Partial membership models for soft clustering of multivariate football player performance data

The standard mixture modeling framework has been widely used to study heterogeneous populations, by modeling them as being composed of a finite number of homogeneous sub-populations. However, the standard mixture model assumes that each data point belongs to one and only one mixture component, or cluster, but when data points have fractional membership in multiple clusters this assumption is unrealistic. It is in fact conceptually very different to represent an observation as partly belonging to multiple groups instead of belonging to one group with uncertainty. For this purpose, various soft clustering approaches, or individual-level mixture models, have been developed. In this context, Heller et al. (Statistical models for partial membership. In: Proceeding of the 25th International Conference on Machine Learning, 2008) formulated the Bayesian partial membership model (PM) as an alternative structure for individual-level mixtures, which also captures partial membership in the form of attribute-specific mixtures. Our work proposes using the PM for soft clustering of count data arising in football performance analysis and compares the results with those achieved with the mixed membership model and finite mixture model. Learning and inference are carried out using Markov chain Monte Carlo methods. The method is applied on Serie A football player data from the 2022/2023 football season, to estimate the positions on the field where the players tend to play, in addition to their primary position, based on their playing style. The application of partial membership model to football data could have practical implications for coaches, talent scouts, team managers and analysts. These stakeholders can utilize the findings to make informed decisions related to team strategy, talent acquisition, and statistical research, ultimately enhancing performance and understanding in the field of football.