Well, it's kind of like gauge on a shotgun. I mean, a 12 gauge should be less effective than a 20 gauge, right? But I'm not the one who makes up the rules. Um ... wait ... actually I was in this case.
In any case, I guess I could call it a jo staff but then people would look at me funny and ask me what a jo staff is*. Maybe I should call it a fighting cane? But yes, a half staff is roughly half the size of a quarterstaff.
*
And of course someone would inevitably point out that I don't know squat about martial arts weapon categorizations (true enough) and my eyes would glaze over as they discuss the various permutations.