Reference charts are widely used as a graphical tool for assessing and monitoring children's growth given gender and age. Here, we propose a similar approach to the assessment of driving risk. Based on telematics data, and using quantile regression models, our methodology estimates the percentiles of the distance driven at speeds above the legal limit depending on drivers' characteristics and the journeys made. We refer to the resulting graphs as percentile charts for speeding and illustrate their use for a sample of drivers with Pay-How-You-Drive insurance policies. We find that percentiles of distance driven at excessive speeds depend mainly on total distance driven, the percentage of driving in urban areas and the driver's gender. However, the impact on the estimated percentile for these covariates is not constant. We conclude that the heterogeneity in the risk of driving long distances above the speed limit can be easily represented using reference charts and that, conversely, individual drivers can be scored by calculating an estimated percentile for their specific case. The dynamics of this risk score can be assessed by recording drivers as they accumulate driving experience and cover more kilometres. Our methodology should be useful for accident prevention and, in the context of Manage-How-You-Drive insurance, reference charts can provide real-time alerts and enhance recommendations for ensuring safety.
Keywords: Motor insurance; Quantile regression; Reference curves; Risk score; Speed; Telematics.
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