Pointing with fingers on touchscreens has become the primary input method of today. In the touch pointing process, the center of the hit distribution of a user’s touch is generally not positioned at the center of the target; instead, it has a certain offset. This study explains why such touch offsets occur, and presents a mathematical model for predicting how the degree of offset changes with a given angle of approach to the target (i.e., directional effects). Specifically, the model explains that it is natural for the user to undershoot the target to minimize the expected squared touch error. In the user study of single target touch pointing task with a circular target using the index finger, the model successfully predicted the offsets of the touch ($R^2$= 0.8751). Furthermore, this paper also verifies whether the model can predict the touch offset for each key in the mobile soft keyboard through the user study of the touch typing task. The paper concludes with the discussions, including the limitation of the current model and possible future works.