Wrongful death?

One of the hardest parts about learning about the law is that the law is constantly changing. Of course, no two court cases are exactly the same. Then why do we use precedents to determine the outcome of another case??
Today, in class we were discussing the costs and beliefs of capital punishment. The debate can go on forever and right, morals, freedom, and justice. In the U.S we have decided that we do need capital punishment to deter crime and punish murders. Except, there are no study that proves that the death penalty actually deters crimes. Regardless, it defiantly punishes murders. What about cases that result in a death penalty verdict on an innocent person. How can we be 100% sure that we got the right guy??
After being accused of burn his own home down, with his children inside, Cameron Willingham was sentenced to death. He was convicted of murder in 1992 and executed in 2004. After his executed, four national arson experts concluded that the investigation may have be flawed. They proclaimed that the fire may have been set accidently and Willingham could have been innocent. During the trial, the jury found him guilty because investigators said that the scene looked like arson. Also, a jail house snitch told the jury that Willingham confessed to the crime in jail. The snitch was a drug addict and was on psychiatric medication.
I haven’t made up my mind if I am for or against the death penalty and I would need to do a lot more research before making my decision, but this is just one story of mistaken charges by flawed evidence. When it comes to a human life, prosecutors need to be much more careful.