As far as I can tell it's the Captains choice. I have been on ships that the Capitan always backed into the slip, always docked on the Port or starboard side, or alternated between Port or Starboard side. I do not think it is possible to predict with some assurance which side of the ship will be the pier side, it might also be influenced by the wind and currents.
Is there a "madness to the method" regarding whether a ship moors with the pier to the port or starboard? If it is the Captain's choice, is there a pattern that most use?
In short...is it possible to predict with some assurance which side of the ship will be the pier side when they dock at each of the ports of call on a cruise?
It's totally random.
Well, not quite -- but it depends upon considerations such as the layout of the berth to which the ship is assigned, actual conditions in the harbor when the ship enters, and anticipated conditions when the ship expects to leave. Since the port or terminal authorities may assign the ship to a different berth from one cruise to the next, there's no way that you and I, as passengers, can predict in advance where or how a ship will moor or anchor in any port on a particular cruise.