If it is a dog of any size and good condition, the odds are strongly in favor of the dog. Dog's are very fast over short distances. I've outran many dogs on my road bike but that is usually because you start with the advantage. You usually have some form of distance and/or angle on them before they give chase.
But if you were to be running side by side, most dogs will smoke you. There is a HUGE sheep dog out in the country where i ride my mountain bikes almost every morning. His is penned up with several hundred sheep which he watches over. (probably a good thing cuz I am a bit of a romantic.
)
Anyway, since he is penned he always runs directly parallel to me. I've never ONCE outrun him when we started evenly. And this dog appears to be huge and slow until he starts to run. He can easily top 20 mph and keep it there for the length of his pen which is probably around 400 yards or so.
I get chased by dogs all the time. I used to be more uptight until we got our own dog this past summer. Getting a dog, helped me to realize how playful
most dogs are. So generally i just squirt them with water or yell at them to go home. I know a few of the dogs i see by name because i have heard their owner's screaming at them.
I still carry a can of HALTS in my trunk bag for the critter that won't be deterred.