A State-Space Perspective on Modelling and Inference for Online Skill Rating

TL;DR

This paper presents a comprehensive state-space framework for online skill rating, integrating sequential Monte Carlo and hidden Markov models, with practical implementation and scalability considerations.

Contribution

It introduces a novel state-space model perspective for skill rating and provides an open-source Python package for implementation and extension.

Findings

Effective modeling of time-varying skills

Scalable inference methods for large datasets

Open-source tool for reproducible research

Abstract

We summarise popular methods used for skill rating in competitive sports, along with their inferential paradigms and introduce new approaches based on sequential Monte Carlo and discrete hidden Markov models. We advocate for a state-space model perspective, wherein players' skills are represented as time-varying, and match results serve as observed quantities. We explore the steps to construct the model and the three stages of inference: filtering, smoothing and parameter estimation. We examine the challenges of scaling up to numerous players and matches, highlighting the main approximations and reductions which facilitate statistical and computational efficiency. We additionally compare approaches in a realistic experimental pipeline that can be easily reproduced and extended with our open-source Python package, https://github.com/SamDuffield/abile.