According to local statistics most accidents are caused by drugs and failures to follow traffic rules. Our police keep on going on about how speed kills and there are articles in the paper quite frequently about how these people were racing, or just driving really fast. The thing I find funny about these articles is that usually they will have the smallest line about them being way over on their blood alcohol level, high on heroin, or stoned on marijana, but they really try to downplay these parts.
Right now self driving cars would stop the majority of accidents.
How about that 5%? Well as more self driving cars would get on the road, that 5% would probably shrink to less than 1%, depending on the area. Plus there are already real time algorithms for detecting moving objects, coupled with multiple cameras the car can see things like deer and children much sooner than humans and react to them.
The main problems will be in the transition where there are still human drivers doing really stupid things and the self driving cars. We humans are affected by lack of sleep, by drugs, but not getting enough vitamins, distractions, tunnel vision, bad driving habits, missing signage, having two eyes facing one direction at a time, and sometimes just pure stupidity.