Although largely intuitive to many of us, it is worth mentioning in this context (and for lathe work in general), that the stiffness (resistance to bending) of a round bar, projecting from a chuck (cantilever style) is nonlinear in relation to both its length and its diameter.
Although more complex when considering for example a fluted drill, the stiffness of a round bar relates to the cube of the length and the fourth power of the diameter.
Put simply …
Halving the length (overhang) increases the bending resistance by eight times.
Halving the diameter decreases the bending resistance by sixteen.
I'm pleased to know Roger, that your drilling project was a success.
Regards,
Sam 