The aim of the studies was to predict individual traffic accident involvement by the quantification of driving style in terms of speed changes, using bus drivers as subjects. An accident database was constructed from the archives of the bus company whose drivers were used as subjects. The dependent variable was also discussed regarding whether responsibility for crashes should be included, and what time period to use for optimal prediction. A new theory was constructed about how accidents are caused by driver behavior, more specifically the control movements of the driver, i.e. all actions taken which influence the relative motion of the vehicle in a level plane when v>0. This theory states that all traffic safety related behavior can be measured as celerations (change of speed of the vehicle in any direction of a level plane) and summed. This theoretical total sum is a measure of a person's liability to cause accidents over the same time period within a homogenous traffic environment and a similarly homogenous driving population. Empirically, the theory predicts a positive correlation between mean driver celeration behavior and accident record. The theory was tested in three empirical studies. The first tested equipment and methods, the second studied the question whether driver celeration behavior is stable over time. Celeration behavior turned out to be rather variable between days, and repeated measurements were therefore needed to stabilize the measure. In the third study, a much larger amount of data brought out correlations of sizes sufficient to lend some credibility to the theory. However, the predictive power did not extend beyond two years of time. The reported results would seem to imply that the celeration variable can predict accident involvement (at least for bus drivers), and is practical to use, as it is easily and objectively measured and semi-stable over time.