As a recipient of punitive justice myself, being punished had a tangible effect on how I thought about crime and thus how I behaved post-punishment. Whether you believe that was deterministic or due to my own free will doesn’t change the outcome.
There are plenty of medical interventions, particularly for mental illnesses, that would dream of 1/3 effectiveness. Now consider the fact that recidivism rates are often much lower than 2/3, and in many cases are closer to 1/3. That tells me that punishment actually is quite effective at reducing crime.
See e.g. the debates over lenient prisons in Scandinavia such as Bastøy Prison, where the lenient treatment is seen as justified on a deterrence and recidivism basis but which would be seen as negative if you see the goal of the sentencing to be harsh in order to punish.