Evidence, Deterrence, and the Death Penalty

What type of evidence is relevant to the question of whether the death penalty deters? It seems to me that one kind of evidence, statistical comparison of relevantly similar jurisdictions which have, and do not have, the death penalty, is relevant and acceptable. But defenders of the death penalty suggest another type of evidence, the fact that convicted capital criminals, when given a choice in the matter, choose life imprisonment over death, is given as a reason supporting the deterrence claim.

This just strikes me as a bad argument. It seems to me that what a prisoner decides in his jail cell has little to do with what he might choose when he is thinking of committing a murder and thinks he probably will get away with it.

In any event, even if it is evidence, it is not very good evidence compared to statistics.