I may have some things to offer.  I have been training in Aikido for three years.  First, you gain confidence simply by working toward belt tests and watching your skills gradually improve over time.  Secondly, as your skills improve, you gain more control over your body and mind and your ability to focus and accomplish goals in all aspects of life notably improve.  Thirdly is the self-defense aspect.  However, for tradiational martial artists at least, they would be the last to actually get into a confrontation.  They (and I) are more interested in avoiding and preventing confrontation.  Having said that, though, the calm control you gain over your mind and body through regular training is what will save you in a self-defense situation.  Of course you learn techniques in the dojo, but with the understanding that the dojo is a controlled place and techniques are really more as "reference points" and tools to build fundamental principles.  With enough training you learn to see techniques for what they are and eventually go beyond particular techniques to the essence of the art.

As an example of the "control" I was talking about I (and a few others in my dojo) have experienced situations like this-- I was walking downtown late one night when a guy came up to me acting very strange and I couldn't really understand what he was saying to me.  From his body language I interpreted this as a threatening situation (he also seemed to be hiding one hand which made me think he might have had a weapon). Suprisingly to myself (I had only been training a year at most), I totally snapped into the present moment, was totally calm and "connected" with him.  I didn't aggress but didn't back down either and he just kinda got a confused look on his face and walked away. 

Hope that helps!  Of course, I can only speak for myself and my history which is in traditional Japanese Budo (Aikido) which inherently incorporates "zen" elements into it dating back to its samurai lineage.  I can't say what someone with a sporting background would tell you (like a UFC-type person).

As well as everything stated in the previous post, there is something to be said for the confidence that you are more likely to come out on top if things continue to escalate. Self-defense is not something about which you should adopt a halfway attitude. If it has reached the point of physical violence regardless of your best efforts to prevent such a situation, you do not owe your attacker gentle treatment.

Your training is what will save you. It will give you the confidence and means to act appropriately should it become necessary, resulting in less stress about an initial confrontation. Simply put: I'll try to avoid this, I don't want to fight, but if I have to, I'll win.

I started training in karate when I was 16. At the time I was going off the rails... I had very low self-esteem and confidence. I was an orphan and was raised by my grandparents and I started to spiral out of control when my grandpa died. I dropped out of school early and I was abusive and agressive towards loved ones, which in the end led me to leave home for fear that I would end up harming someone permanently. I couldn't control myself and although I went to a doctor, they just prescribed me with valium. I was not referred for counseling or therapy of any kind and I was in desperate need of professional help. I figured that the only way I could protect my friends and family from myself was to stay away from them and be on my own. While I was living on the streets, though I met someone who practiced martial arts. I think she did karate too, which was what influenced me to give it ago. She recommended martial arts training to me and initially I took kick-boxing lessons, which I didn't particularly enjoy for some reason. Although it semed like a legitimate way to have a good fight and give someone a good thumping, I didn't feel like it was helping me to gain any control over my mental state or behaviour. After a class on one particular day, I saw traditional karate class practicing in the adjacent sports gym. I stopped to watch for a while and the instructor came out to see me. he asked me if I wanted to join in. I was shy and I took some persuading but I eventually agreed and had a go. It had all of the elements that I was looking for in training. It taught discipline, self-control and it was very structured, which was something that I wasn't. Above all, it was the instructor that made the greatest impression. He was very controlled and disciplined and although he was physically small and slight in build, he came across as very strong. His nature was very pleasant and he had a very calming effect on people. He was encouraging and motivated you without putting you down. The thing that struck me most about this instructor was that he commanded immediate respect without seeming to demand it. It was just taken for granted. I knew as soon as I met him that he would not take any crap from me or tolerate me behaving inappropriately. If I wanted to learn I had to behave, listen, keep an open mind and trust him. I don't think I had trusted anyone in my life until then. This instructor asked me why I was interested in learning martial arts and before I even had a chance to answer him, he took off his black belt and gave it to me. "Here you are," he said. "Take it. It's yours." I told him that he had misunderstood me and that it wasn't this that I wanted from my training. He then asked me again: "What do you want then?" I replied, "I want to be the kind of person you are." He looked deeply into my eyes and studied me for a moment and then put his belt back on and said, "well you better stick around for a few years then." After the class he asked me if I was going to come back. I said I was and he said, I'll see you next week then." That was 23 years ago and I have been training ever since. Training did not transform me over night, I had to "stick around for a few years" but it did change me. I am a completely different person to what I was back then. Karate helped me to gain confidence and build self-esteem. As I made progress I started to believe in myself and what I could achieve with my own effort and this prompted me to go back to school and improve other areas of my life by getting an education. If it wasn't for martial arts I would have gone to University and got a degree. The idea going so far in education didn't even occur to me before. I didn't think I was capable. And I did it all without drugs! I did get some counselling from time to time but most of the changes I made came directly as a result of what I had learned as a result of my training in karate, the first lessons being: "Karate begins and ends with curtesy" and "there is no first attack in karate" (Gichin Funakoshi).