I have been a longtime runner, and only recently switched to cycling and commuting. I was never without a handgun when running, and I carried that practice over when I swapped my running shoes for a bike. You and you alone are responsible for your safety when out and about.
Being alert, assertive and using your head will almost always keep you from getting into a true self-defense situation. But that is not always enough, and having the ability to defend yourself in that very rare last-ditch survival situation cannot be overstated. I have come very close to having to use my firearm in self-defense while running, and I am thankful that my state has very good self-defense laws and decent carry laws.
Use your head first, avoid confrontations if at all possible, but don't think that it can't happen to you even IF you are the most non-confrontational person alive. I have frequently kicked myself for NOT packing in some situations, but I have never once regretted carrying.
Stay safe...