The First Mate Band is new and, so far, has been reported to drop from Mr. Smite in the Deadmines Dungeon. As displayed in-game, the set's bonus is:
(2) Set: Chance on melee swing to become Angry, increasing strength by 50 for 10 sec.
(2) Set: +20 Strength
What makes this set very interesting, though, is that the Epic half of it (The Better Half, if you will) is a level 60 item. This has implications for your future gearing (as well as your bank space), as it implies you may be looking for Deadmines loot for a very long time to come. It's also possible that other dungeons will feature a similar setup, where one item might be the first half of a set that can't be completed until much later in the leveling process.
As of now, we do not know where the Band of the Better Half is found in-game.
