Sparky66wv: #4 solid is for unprotected grounding conductors. If protected, then #6 is ok.
George, what happens during a lightning surge? Your explanation works for a ground fault, tho the ground electrode and conductor has just a small parallel current compared to the equipment ground current during a ground fault.
The real issue of grounding electrode sizing comes in when dealing with lightning, doesn't it? In the IEEE green book it calls for all sorts of multiple ground rods in order to keep the earthing resistance low enough to keep people from getting killed. The more ground rods you install, the higher the current you can dissipate from a lightning surge, so the grounding electrode conductor rightfully should be increased in size to keep from limiting that dissipation capacity.