I was watching a show called "gator boys" and I believe they said an alligator can run 15mph for a short distance. I bet it depends on how big the thing is too. On that show, some of them little ones sure could spin around and face their aggressor fast.
And I once had a gang of workers roof a house I owned, for me. One of the men was from Louisiana but I don't remember where. He was telling me when he was a kid, they used to tease the alligators and if they ever ran after them to make a sudden right turn. He claimed they can .. for a short distance, out run a man. He was a good worker, but I could hardly understand his English when he talked. especially when he'd get excited. He was also telling us about a swamp beast called a Rugaru. Like I said, he was hard to understand but could sure tell a story or two.