A Systems Model of the Effects of Training on Physical Performance

Abstract
A systems model is proposed to relate a profile of athletic performance to a profile of training. The general model assumes that performance has four components: endurance, strength, skill, and psychological factors. Each of these factors is discussed and ascribed a transfer function. A major problem is the quantification of both training and performance. The case of a swimmer is studied in detail. It is shown that if a time series of training impulses is used as input, his performance in 100 m criterion performances can be modeled rather well with a simple linear system. The major conclusion is that performance appears to be related to the difference between fitness and fatigue functions. The fitness function is related to training by a first-order system with time constant 50 days, whereas the fatigue function is related to training by a similar system with time constant 15 days. An appendix is provided to show how these systems can be simulated on a simple electronic calculator. The relationship of these relatively short-term efects on the individual performer (six months) to longer term effects on the same indiviudal is also discussed.

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