Angular intraprediction (AIP) is a coding tool that has been incorporated into the video coding standards H.264/AVC (Advanced Audio Coding) and High Efficient Video Coding. In this paper, we study how the efficiency of AIP depends on its prediction parameters. To carry out this paper, we first theoretically analyze the variance of the error incurred when a perfectly directional signal is predicted in a certain direction. The results of this analysis are then used to study the efficiency of AIP when it is applied to a distribution of directions. To facilitate mathematical derivations, we make several assumptions about the signal and the prediction process, and we use some approximations. This allows us to obtain simple expressions for the variance of the AIP prediction error as a function of signal and prediction parameters. Finally, we compare our theoretical results with the results obtained from the prediction of images containing rectilinear edges. This comparison shows that our theoretical expressions follow the main trends of the experimental results except when AIP is performed with a very high accuracy.