It's difficult to determine the actual percentages of obtaining loot because the variable of who is rolling on what items changes from party to party. All you can determine as a definite value would be the chance that something you want will drop.
Basically the chance to see an item you want drop increases by a significant amount but the chance to actually obtain the item will vary from party to party based on loot preferences.
As far as I can tell, if 3 other players specifically want the loot you want and nothing else then your chances are the same as coil. If more than that want the same specific item as you then your chances are lower.
The other factor to consider however is that if you're willing to roll on any of the available loot that drops rather than a specific piece, you will have a slightly higher chance to obtain loot than you did before in coil picking specific items or jobs. If some people in the party are passing specific items then your chance will increase further by rolling on anything that drops.