Prediction and Quantification of Individual Athletic Performance of Runners.

We present a novel, quantitative view on the human athletic performance of individual runners. We obtain a predictor for running performance, a parsimonious model and a training state summary consisting of three numbers by application of modern validation techniques and recent advances in machine learning to the thepowerof10 database of British runners' performances (164,746 individuals, 1,417,432 performances). Our predictor achieves an average prediction error (out-of-sample) of e.g. 3.6 min on elite Marathon performances and 0.3 seconds on 100 metres performances, and a lower error than the state-of-the-art in performance prediction (30% improvement, RMSE) over a range of distances. We are also the first to report on a systematic comparison of predictors for running performance. Our model has three parameters per runner, and three components which are the same for all runners. The first component of the model corresponds to a power law with exponent dependent on the runner which achieves a better goodness-of-fit than known power laws in the study of running. Many documented phenomena in quantitative sports science, such as the form of scoring tables, the success of existing prediction methods including Riegel's formula, the Purdy points scheme, the power law for world records performances and the broken power law for world record speeds may be explained on the basis of our findings in a unified way. We provide strong evidence that the three parameters per runner are related to physiological and behavioural parameters, such as training state, event specialization and age, which allows us to derive novel physiological hypotheses relating to athletic performance. We conjecture on this basis that our findings will be vital in exercise physiology, race planning, the study of aging and training regime design.