Random is just that… random. So you will see some players be assigned the #1 spot more often than others. It’s rare that random is the best choice for any of the settings because random doesn’t feel random to humans.
To get a more balanced distribution pick the… “balanced” option. It’ll make sure that players play every position evenly (or as good as it gets, nothing is perfect).
“Rotating” is a pretty specialized option. It only works when you have more than one game per round. It’s best if you have four-player groups and four games per round. In that case every player plays every position once in each round.