It used to be a matter of choice for the referee where his assistants patrolled. Around 1994 I think FIFA started advising that they should always run left backs. They've become more insistent over the years so left backs is now the expected patrol path; especially if you want or progress.Just watching a BBC documentary on the FA Cup Fourth Round and noticed something interesting.
York v Arsenal (1985). The AR's were on the 'wrong' side of the pitch (right backs). When did this change?
This is probably one for the older members of the forum