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Did the year zero never exist ?
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I think the only reason that the nativity would be a year closer to 233 ad than 233 bc is because Jesus was born in late December. Had he been born a week later on the 1st of January, it would work out, with 1 ad starting a year after his birth and 1 bc starting a year before (year 0 being that of his birth)
The year was built around it, not the other way. It's all derived from the Christian calendar. I'm not sure off the top of my head how Christmas ended up a few days before New Years, but they're deliberately very close. It has been argued that the real life birth might not have been in winter at all (or even Bethlehem).
I digress, though. It would inevitably be lopsided somehow, because you've centered the numbering system around six months off of the New Years points.