The success of continuous improved drill performance in cutting applications has to date largely been based on significant advances through tool surface coatings and modifications of drill point geometry, i.e. optimisation of the rake angle distributions along the drill lips and the chisel edge. It has been recognised that due to the complexity of equations for the force and power predictions, computer assistance is needed. Consequently, this paper presents the results of a systematic -computer-assisted -study focused on determining, and describing, from a mathematical point of view, the relationship between the drill point geometrical features and the performance measures as assessed by the cutting forces and power in drilling. This is followed by a study of predicted influences of drilling variables on the generated thrust, torque and power. The results are presented for different types of modern commercial tool surface coatings and work-piece materials. It is suggested that this sort of information may be used, by both tool manufacturers and users, to assist in the optimisation, and selection, of the drill point geometrical features for 'best' performance.