Highlights • Surveys show that a majority of drivers regard themselves as safer than the average driver. • This has been discounted as showing something that cannot be true. • It is entirely possible for a majority of drivers to be safer than the average driver. • In eight data sets, the share of drivers who were safer than the average driver ranged from 70% to 90%. • This does not necessarily mean that all drivers who claim to be safer than the average driver actually are so.

Abstract Surveys finding that a large majority of drivers regard themselves as safer than the average driver have been ridiculed as showing that most drivers are overconfident about their safety and as showing something which is logically impossible, since in a normal distribution exactly half are below average and half above. This paper shows that this criticism is misplaced. Driver accident involvement does not follow a normal distribution, and it is mathematically entirely possible that a huge majority of drivers could be safer than the average driver. The distribution of accidents in a population of drivers is typically skewed, with a majority of drivers not reporting involvement in any accident in the period covered by the data, often a period of 1–3 years. In this paper, examples are given of data sets in which the percentage of drivers who are safer than the average driver ranges from about 70% to 90%. The paper explains how, based on knowing the mean and variance of the distribution of accidents in a population of drivers in a given period, the long-term expected number of accidents for drivers who were involved in 0, 1, 2, or more accidents can be estimated. Such estimates invariably show that the huge majority of drivers are safer than the average driver.