"Score" means a mark on a stick. Folks would make notches on a stick called a tally for accounts and the like; they'd cut the stick in two lengthways, and each would keep one half. If either tried to alter his copy, it would no longer tally with the other, so it was a fraud-free method. Can't quite remember the "score=20" thing, but it was literally the case--but probably nothing to do with tallies.
I've always wondered why shepherds couldn't just go "one-two-three..." (in whatever language they spoke) like everybody else. Wasi it to keep fom falling asleep? And what sort of size limit would there be on a flock? I guess no-one would have thousands, but hundreds may have been a possiblility, especially if they were communal herds (i.e. everyone's small flock, duly marked, kept on the same grazing).
Steve