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PreprintCC BY 4.0arXiv

A Markov Chain Approach to Modeling Rugby Union

  • Kenny Watts
  • Jonathan Pipping-Gamón
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Abstract

Rugby Union's continuous play, variable-length possessions, and multiple scoring outcomes make it difficult to model with standard approaches. We present a Markov Chain framework that represents Rugby Union as a finite state space over score differential, remaining time, and pitch location, with transition probabilities estimated from historical match data. The resulting model supports simulation and analysis of in-game trajectories, including win probability and expected point estimates from any given state. We validate the model through calibration analysis and comparison to models that predict only final outcomes. Our state-space approach produces well-calibrated, competitive estimates while additionally enabling analysis of how games evolve between states.

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Cite

BibTeXRIS
BibTeX
@misc{watts2026markov,
  title = {{A Markov Chain Approach to Modeling Rugby Union}},
  author = {Kenny Watts and Jonathan Pipping-Gamón},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.04813},
  eprint = {2610.04813},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.04813},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A Markov Chain Approach to Modeling Rugby Union
AU  - Kenny Watts
AU  - Jonathan Pipping-Gamón
PY  - 2026
DA  - 2026/10/03
PB  - arXiv
DO  - 10.48550/arxiv.2610.04813
UR  - https://arxiv.org/abs/2610.04813
AB  - Rugby Union's continuous play, variable-length possessions, and multiple scoring outcomes make it difficult to model with standard approaches. We present a Markov Chain framework that represents Rugby Union as a finite state space over score differential, remaining time, and pitch location, with transition probabilities estimated from historical match data. The resulting model supports simulation and analysis of in-game trajectories, including win probability and expected point estimates from any given state. We validate the model through calibration analysis and comparison to models that predict only final outcomes. Our state-space approach produces well-calibrated, competitive estimates while additionally enabling analysis of how games evolve between states.
ER  -