Your neighbor's dog backed down because of his inbred inhibition against biting humans and his feelings for you. You never held any cards at all - that broom would have splintered like a toothpick or he could have avoided it altogether at any time, not that it was more than an annoyance to him at best. It's a testament to his good nature that he didn't decide to bite you for smacking him! Don't ever fool yourself that you hold the upper hand in a physical contest against even a medium sized athletic dog - you don't. That's one way that many people end up getting bitten.