For a less scientific approach, do this: Buy as short an ice axe as you feel comfortable with. Ice axes used to be very longI can remember using an ice axe as a walking stick when out hiking. But today most people use trekking poles on the trail, and want their ice axe to be short and versatile. I've found that for all-around use, a 70 cm length is about right (I'm five-foot-nine). Or, if you pick up an axe, hold it in either hand and dangle it to your sideyou want the point to be at about the same level as your boot top. That way it's usable on moderate terrain, but not so long as to be unmanageable when you're working your way up a steep slope, driving the ice axe into the uphill side.
True ice tools, of course, are much shorter45 cm is a pretty common length. But they're designed to be swung above your head, one in each hand. An ice axe can be used in that manner, but must be long enough so it can function as an anchor point or held in two hands during self-arrest.
And you're right, I am the man!