These last couple of fellows are right, it was my experience that 95% of the gentlemen wore their tuxes on formal nights, and some even on the Informal (semi-formal) nights. The were dark suits yes, but the vast majority of the men were in tuxes. I was on the 10 May Caribbean sailing which I thought might be a little less formal than a crossing. Our two seatmates at dinner -- two gentlemen from Austrailia even wore their Indian Formal "Raja" Suits one night for a birthday celebration on the optional formal night.
My husband got a great deal on a tux on sale which he'll wear on cruises and to the daughter's weddings, so we figured you couldn't beat the $160.00 he paid for it.
Daytimes were definitely NOT workout clothes. Even in dressy long shorts and nice polo shirts one could feel not dressed up enough depending on what venue you were visiting. Most people were definitely in nice resort clothing all day.
My suggestion -- leave the sweatsuits home and pack the tux.