We analyze real telematics information for a sample of drivers with usage-based insurance policies. We examine the statistical distribution of distance driven above the posted speed limit – which presents a strong positive asymmetry – using quantile regression models. We find that, at different percentile levels, the distance driven at speeds above the posted limit depends on total distance driven and, more generally, on such factors as the percentages of urban and nighttime driving and on the driver’s gender. However, the impact of these covariates differs according to the percentile level. We stress the importance of understanding telematics information, which should not be limited to simply characterizing average drivers, but can be useful for signaling dangerous driving by predicting quantiles associated with specific driver characteristics. We conclude that the risk of driving long distances above the speed limit is heterogeneous and, moreover, we show that prevention campaigns should target primarily male, non-urban drivers, especially if they present a high percentage of nighttime driving.