The usual method for calculating these percentages is to calculate a power rating for each team, then to use the log5 formula[1] to arrive at the percentage chance of a team winning.
So, the 1-4% chance of a 16 winning is the result of applying the log5 algorithm to their power ratings.
Also remember that there's only 80 16-vs-1 games in 20 years, and only expanded to 64 teams in 1985, so it's totally possible that there is a 1-4% chance for a 16 to beat a 1 and it just hasn't happened yet.
So, the 1-4% chance of a 16 winning is the result of applying the log5 algorithm to their power ratings.
Also remember that there's only 80 16-vs-1 games in 20 years, and only expanded to 64 teams in 1985, so it's totally possible that there is a 1-4% chance for a 16 to beat a 1 and it just hasn't happened yet.
[1] https://en.wikipedia.org/wiki/Log5