The experience you describe almost certainly mirrors that of someone somewhere at some school at some time but a school caning was by no means a ‘standard’ experience.
A school caning could be almost painless or it could be utterly agonising. It was usually somewhere between the two extremes but, as the spectrum is wide, there are many points at which any individual’s experience might fall.
Only one thing is certain: over 99% of school CP stories are pure fantasy (a certain lady’s alleged birching being a classic example).