Sebastian did indeed suffer through the imperial Roman equivalent of a firing squad, but according to traditional belief he survived the ordeal. His actual martyrdom occurred at a later date when he reportedly accosted Diocletian in Rome. Though taken aback by Sebastian's unexpected appearance, the Roman emperor quickly ordered his men to cudgel Sebastian to death.
So cudgels, not arrows, led to St. Sebastian's martyrdom; but I can understand why artists generally found the shot full of arrows image of St. Sebastian far more powerful than the actual clubbed to death image of his martyrdom.