This idiom has two different origins, resulting in two slightly different meanings. The first is that, before the invention of microphones and loudspeakers, people at noisy sporting events needed a signal that was easy to see at a distance in order to know when to begin. One way to do this was to have an official at that event lift his hat high and then drop it. From this origin, "at the drop of a hat" means something done at a moment's notice. Some people are eager to do something they like very quickly "at the drop of a hat," if they get the chance.

Another origin of this idiom is that when two men were thinking to fight, one of them would throw off his hat. This was a signal he was ready to fight. From this origin, "at the drop of a hat" means something done for the slightest reason.