Traffic accidents are one of the major problems in the developed societies nowadays. The main purpose of this paper is to analyze the most significant factors that explain the number of this type of accidents. This aspect represents a very useful question for the automobile insurance sector. The literature points out that count data models are the most used ones on this important topic of the whole of the insurance industry. Traditionally, the Poisson regression and the negative binomial model have been the most provided specifications of this type of methodology we can find. However, zero-inflated models could be more appropriated to explain the existing underlying processes in accident situations. In the present study, we use a database that has been kindly provided by a Spanish private insurance company. After carrying out a thorough descriptive analysis with these data, we compare the results we have obtained from the application of the three referred types of count models to them. Finally, we discuss about the differences pointing up the general advantages of the zero-inflated models. Nevertheless, all results are quite similar in a qualitative way, suggesting the existence of adverse selection and moral hazard processes in the automobile insurance market.