The drop rate for me has been pretty consistent over time, but can vary greatly day to day or even minute to minute. I pulled 2 shards of Dooku in 22 attempts and then pulled 6 straight before coming up empty 1 more time and decided to stop. I got 5/6 Rey today and 1/6 Barris, 1/6 JC and 3/6 Dooku. I usually expect a 1/3 drop rate, but I don't expect that every day or every character. I expect that over an extended time. So while I may not get a 1/3 drop rate of 1 character over a 30 day period, I expect that I have gotten a shard 1/3 of the time I have done a mission. Purple gear drop rates are a whole different story for me though, as well as purple mats. It seems like I am 10% most days.