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RESEARCH PRODUCT

General mathematical concept of compensation in sports science with quantitative analysis in the case of sprinting performance

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In many of the known sports disciplines, especially in athletics, the criterion which determines the positions of the competitors is a simple physical value, mostly a time or a distance, and the athlete with the minimum or maximum, respectively, takes the first place. Moreover, sports science explains this criterion by a set of the so-called basic abilities. Compensation means the balance of the inferiority of such a basic ability by the superiority of another one. In the following paper, a general abstract concept to analyse compensation in a quantitative way is presented first. It can be applied to any discipline with a measurable criterion, if, in addition, the performance can be described by a kinematic function. Second, the proceeding is worked out in detail for the short sprint based on the modelling of the velocity function of a sprinter and the indicators for his basic abilities in [6]. The two aspects of compensation, namely the set of indicators which belong to the same criterion and the improvement of the criterion caused by the improvement of a basic ability, are discussed in a quantitative way. They turn out to be describable by the mathematical structures of ‘surfaces of constant pure running time’ and certain gradients, respectively.