Because your subordinate clause following which is here an “optional” non-restrictive clause rather the type of “required” restrictive clause which I have just now used here, the orthographic convention in standard written English is to always use a comma.
This is quite different from the standard orthographic conventions of written German. In German, you’ve been trained to put a comma before subordinators like das even when these are used restrictively. So where in English we might write:
- This is the house that Jack built.
In German you would need an obligatory comma there:
- Dies ist das Haus
, das Jach gebaut hat.
We don’t do that for restrictive subordinate clauses in English, so you have probably gotten used to not doing so in English.
But there’s a different convention in play here for English. When your subordinate clause is merely adding optional information, the clause is considered non-restrictive. You can delete it without changing the overall meaning of the sentence. This kind of clause we do indeed precede with a comma in English. This strategy allows us to to distinguish these two very different statements:
- This is Jack’s house, which I have never seen before now.
- This is Jack’s house that I have never seen before now.
The first sentence says it’s Jack’s house — then, almost as a parenthetical aside, mentions that you haven’t seen it before now. You could have used a dash there instead of a comma, even, although this is more abrupt. Both represent an actual change in the cadence of the phrase, a little “pause” if you would. It is not a “silent” comma; it can be heard in speech.
The second sentence suggests that Jack has other houses besides this one, ones which you have seen previously. If you deleted the clause, you would lose that meaning.
Because your cited sentence is only adding descriptive information rather than restricting exactly which particular Dummkopf it is that you mean, it should take a written comma.