A recent survey showed that about 48% of drivers have current points on their licence. This means that 52% do not. However, although your question specifically mentions points, there are two other groups to consider. There are drivers who have received a disqualification for a single offence. They may or may not have current points still effective from earlier offences. There are also those who have been disqualified under the totting up rules (12 points in three years). Their points are reduced to nil when they receive their mandatory disqualification. Drivers in neither of these groups can be considered to hold a "clean" licence (certainly for insurance purposes) until the required period without offending has elapsed.