You beating up a bully as a kid put a smile to my face, not that violence is funny but that I think you did the right thing. Not to say that we should run around beating up bullies all day. I'm generally against violence.
But I prefer the kind of humor that is not Three Stooges in being just slap-stick where people get hurt and you laugh at them instead of with them. I prefer more nerd humor or geek humor, like sophisticated logic humor or silly crazy humor.
I'm just generally not into violence; I've generally believed in the idea that "violence begets more violence" never ends up solving anything.
Did I do the right thing? Maybe... that guy mostly left me alone, or he only came near me when he was with 2-3 of his other friends.
The only thing that might have been better than beating up the bully would be in having the confidence to try to calmly talk sense into him every once in a while, to try to counsel him in a sense, etc.
So, of course there are better long-term approaches if you're able to be like a friend to the bully, but there is also a higher probability of risk in attempting to help the bully. In the short-run, beating up a bully solves a problem temporarily.
I say it depends on the variables and I would try my best not to fight back kind of thing. Beating up a person can escalate the problem like you said, like he could have tried to start a new fight with you with his friends.
I believe in violence but I also believe in more long-term approaches at the same time which should be emphasized upon most of the time. I know some if not most bullies do things in order to get certain types of reactions and responses.
People should try not to give the bullies what they want. Don't let it get to you, don't let it bother you.
I've encountered bullies as a kid. I remember one kid during high school and he was bothering me at times and I didn't fight back. Other teens told me they thought I should have done something and I said no basically.
I guess for the most part, I believe in self-defense in a life or death situation where a person is about to kill a baby or something very bad like with a gun, a knife, or anything that appears potentially dangerous and immediate, then you step in kind of thing. Anything less than that should be resisted and procrastinated against.