What basket says is very true and deep. Biarta Hara is for the sake of the world, not the individual. The world needs the justice, Lo Sachnif Ha’aretz. However, I’m not that sure I would want to trust the system with a death penalty, for what charlie pointed out, that often times an innocent person can get indicted.
As for statistics, there are many things that come into play and a big shortcoming of our times is the fact that too much is put into the numbers. All you need is a “link” between two things and there you have it. That’s how you get a study showing the “association” between heavy people and diet soda! I understand that the knowledge that there exists, in theory, a death penalty wouldn’t deter a wacko, if it would be common knowledge that if you kill you die, there can be no doubt that it will be a much scarier thing for anyone.
According to the Rambam, a king can institute any system that he finds necessary for the sake of society. Having said that, technically, there is no mention in the Torah that death is a better deterrent than other punishments. You can argue that a death punishment in the Torah is to show the seriousness of a certain sin, and as mentioned above, to bring justice to the world.