@SomebodyBIG AnswersHQ is setup so community members can help each other out. I answer a bunch of questions because I have years of experience at the game, and I consider myself fairly knowledgeable.
The team on the Planet Coruscant has tracked hundreds of thousands of farming attempts. Given any probability-based system, individual players will see a variety of results, and that data can be collated into a probability curve. The higher the number of samples that are collected, the higher confidence we have on the conclusion of an average drop rate.
Shards seen to be 33%.
Gear is 20%.
Relic pieces vary - 120%, 90%, and 67% for the three different materials.
Any variation seen in that has never been corroborated over any statistical sample size. EA has not (and likely will not) confirmed the drop rates, but the community effort has given us a fairly high confidence.