A method for predicting the rate of penetration (ROP) of a drill bit drilling a well bore through intervals of rock of a subterranean formation is provided based on determined relationships between a bit-specific coefficient of sliding friction μ and mechanical efficiency EFFM and confined compressive strength CCS over a range of confined compressive strengths CCS. Confined compressive strength CCS is estimated for intervals of rock through which the drill bit is to be used to drill a well bore. The rate of penetration ROP is then calculated utilizing the estimates of confined compressive strength CCS and those determined relationships.