Identifying the causes of road traffic crashes (RTCs) and contributing factors is of utmost importance for developing sustainable road network plans and urban transport management. Driver-related factors are the leading causes of RTCs, and speed is claimed to be a major contributor to crash occurrences. The results reported in the literature are mixed regarding speed-crash occurrence causality on rural and urban roads. Even though recent studies shed some light on factors and the direction of effects, knowledge is still insufficient to allow for specific quantifications. Thus, this paper aimed to contribute to the analysis of speed-crash occurrence causality by identifying the road features and traffic flow parameters leading to RTCs associated with driver errors along an access-controlled major highway (761.6 km of Highway 15 between Taif and Medina) in Saudi Arabia. Binomial logistic regression (BNLOGREG) was employed to predict the probability of RTCs associated with driver errors (p < 0.001), and its results were compared with other supervised machine learning (ML) models, such as random forest (RF) and k-nearest neighbor (kNN) to search for more accurate predictions. The highest classification accuracy (CA) yielded by RF and BNLOGREG was 0.787, compared to kNN’s 0.750. Moreover, RF resulted in the largest area under the ROC (a receiver operating characteristic) curve (AUC for RF = 0.712, BLOGREG = 0.608, and kNN = 0.643). As a result, increases in the number of lanes (NL) and daily average speed of traffic flow (ASF) decreased the probability of driver error-related crashes. Conversely, an increase in annual average daily traffic (AADT) and the availability of straight and horizontal curve sections increased the probability of driver-related RTCs. The findings support previous studies in similar study contexts that looked at speed dispersion in crash occurrence and severity but disagreed with others that looked at absolute speed at individual vehicle or road segment levels. Thus, the paper contributes to insufficient knowledge of the factors in crash occurrences associated with driver errors on major roads within the context of this case study. Finally, crash prevention and mitigation strategies were recommended regarding the factors involved in RTCs and should be implemented when and where they are needed.