Road accident counts are influenced by random variation as well as by various systematic, causal factors. To study these issues, a four-country, segmented data base has been compiled, each segment consisting of monthly accident counts, along with candidate explanatory factors, in the various counties (provinces) of Denmark, Finland, Norway, or Sweden. Using a generalized Poisson regression model, we are able to decompose the variation in accident counts into parts attributable to randomness, exposure, weather, daylight, or changing reporting routines and speed limits. To this purpose, a set of specialized goodness-of-fit measures have been developed, taking explicit account of the inevitable amount of random variation that would be present in any set of accident counts, no matter how well known the accident generating Poisson process. Pure randomness is seen to "explain" a major part of the variation in smaller accident counts (e.g. fatal accidents per county per month), while exposure is the dominant systematic determinant. The relationship between exposure and injury accidents appears to be almost proportional, while it is less than proportional in the case of fatal accidents or death victims. Together, randomness and exposure account for 80% to 90% of the observable variation in our data sets. A surprisingly large share of the variation in road casualty counts is thus explicable in terms of factors not ordinarily within the realm of traffic safety policy. In view of this observation, it may seem unlikely that very substantial reductions in the accident toll can be achieved without a decrease in the one most important systematic determinant: the traffic volume.