Mathematical Models That Describe and Predict Performance Change in Mens And Womens Athletic Events: 1960-2014

The prediction of athletic performance is a recurring theme as coaches and sports scientists endeavour to understand limits of sports performance. Predictive models based on Olympic data for athletics have derived some accurate predictions of performance in the 2000, 2004, 2008 and 2012 Olympic Games. However, best fitting mathematical functions varied with different events. The aim of this research was to develop descriptive and predictive mathematical models of changing performance over time for track and field events for both men and women to assess if athletes in different events are increasing or decreasing
performances. Data was provided by International Association of Athletic Federations (IAAF) and by averaging scores of the top twenty performances for the major track and field events for years 1960 to 2014 for men and women senior outdoor athletes. Mens events were 100m, 200m, 400m, 1500m, 110mH, 400mH, long jump, high jump, shot put, discus, javelin and hammer and womens events were 100m, 200m, 400m, 1500m, 100mH, long jump, high jump, shot put and discus. The mathematical approach utilised regressioncurve estimation time series analysis by evaluating data fits to linear, logarithmic, inverse, quadratic, cubic, compound, power, sigmoidal, growth exponential and logistic functions. The calculations were conducted using SPSS Version 22 software. Results indicated cubic functions consistently displayed best fits with the data. Mens track events displayed Rsquare
values of 1500m (.955) to 100m (.791), in field events high jump (.958) to javelin (.514) with increasing performances for 100m, 200m, 110mH and discus. Womens track events displayed R- square values of 400m (.957) to 100mH (.866), in field events high
jump (.967) to javelin (.456) and increasing performances for 100m, 100mH and 1500m. Current trends indicated most events performances were decreasing suggesting track and field events have reached limits of performance or training adaptations are declining.