Mathematical analysis of the relationship between training and performance has contributed to the understanding of the effects of tapering on performance. This type of model analysis is based on systems theory. The system is an entity characterized by at least one input and one output, which are related by a mathematical law called transfer function. The output corresponds to the system`s response to the stimuli represented by the input, and the transfer function characterizes the behaviour of the system, on the basis of parameters estimated from real life observations. When applied to athletic performance, this type of mathematical modelling intends to describe training responses based on a whole-body-approach that considers performance as the system`s output, which varies according to past training, which of course represents the system`s input. Various studies have indicated that the development of such mathematical models can contribute to a better understanding of the effects of tapering and optimizing athletic performance. This type of application has been specifically used to explain the taper-induced gains in swimming performance and estimate the optimal duration of the taper. This approach was also used to establish that a progressive reduction of training can be more effective than a step reduction in triathletes. Another possible application is the simulation of changes in performance for variations in training other than that actually done. A recent computer simulation study on elite swimmers showed that an overload period before the taper is essential to maximize performance, but imposes specific requirements during the taper period. A progressive taper is preferable to a step taper after prior overload training, but it should last nearly twice as long as the step taper. Another computer simulation tested the hypothesis that a two-phase taper with a final increase in the training load at the end of the taper is more effective than a traditional linear taper. The available data on performance modeling confirm the relevance of the modeling approach in the study of individual responses to training and the optimisation of tapering strategies.
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