  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.
