Archetypoid analysis for sports analytics

Abstract

We intend to understand the growing amount of sports performance data by finding extreme data points, which makes human interpretation easier. In archetypoid analysis each datum is expressed as a mixture of actual observations (archetypoids). Therefore, it allows us to identify not only extreme athletes and teams, but also the composition of other athletes (or teams) according to the archetypoid athletes, and to establish a ranking. The utility of archetypoids in sports is illustrated with basketball and soccer data in three scenarios. Firstly, with multivariate data, where they are compared with other alternatives, showing their best results. Secondly, despite the fact that functional data are common in sports (time series or trajectories), functional data analysis has not been exploited until now, due to the sparseness of functions. In the second scenario, we extend archetypoid analysis for sparse functional data, furthermore showing the potential of functional data analysis in sports analytics. Finally, in the third scenario, features are not available, so we use proximities. We extend archetypoid analysis when asymmetric relations are present in data. This study provides information that will provide valuable knowledge about player/team/league performance so that we can analyze athlete's careers.

Forecasting basketball players' performance using sparse functional data*

“…As mentioned before, in ADA each datum is expressed as a mixture of actual observations (archetypoids). In particular, the α coefficients of each player are of great utility because they allow us to determine the composition of each player according to the archetypoid players, and to establish a clustering of similar players . A discussion of the implications of the resulting archetypoid coefficients is given next.…”

“…, FDA was introduced for the study of players' aging curves and both hypothesis testing and exploratory analysis were performed. Vinué and Epifanio extended archetypoid analysis (ADA) for sparse functional data (see also refs. ), showing the potential of FDA in sports analytics.…”

“…In particular, in ref. [31, section 5.2] it was demonstrated that advanced analysis with FDA reveals patterns in the players' trajectories over the years that could not be discovered if data were simply aggregated (eg, averaged). We take advantage of this fact and continue the work done in ref.…”

“…We take advantage of this fact and continue the work done in ref. [31, section 5.2] with a view to predict how players will evolve.…”

Robust multivariate and functional archetypal analysis with application to financial time series analysis

“…In Archetypoid Analysis (ADA) each observation in the data set is approximated by a convex combination of a set of real extreme observations called archetypoids. AA and ADA were extended to dense functional data by Epifanio (2016) and to sparse functional data by Vinué and Epifanio (2017). In the functional context, functions from the data set, which can be multivariate functions, are explained by mixtures of archetypal functions.…”