A naive understanding of self-driving cars is, that the human operator is no longer in charge and the drive can steer by it's own. Thinking this idea further results into a car which is able to drive without a human driver to the destination. That means, the owner can stay at home and sends to his a car the goal position somewhere in the world and the car will do all the actions by it's own.
This description emphasizes the economic benefit. The idea behind autonomous driving is – according to the description – to utllize existing vehicles more efficient. The idea is to replace human drivers with a software and this will reduce the costs in truck driving and taxi companies. It's important to know, that such kind of economic outlook can't be realized with the technology. Self-driving cars are working very different from it. They are not improving the car but they are motivating humans to become a better driver.
A practical usecase in which a self-driving car can show it's full potential is, if the vehicle is attended by 4 persons at the same time. 2 on the front seat, and 2 on the backside. The task for the humans is to learn driving. And the person who has the most problems is asked to take the position behind the wheel. Basically spoken it's a situation known as a driver school. The self-driving car is a computer game which is more entertaining than a PC based driving school. It allows to check the own skills in a life situation. This is especially important in questions of the allowed speed, the distance to other vehicle and which or the vehicles on the street are allowed to drive first.
What the human in the car are able to learn is if they are familiar with the traffic rules. They can compare their own decision with the car's decisions and open problems can be discussed during the ride. The bottleneck in the game is not the car. Because the car is only a machine who cares about nothing. The only thing what is important are the humans in the car and their ability to take the right decision.
Let us take a look why every year around 1 million people are dying in traffic accidents. It's not because of external reason which are located in the technology, but the main reason for nearly all of the accidents is that the humans are driving the wrong way. They are driving too fast, they are not respect the traffic light and they are not focussed on secure driving. Basically spoken, the human drivers are not educated well in safe driving. And exactly this issue can be solved with self-driving cars.
A self-driving car is a personal driving school which provides feedback to the driving style of the human. The car rewards, if the human is driving with the right speed and do not crashes into other vehicles. It's a serious game with the goal to educate the human in driving secure.
Crash statistics
A common statistics to measure the crash probability is to ask how many miles a certain has driven before an accident happens. The problem is, that exact statistics are not known, because a crash is always an exception. According to a blog entry a normal car has 4 crashes for 1 million miles, while a self-driving car has 9 crashes. https://carsurance.net/blog/self-driving-car-statistics/
But in the internet there is also a different statistics available in which the relationship is the other way around. A valid statistics is known for sportscar. According to the facts, they have a greater crash rate. The reason is, that Sports car are driven more risky. The question is now if the cars available today have to be categorized as sports car or not.
In general it make sense to estimate, that it's not up the car how secure it is, but it depends on the driver. Even a sportscar can be driven very safe, unfortunately this is seldom done. So we have to ask under which conditions, the human is driving carefully and under which condition not. Let us make a simple thought experiment. Suppose the idea is to drive 1 million miles without a single crash. In theory, this is possible, all what the driver has to do is to drive in the normal speed and take care of the traffic lights. The open question is how to educate the humans so that they will drive in this safety first style. If all the human drivers in the world can be convinced to drive safe, the crash rate would become much lower. The interesting question for self-driving cars is, if they are motivating the human driver to drive more aggressive or more carefully.