It doesnt work as a deterrent.
While discussion of the Death Penalty is somewhat OT as regards Thompson and Vennables as ten year olds (It might not be as regards their additional re-offending as adults mind)
You cannot say that it does not act as a deterrent. All you can say is that it does not deter the people who are not deterred.
It is difficult to scientifically ascertain the numbers of people who
are deterred because obvious...
However, anecdotal evidence is available.
After Britain abolished capital punishment the Murder rate almost immediately started to rise, quite sharply really.
Today, especially when you allow for the fact that trauma care is far better than it was 60 years ago, the effective Murder rate (IE the rate at which murderous assaults take place that would almost certainly have resulted in death and the noose for the murderer 60 years ago) are probably ten times or even more the rate that they were back then.
Not only that but the nature of these modern murderous assaults are quite diferent to the sorts of assault that happened 60 years ago and involve assaults of a sort that simply didnt happen back in Pierrepoints day. (Or if they did were really rather rare)
Of course, then as now, You got people who killed in rage on the spur of the moment and of course the classic planned murders (Money, revenge, or even simply because they enjoyed it) by people who really thought they would get away with it. Obviously such people are unlikely to be deterred by the prospect of execution because they either were not thinking straight or because they thought they would not get caught.
You also got street gangs fighting one another, and they hurt each other too, sometimes badly (Face slashing was common).
But they were generally
very careful indeed to avoid inflicting injuries that might actually kill. Even at the height of the Mods and Rockers, actual deaths were very rare indeed.
Housebreakers and even bank robbers would either flee or submit to arrest rather than run the risk of actualluy killing somebody, even if they were armed.
You may joke about it now, but "Its a fair cop Guv" was actually a very common comment on arrest as recorded in court transcripts of the time.
What you did
not get was the casual street knifings, street robberies with violence, householders being beaten to death in "Botched" burglaries that are now daily news to the point that most people just accept it as part and parcel of daily life. Sure these things did happen in the past, but they were very rare.
The really shocking thing about the Craig/Bentley case wasn't so much that Bentley was Hanged, and Craig wasn't (Which was seen as being unfair. many people felt it Should have been both or neither, preferably both)
No, the shocking thing was that the crime happened at all. Nowadays nobody bats an eye at the idea of a pair of teenagers engaging in a murderous armed robbery. But back then it was just as unusual and shocking as the idea of a pair of ten year olds murdering a toddler was back in 1993.
Elsewhere in the world,
In Texas, Abolition resulted in a similar sharp rise in what would previously have been capital cases, on reintroduction, the rate fell. So, despite the fact that only a small proportion of capital sentences are ever actually carried out, even in Texas. there is a strong inference that the threat of the noose/needle/whatever does affect peoples criminal behavior. (As indeed, does "Three Strikes" even if it only means that incorrigibles move to states without "Three Strikes" rules, which they do...).
Agin, America has very diferent problems with violent crime than the UK (Well, at least in the past anyway. Sadly they are becoming more similar recently) So making a direct comparison between the UK and Texas is not really possible, however the anecdotal evidence in both cases is that the prospect of execution does affect peoples behaviour. It wont necesarrily make everybody less likly to kill, but it does seem to affect the majority.
. 
