It's not necessary that most other drivers have had an accident for most people to have had below the average number of accidents. Consider a population of 100

It's not necessary that most other drivers have had an accident for most people to have had below the average number of accidents. Consider a population of 100 drivers, none of whom have ever had a traffic accident. The average number of accidents per driver is therefore zero. Suddenly, two of them collide. Now, 2/100 drivers have had an accident, and 98/100 drivers have still never had an accident. The average number of accidents per driver is now therefore 0.02. Since 98/100 drivers have had 0 accidents, but the average number of accidents per driver is 0.02, then 98% of drivers have had below the average number of accidents.