Prediction and Quantification of Individual Athletic Performance

TL;DR

This paper develops a low-rank model for predicting individual athletic running performance, demonstrating its ability to unify various phenomena in sports science and outperform existing methods like Riegel's formula.

Contribution

It introduces local matrix completion (LMC) as a novel, superior method for individual performance prediction and provides a scientific foundation linking multiple sports science phenomena.

Findings

LMC outperforms other prediction methods

Performance data follows a low-rank power law model

Various sports phenomena can be explained by the model

Abstract

We provide scientific foundations for athletic performance prediction on an individual level, exposing the phenomenology of individual athletic running performance in the form of a low-rank model dominated by an individual power law. We present, evaluate, and compare a selection of methods for prediction of individual running performance, including our own, \emph{local matrix completion} (LMC), which we show to perform best. We also show that 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.