Driver behavior refers to the actions and attitudes of individuals behind the wheel of a vehicle. Poor driving behavior can have serious consequences, including accidents, injuries, and fatalities. One of the main disadvantages of poor driving behavior is the increased risk of road accidents, higher insurance premiums, fines, and even criminal charges. The primary aim of our study is to detect driver behavior early with high-performance scores. The publicly available smartphone motion sensor data is utilized to conduct our study experiments. A novel LR-RFC (Logistic Regression Random Forest Classifier) method is proposed for feature engineering. The proposed LR-RFC method combines the logistic regression and random forest classifier for feature engineering from the motion sensor data. The original smartphone motion sensor data is input into the LR-RFC method, generating new probabilistic features. The newly extracted probabilistic features are then input to the applied machine learning methods for predicting driver behavior. The study results show that the proposed LR-RFC approach achieves the highest performance score. Extensive study experiments demonstrate that the random forest achieved the highest performance score of 99% using the proposed LR-RFC method. The performance is validated using k-fold cross-validation and hyperparameter optimization. Our novel proposed study has the potential to revolutionize the early detection of driver behavior to avoid road accidents.