This paper focuses on the characteristics of a model interpreting the effect of training on athletic performance. The model theory is presented both mathematically and graphically. In the model, a systematically quantified impulse of training produces dual responses: fitness and fatigue. In the absence of training, both decay exponentially with time. With repetitive training, these responses satisfy individual recurrence equations. Fitness and fatigue are combined in a simple linear difference equation to predict performance levels appropriate to the intensity of training being undertaken. Significant observed correlation of model-predicted performance with a measure of actual performance during both training and tapering provides validation of the model for athletes and nonathletes alike. This enables specific model parameters to be estimated and can be used to optimize future training regimens for any individual.