The tough on crime “deterrent” argument falsely assumes that murderers are rational actors that are trying to maximize utility (sadistic pleasure I guess) and would abstain from killing if the cost were too high. Of course, criminals aren’t rational calculators of consequences and neither are any other humans (which is why classical economics also fails). Besides that, the deterrent argument is usually devoid of any meaningful context that might make it plausible outside of a hypothetical situation in someone’s head. Some murders are crimes of passion in which case we can be sure that the perp didn’t do any reasoning about the punishment beforehand. Other murders are a consequence of gang wars over turf and drug trade, which you could consider rationally calculated, but are usually done under ambiguous circumstances and usually by people the victim doesn’t know (e.g. hit men). Of course, there's also the fact that many murder cases, such as the aforementioned, go unsolved when the police have no leads to work off of. The clearance rate for homicide cases in the U.S. is 61.4%, which is a lot better than it is for other crimes like rape (32.9%) and Burglary (14.1%), but it still means that in the other 38.6% of homicides the perpetrator is never charged, so murderers have a decent probability of getting away with murder especially if they aren’t in their victims’ social circles and know how to cover their tracks. Someone that kills strangers is very likely a psychopath without a conscience so the possibility of the death penalty doesn’t bother them.