Yan, Tan, Tether - Sheep Counting

It is said that counting sheep is one way to fall asleep but there is more than to counting sheep than seeing them jump over a gate in your head. There is an article on Wikipedia that describes the sheep counting rhyme that has been used all over the British Isles and was in constant use before the early twentieth century:

Yan, Tan Tether, Mether, Pip, Azer, Sezar, Akker, Conter, Dick, Yannadick, Tannadick, Tetheradick, Metheradick, Bumfit, Yanabum, Tanabum, Tetherabum, Metherabum, Jigget is the Swaledale version of the sheep counting rhyme.

It is said that this form of pre-Industrial Revolution counting and is based on the Brythonic Celtic language (the language shared by the Bretons, the Cornish and the Welsh).

Despite this form of counting falling out of fashion in the early twentieth century; it has been embraced into the cultural sphere with composers, singers and writers alike all using it in their work - including Joan Aiken, Harrison Birtwhistle, Bernard Cornwell, Adrian Edmondson, James Joyce, Terry Pratchett and Jake Thackerary.The latter example gives a brief and comprehensive method of the sheep counting system and then weaves a story in it.

Why was it necessary to count the sheep? It is said that between the 5th and the 15th centuries, and still continuing in some areas today, certain farms were given fell rights - the permission to graze livestock on the common ground. But to reduce the potential for overgrazing, an accurate method of counting was needed as was the prevention of straying livestock. It is suggested that sheep are counted first thing in the morning and at the end of the day as well as when the flock is moved from one pasture to the other and after any sheep handling exercise that may include foot-trimming, dipping, mulesing or shearing.

This form of counting is based on base 20 (also known as vigesimal) and led to the recording of sets of twenty by either making a mark on the shepherd's crook or moving a pebble or piece of wood  from one pocket to another.  Does anyone know why 20 was the key number?

Wikipedia records a minimum of 14 counting systems for Cumberland, Cumbria, the Dales, Derbyshire, County Durham, the Lake District, Lancashire, Lincolnshire, Scotland, Southern England, Wales, West Country, West Morland and Wiltshire. Although there will often be regional variants of the same counting system. Wikipedia also shows a table of comparable Brythonic Celtic languages.

This form of counting has been used to count stitches in knitting, I guess there is more than one connection to sheep and knitting.