Since a real and very precise calendar date of the eruption must have existed, variation in estimations can only be the result of limitations to the carbon-dating method, which, given a plenitude of reliably emplaced samples, can only produce a date within a window of roughly 500 years in a maximum elapsed time of roughly 4000 years or  (12.5%).
Because a precise calendar date for the eruption must have existed, discrepancies in estimates are likely caused by limitations of the carbon-dating method, which, with numerous reliably placed samples, can only yield a date within a margin of error of around 500 years at most, over an elapsed period of roughly 4000 years or approximately 12.5%.