Mathematical Models Predicting Performance in Track and Field at the 2011, 2013 and 2015 IAAF World Championships

Mathematics and science are based on principles of description and importantly prediction. The ability to make substantive and accurate predictions of future elite sportsperformances indicates such approaches reflect “good” science. Often these predictions arepurely speculative and are not based upon any substantial evidence; however they providecriteria for athletes in terms of performance standards to be achieved to be competitiveinternationally, resetting international qualifying standards for IAAF sanctioned competitions such as World Championships, to focus on limits of human athletic performance andevaluating long term adaptations of athletes to chronic training. The research aim wasto further develop predictive mathematical models using IAAF World Championship datain athletics outdoor championships 1983 to 2009 (previous model) for men’s and women’s100m, 400m, long jump and high jump and then evaluate a revised model based on theaddition of 2011 and 2013 data to predict the 2015 performances. Data sets consisted ofaverage scores of the top eight performances in the finals of each event. The mathematical approach utilised regression-curve estimation time series analysis by evaluating datafits to linear, logarithmic, inverse, quadratic, cubic, compound, power, sigmoidal, growthexponential and logistic functions. The calculations were conducted using SPSS Version22 software and goodness of fit by R2, significance, accuracy of prediction and residuals.The results for mens and womens events indicated cubic functions consistently displayedthe best fits with R2 values for 100m (.723), 400m (.336), long jump (.221) and highjump (.920) for men and 100m (.366), 400m (.526), long jump (.692) and high jump (.496)for women. The inclusion of the 2011 and 2013 data improved the fits very marginally.The outcome was, although some variability existed in R2 the predictions for events wereaccurate indicating in the majority of events the cubic functions displayed good model fits.