Unruly teenagers who plague their communities get exam results on average 20 per cent lower than those with perfect conduct, a new government study has found.

While a link between breaking the law and underperformance at school is widely acknowledged as common sense, it is the first time researchers have tried to pinpoint the effect on exam grades.

Thirty per cent of all 14-year-olds take part in either shoplifting, fighting, vandalism or graffiti, according to the report. The proportion rises to half when they reach 16, but then falls to 20 per cent after that age.

Three per cent of 16-year-olds took part in all of these “external” bad behaviours, the study found.

Teachers are unlikely to be shocked by the fact that pupils who took part in sport and other “self-development” activities had GCSE scores 10-20 per cent higher than those who did not; nor by the finding that those taking part in “risky behaviours” are more likely to become Neets - not in employment, education or training.

Two in 10 experiment with either smoking, drinking or drug taking - “internal” risky behaviour - at 14, rising to half at 16. The study, by Andreas Cebulla and Wojtek Tomaszewski from the National Centre for Social Research, also found 4 per cent had experimented with all three by the age of 16.