Learning curves in highly skilled chess players: a test of the generality of the power law of practice.

The power law of practice holds that a power function best interrelates skill performance and amount of practice. However, the law's validity and generality are moot. Some researchers argue that it is an artifact of averaging individual exponential curves while others question whether the law generalizes to complex skills and to performance measures other than response time. The present study tested the power law's generality to development over many years of a very complex cognitive skill, chess playing, with 387 skilled participants, most of whom were grandmasters. A power or logarithmic function best fit grouped data but individuals showed much variability. An exponential function usually was the worst fit to individual data. Groups differing in chess talent were compared and a power function best fit the group curve for the more talented players while a quadratic function best fit that for the less talented. After extreme amounts of practice, a logarithmic function best fit grouped data but a quadratic function best fit most individual curves. Individual variability is great and the power law or an exponential law are not the best descriptions of individual chess skill development.

[1]  Robert W Howard.  A complete database of international chess players and chess performance ratings for varied longitudinal studies , 2006, Behavior research methods.

[2]  P. Ackerman.  New Developments in Understanding Skilled Performance , 2007 .

[3]  N. Charness.  The impact of chess research on cognitive science , 1992 .

[4]  M. Smyth.  The role of mental practice in skill acquisition. , 1975, Journal of motor behavior.

[5]  Robert J. Crutcher,et al.  The role of deliberate practice in the acquisition of expert performance. , 1993 .

[6]  John R. Anderson,et al.  Reflections of the Environment in Memory Form of the Memory Functions , 2022 .

[7]  R. Howard.  Individual differences in expertise development over decades in a complex intellectual domain , 2009, Memory & cognition.

[8]  Flávio Sanson Fogliatto,et al.  Learning curve models and applications: Literature review and research directions , 2011 .

[9]  D. Ungerer.  [Sport psychology]. , 1974, Therapie der Gegenwart.

[10]  C. Shea,et al.  Principles derived from the study of simple skills do not generalize to complex skill learning , 2002, Psychonomic bulletin & review.

[11]  G. Logan.  Toward an instance theory of automatization. , 1988 .

[12]  Sara Fripp.  A learning curve. , 2014, Midwives.

[13]  R. Leach.  The learning curve , 1992 .

[14]  K. A. Ericsson,et al.  Science Current Directions in Psychological of Expert and Exceptional Performance Capturing the Naturally Occurring Superior Performance of Experts in the Laboratory : toward a Science on Behalf Of: Association for Psychological Science , 2022 .

[15]  Karl M. Newell,et al.  Human learning: Power laws or multiple characteristic time scales? , 2006 .

[16]  Richard B. Anderson.  The power law as an emergent property , 2001, Memory & cognition.

[17]  A. Elo.  The rating of chessplayers, past and present , 1978 .

[18]  Stellan Ohlsson,et al.  The Learning Curve for Writing Books: Evidence from Professor Asimov , 1992 .

[19]  R. Howard.  Practice other than playing games apparently has only a modest role in the development of chess expertise. , 2013, British journal of psychology.

[20]  Karl Halvor Teigen.  One hundred years of laws in psychology. , 2002, The American journal of psychology.

[21]  Scott D. Brown,et al.  The power law repealed: The case for an exponential law of practice , 2000, Psychonomic bulletin & review.

[22]  Antonio G. Chessa,et al.  Power laws from individual differences in learning and forgetting: mathematical analyses , 2011, Psychonomic bulletin & review.

[23]  Allen and Rosenbloom Paul S. Newell,et al.  Mechanisms of Skill Acquisition and the Law of Practice , 1993 .

[24]  R. Howard.  Longitudinal Effects of Different Types of Practice on the Development of Chess Expertise , 2012 .

[25]  Stellan Ohlsson,et al.  Learning from Performance Errors. , 1996 .

[26]  K. Kirsner,et al.  Transfer of training and its effect on learning curves , 2006 .

[27]  Andrew Heathcote,et al.  Bias in exponential and power function fits due to noise: Comment on Myung, Kim, and Pitt , 2003, Memory & cognition.

[28]  Denis Cousineau,et al.  The introduction to the special issue on "RT(N) = a + b N-c: The power law of learning 25 years later" , 2006 .