What part of "substantial risk" are you not getting?
Where are you getting the words "substantial risk" from? We have 50 states, and then we have federal law. I don't claim to have read the self defense laws of even half the states, but I have read a number of them and I have not yet encountered the words "substantial risk." The usual language is something along the lines of "in danger of suffering death or grievous bodily injury."
The other thing you're either forgetting or choosing to overlook is that ALL the states' self defense/lethal force laws are based on the victim's (meaning the person who engaged in the self defense act) perception of the risk of death or grievous bodily injury. In other words, you don't really have to be in danger (that punk trying to stick you up doesn't have a real gun, it's an unloaded airsoft replica), you only have to reasonably believe
that you're in danger ("It looked like a real gun when he pointed it at me, your Honor").