if speeding was punishable by death but i were as likely to be caught as to die in a terror attack, i would definitely speed as much as i wanted.

Per local German coverage on reported crime statistics, many crimes go unreported, and a number of crimes that would be included in US crime statistics are exempted from German reporting.

Also, now that Germany has...diversity...the crime rate went up pretty significantly.

So I would say, all in all, that homogenous populations are the greatest deterrence, followed by the magnitude of punishment being significantly more important at a societal level, though the risk of getting caught dominates the thought process for regulatory/low-punishment crimes.

There’s also another aspect: whether it’s one life sentence or 5 consecutive might make very little difference. Since prisons in US are big business nobody deals in short sentences. Rehabilitation or deterrence are not the goals, so of course the strategy won’t have the effect you imagine.

When punishments are so disproportionately high a good chunk of the ofenders will stop caring. The preventative effect is gone, it’s more an incentive to escalate the crime to a level where it matches the punishment.

But without knowing how many murders and the relevant population sizes I'm not sure that your point is made.