The coefficient of determination, R2, i.e. the squared correlation coefficient between observed and fitted values, is often used as a measure of how well a model predicts the number of accidents at road junctions, for instance. The purpose of this article is to show that the R2 values obtained in different studies are rarely comparable with each other and that a prediction model can be "nearly perfect" even if the coefficient of determination is small. Another purpose of the article is to present some results of interest from a practical viewpoint in regard to accidents where pedestrians and cyclists are involved. Empirical R2 values for models predicting accidents at junctions where pedestrians or cyclists are involved are compared with the maximal R2 values that could possibly be obtained. The latter can be calculated both theoretically and with the aid of simulation. How the maximal R2 value depends on the average accident level and the relative dispersion of the expected values for the studied junctions is also shown theoretically. The results obtained show how difficult it can be to determine whether and how far the number of accidents is influenced by additional factors, over and above the traffic flows, which describe the design in greater detail.