A mathematical model of speedskating performance improvement for goal setting and program evaluation

An analysis of world class performance improvement over chronological time was used to develop mathematical curves of performance for each speedskating event. The equations were calculated using an unconstrained non-linear least squares iterative curve-fitting technique. A non-linear model was selected to satisfy the principle of diminishing returns, that is, it is more difficult to achieve a unit of performance improvement as performance approaches the theoretical limits of man. Minimum criteria of acceptance for each curve were: 1) the coefficient of determination must be 0.90; 2) the year 2000 predicted value must be less than the current world record; and 3) the curve must be progressive, i.e. satisfy the principle of diminishing returns. Satisfactory curves were calculated for seven of the eight male and female events studied. A four year Olympic cycle was noted and a definite change in performance trend was identified as occurring in the mid 1960's. The calculated mathematical curves can be used in three applications: 1) setting objective individual goals and evaluating these goals; 2) evaluating and comparing training programs on successive years; and 3) evaluating total programs.