Haha, THAT is an excellent question! Wish I knew the answer to that. I've been banging away at Darkhart, Timmy, Neban, the thrall pool, Menta bridge, and the treasure room since Friday. ATM I have 6 relics across 3 pirates for all that work. My 31 has just one sailing relic. Kat has 2. My level 38 has 3. BTW my 38 always fights with Kat. Go figure why my almost fully mastered pirate can't find the sword off all those different places on multiple servers an all different times of day. The luck o the Irish is most assuredly NOT in Kat.
I know for a fact of at least one person who got it from Neban. Another from Tormenta near the bridge. I have been present for the finding of 3 with Darkhart, 2 from a single Darkhart on just one day. Both of those were in a rather large crew in the evening. The very next day Darkhart gave out in a small crew in the afternoon.
As for odds you got me. In one particular drop there were 4 of us. 3 pirates got relics. Kat got a common. Seems to happen to her rather a lot. So, I have no clue about odds. I just know they don't like Kat!