time the average error at n=5 will be less than 21%. 95% of the time the error will be less than 38% (which is what the 95% confidence interval predicts).