The Power Law of Human Performance or of Practice (PLP) states that the time (T) it takes an individual to perform a given task decreases as the number of times (N) the individual practiced the task increases. In mathematical terminology, the law is: (Education Vol. 115, No. 1, 31, 1994)


T = A + B (N + E)-p      or      T = A + B/(N + E)p


where A, B, E and p are constants that vary (a) with the task at hand and (b) with the individual performing the task. A represents a physiological limit. B and E partly denote prior experiences before the beginning of the practice sessions, and p is the learning rate.  In other words, the law states that “practice renders perfect.”  This law applies to the performance of sensory-motor (or athletic), creative (or artistic), and cognitive (or intellectual) tasks.

          The shorter the time T to perform the task -  completely and correctly - the higher the level of proficiency. Hence, as the number of practices increases, so does the proficiency of the individual. The two figures below graphically show the plot of the above expression for text editing and problem solving tasks.

            The dramatic impact of this law becomes apparent when one considers its application over several tasks and several days, months, and years. Then it becomes clear that genius is mostly the result of sustained, quality practice. The same way adequate practice, at an adequate scope and depth, is needed for the making of Olympic, National Basketball Association, National Football Association, and Major League Soccer champions and for the making of musicians and artists,  the same way it is needed for the making of science, engineering, and mathematics scholars, including scholars in the social and behavioral sciences and any other discipline.

            Further, this law is implacable. It applies whether one likes it or not! It applies to the refinement of the enhancement of the teaching, mentoring, research, and writing skills of a faculty member or of a mentee! These points are discussed further by Bagayoko and Kelley (1994) and Moore and Bagayoko (1994) in connection with the explanation of the creation of educational value added from K through graduate school and beyond.

           The integrated or compound law of human performance (ILP, Bagayoko and Kelley, Education, Vol. 115, No. 1, pp. 31-39 1994),  is the convolution of the power law of performance as simultaneously applied to several tasks over a long period of time. The main difference between the power law and the integrated law is that the former follows a simple equation that involves an exponent or power (i.e., p) while the mathematical form of the latter is yet to be determined. The quintessential point here, however, stems from the fact that according to the integrated law of human performance,  the abilities, skills, and  attributes of students that are meaningfully engaged and challenged in  and outside the classroom (as by mentoring activities) — from K through graduate school and beyond — are the ones that will develop!   The integrated law of human performance provides the scientific basis for high expectations for all students!  This point is rigorously established by Bagayoko and Kelley (1994). Professional mentoring, as defined elsewhere by Bagayoko, provides an almost fail-safe strategy for  promoting the academic excellence of all students (female or male, minority or non-minority, young or mature). Student retention, on-time graduation, and their success in graduate school are partly by-product of the quest for proficiency and excellence-- through quality teaching, mentoring, and learning.  It is critical to note that the same way the ILP applies to the cognitive domain, the same way it applies to non-cognitive (i.e., behavioral) variables. Character is molded through practice. Also see Education, Vol. 115, No. 1, pp. 11-18 & pp.19-25, 1994.

Newel, A.  and P. S. Rosenbloom (1981). Mechanisms of Skill Acquisition,"

 Edited by Anderson, J. R. Hillsdale, N.  J.: Erlbaum