Have just refreshed this to reconstitute my totally vanished literacy worksheet on counting and counting out rhymes, and noticed that nobody had answered the 20 = score part of the system.
A flock of sheep has many ewes, lambs etc, too many to tally individually, so, the rhymes are used up to 20, then the mark is made on a stick. Each tally mark stands for 20. The mark, or cut, is also known as a score - think of scoring card to fold it cleanly, so the score = cut becomes score = 20. To find the total number of sheep, count the tally marks, multiply by 20, and add the odd ones left over at the end. You can do the stick splitting bit if you are rendering accounts, as well. Scoring becomes a synonym for a recorded count, hence is used for game results and so on.