I pulled an original hat knob (1/4" shaft) and measured it. The metal cylinder inside the resin knob which receives the shaft is just over 1/2 inch in depth (.516" on mine). However, the bottom of the hat knob is concave, with the metal cylinder inset about .120" from the bottom rim of the knob. Depending upon what you are using the depth number for, the maximum depth of shaft allowance would be between 1/2" - 5/8", approximately.
Incidentally, the set screw for the shaft is located just above the bottom flare of the knob. Hope this helps.