Transfer of training and its effect on learning curves

Development of Chess Skill from Domain Entry to Near Asymptote

The aim of the present study was to see how well the power law of practice, studied mainly with simple skills acquired over short periods with task time as the performance measure, generalizes to chess skill. Chess playing is a complex cognitive skill acquired over years, and expertise can be measured by a performance rating based on game results and relative strengths of opponents. Participants were 75 highly skilled players who entered the domain very young and improved skill greatly. With number of games as the practice measure, the traditional 2-parameter power law fit the mean curve and most individual curves quite well. However, a new formulation of the power law found by artificial intelligence program Eureqa often worked even better. Power models with an asymptote parameter did not work well with chess skill unless that parameter was set to a constant. Another study aim was to see how well various models predict future performance from varying practice levels. For three models, the less practice the greater was the underprediction of future performance, but the new power law formulation predicted well from early in practice. Another study aim was to test model fits with time as the practice measure. With time, power models fit well, but an exponential model and a quadratic model fitted most individual curves better. The power law as traditionally formulated does generalize well to chess skill development but is not always the best model, and no single model always fit best for all participants.

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.