I think the big thing right now is the fact that it is week one.

Currently everyone run every turn is rolling on nearly every piece. Next week everyone should have close to 4/5 of the 20 pieces they need and there will be fewer parties where 8 people roll need on both drops.

Currently everyone has a 12.5% chance of getting a piece per successful run and a ~4.16% chance of getting the specific piece they are looking for.