Casting

Can anyone tell me the etymology of the word "Casting" as it applies to the assignment of parts and duties to actors or performers?

I can perhaps see how a director would want to "cast" out a metaphorical net to bring in the performers needed for a play. Somehow though, this explanation isn't satisfying.

When was the word first used in this theatrical sense?

I'd be very grateful for the information.

Thanks,

Daniel