McClements J D, Laverty W H
Can J Appl Sport Sci. 1979 Jun;4(2):116-22.
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.
通过对不同时间的世界级成绩提升情况进行分析，得出了每个速度滑冰项目的成绩数学曲线。这些方程是使用无约束非线性最小二乘迭代曲线拟合技术计算得出的。选择非线性模型是为了满足收益递减原则，也就是说，随着成绩接近人类理论极限，实现单位成绩提升会更加困难。每条曲线的最低接受标准为：1）决定系数必须为0.90；2）2000年的预测值必须小于当前世界纪录；3）曲线必须呈上升趋势，即满足收益递减原则。在所研究的八个男女项目中，有七个项目得出了令人满意的曲线。研究发现了四年一届的奥运周期，并确定在20世纪60年代中期成绩趋势发生了明显变化。计算得出的数学曲线可用于以下三个方面：1）设定个人目标并评估这些目标；2）逐年评估和比较训练计划；3）评估整体计划。
