Watt,
As far as grounding electrode conductors go and egcs use the same formula, It is based on a 5 second withstand rating (that is as long as any fault should last in theory), Circular mil area (from Chap 9, table 8) divided by 42.25 gives you that rating.
I keep that one on the top of my head, the ampacity tables I don't, they involve a lot more math, but basically it is from the Neher-Mcgrath, and is a compromise (it may be better to say "most often encountered) of all the conditions a cable can be placed in based on time of load, duration of load, and maximum ampacity that can be conducted for the CMA used.
Soares Grounding workbook has a lot of history of the NEC and grounding in it and can be an interesting read.
