Diminishing Returns and the Limit of Athletic Performance

The purpose of this paper is to estimate athletic performance profiles over time, to establish that diminishing returns is a characteristic of performance functions, to measure the rate of the marginal decline, and to measure the upper (lower) bound or limit of performance. The empirical results yield estimates of the limiting value of athletic performance and the frontier maximum (minimum) record. Since lower bounds in the running events have been shown to be sensitive to choice of the nonlinear model, logistic and an exponential model for the men's running and distance events are estimated as a cross-check on my differential equation model. The issue of the gender gap (whether women will ever catch men) in athletic performance is also explored