What is the origin of shotgun shot size. I know Gauge is the number of balls in a pound of lead. Where did shot size come from?

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Shotgun gauge diameter is determined by how many balls of lead the diameter of that gauge will equal one pound. Thus it takes 10 lead balls of 10 gauge diameter to equal one pound of weight. And 16 lead balls of 16 gauge diameter to equal one pound.Thats why the gauge number decreases when the diameter increases.

SHOT SIZE

It seems the history of shot size is uncertain. There are at least 24 different methods of determining shot size around the world. The method used in the USA currently is to subtract the shot size number from 17 and that number is the diameter in hundredths of an inch. Thus #4 shot would be 17-4=13 or .13" in diameter. Why 17, I cant find anyone who knows, so anybody know?

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What is the origin of shotgun shot size?