The headband serves no purpose to this run, since, as I mentioned, I'm not using any class abilities, features or spells, at all. I'm using all and only Larian's larianisms - Throw and Shove, primarily.
What I meant was that ordinarily you would stack points in intelligence for a wizard, and leave her/him weak in the strength department. Unless you know beforehand about the headband. Did you happen to make your wizard extra strong?