The Bookkeeping Hypothesis: "Balancing the Ledger"
​Before the invention of computers or even modern eras of erasable graphite pencils, commercial transactions were recorded by hand in ink using a "Waste Book" (a daily chronological log) or a permanent accounting ledger.
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We're an American English dictionary, so yes...we call it 'soccer.'
We said there was no clear etymology.
If you want to send evidence for your theory, we'd be happy to take a look!