on the third offence

[pars]

Hi:
What does "on his third offence" mean in the following passage? I have not seen "on offence". Does it mean "he had committed offences offence three times before the last one? It is from the book Persian Petroleum, by Davoudi, p. 120.

An engineer named Martin had abused a native worker to such an extent that he ‘was unconscious for eight hours and, as a matter of fact, might well have succumbed’. 87 Martin was already on his third offence and had denied any wrongdoing, while admitting to his colleagues that he had almost ‘killed the blighter’
Thanks very much.

 

[emsr2d2]

It's not "on offence". It's "He was on + his third offence". I'm struggling to exactly explain it but we sometimes use "on" to express a position numerically.

I'm on my seventh beer.
He's on his third car.
They're on the second instalment of the trilogy.

 

[Skrej]

You might even hear without the following noun.

A: How many of those have you had?
B: I'm on my third.