quick question about floating plywood drawer bottom 1/2 thick

i am using the 1/4 1/4 1/4 method to assemble the drawers all from 1/2" ply BB.

If i make a 1/2 dado for the bottom instead of a 1/4 would it add much strength? These are for clothing. larger drawers about 30x20 with a height of about 9 inches. its all one setup on the saw if i stick with 1/4 dado for the bottom drawer but i wasn't sure it that would have much imp[act on potential sagging of the bottoms.

Also i know they need to be a bit undersize to allow for expansion but how much? 1/16? per side or less?