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Over the past decade, the popularity of installing advanced driver-assistance systems (ADAS) in cars has increased markedly. However, the effectiveness of ADAS is subject to debate, primarily because these systems intervene in drivers’ perceptions and actions and could lead to adaptive behavior. Using complete national data for the installation of three leading safety systems and speeding tickets issued over the course of an entire year, allowed us to pinpoint the impact of these safety systems at a national level. Employing zero-inflated negative binomial regression models, we found that the installation of the three safety systems was associated with higher number of speeding tickets. These findings are in line with the literature that indicates adaptive behavior in the context of risk. However, when we accounted for the proneness to commit other traffic violations, the effect of the safety systems on the prevalence of speeding tickets was evident only for those prone to violations. Further research should be conducted to identify which drivers will be more likely to be affected and under what circumstances and safety system types.