I think internet trolls come in two forms, with subtypes of each.
The first form is the insulting, asshole, provocateur who simply posts insults, stupidity, and vulgarity to get a response. They are less than worthless and have nothing to offer in a thread. Here on JPP, Doc Dutch is such a troll, as one example. Their posts are almost entirely vulgar insults and asininity. They make everyone miserable but offer nothing, usually less than nothing, to a thread. Their comments are irrelevant.
The second form is the insulting, asshole, provocateur who uses a combination of contrary facts, evidence, and stupidity to get a response. While the difference is subtle, this sort of troll makes those with a contrary position uncomfortable and forces those posting to defend their positions. A good troll of this sort uses sarcasm, snark, and puns to create a response that provokes further discussion or makes the shallow, ill-informed, poster STFU.
The first is worthless to the board as they offer nothing of value. The second is like a good comic or talk show host where their banter forces uncomfortable responses from others, or forces them to drop the subject.