In Ditto's case, its revenge killing ability may well have a very large impact under the support characteristic. What it does it essentially make setting up useless until it has been killed. And, as virtually all offensive threats have a way to win a mirror match with themselves, it can revenge virtually anything, which is something no other pokemon can do. Furthermore, when it's done revenging, it still gets to instantaneously fire off boosted moves with literally no set-up required.
Depending on how the opponent reacts to Ditto's presence, it has the potential to fulfill two of the characteristics:
(a) Support clause, as it can either force out or kill anything the opponent has set up regardless of any other circumstances, OR by its very presence stop an opponent from using any setup moves in the first place for fear of getting copied, revenged, and potentially swept. In both of these situations, it helps other team members stay around for significantly longer than they otherwise would.
(b) Offensive characteristic if it is able to come in, steal a boost, and sweep.
