Luck does not play a role in the guaranteed drop that is awarded to a random "top attacker" by killing a Captain. It's completely random. The Lighthouse is a guarantee to everyone on the "top attacker" list, again luck not involved.
Where luck DOES come into play in a big way are the points you accumulate by killing creatures. The points are awarded based on the fame of the creature you kill grounded on the principle that the more difficult a creature, the more fame it will have. As you acquire more and more points your chances of getting a minor artifact drop approach 1 in 1.
Kyronix thank you for being patient with us and answering our questions. This question is more for the other players: Kyronix mentioned ONE "guaranteed drop" awarded from killing Captains and destroying the lighthouse. Are these drops also minor artifacts that can be turned in or are they different and part of a new group of items?