Yes: if punishment was an effective deterrent, then the natural expectation is that there is strong correlation relationship between the level of punishment use

Yes: if punishment was an effective deterrent, then the natural expectation is that there is strong correlation relationship between the level of punishment used and the deterrence effect. Saying punishment doesn't provide deterrence only claims that punishment is not correlated with deterrence. Maybe the examples shown gave the impression that an anti-correlation was claimed, but that is purely an invention of the reader.