This paper defines a training theory with which to predict the effectiveness of various formats of taper in optimizing physical performance from a standardized period of training and taper. Four different taper profiles: step reduction vs exponential (exp) decay and fast vs slow exp decay tapers, were simulated in a systems model to predict performance p(t) resulting from a standard square-wave quantity of training for 28 days. The relative effectiveness of each of the profiles in producing optimal physical improvement above pre-taper criterion physical test standards (running and cycle ergometry) was determined. Simulation showed that an exp taper was better than a step-reduction taper, and a fast exp decay taper was superior to a slow exp decay taper. The results of the simulation were tested experimentally in field trials to assess the correspondence between simulation and real-training criterion physical tests in triathlon athletes. The results showed that the exp taper (tau = 5 days) group made a significantly greater improvement above a pre-taper standard (P < or = 0.05) than the step-reduction taper group in cycle ergometry, and was better, but not significantly so, in a 5-km run. A fast exp taper group B (tau = 4 days) performed significantly better (P < or = 0.05) in maximal, cycle ergometry above a pre-taper training standard than a slow exp taper group A (tau = 8 days) and was improved more, but not significantly so, than group A in a 5-km criterion run. The mean improvement on both physical tests by exp decay taper groups all increased significantly (P < or = 0.05) above their pre-taper training standard. Maximum oxygen uptake increased significantly in a group of eight remaining athletes during 2 weeks of final taper after three athletes left early for final preparations at the race site.