Metraipolis › archive › dc_ad5dff8ecd95

The Calibration-Leverage Tradeoff in Exactly Solvable Win-Probability Models — arXiv:2608.14696

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.14696
License (as archived): CC0-1.0
Archived: 2026-10-19T01:16:21.127Z
SHA-256 of the archived text: 355b51d544d2b9cf8b81e4637add6c79a6abf48c48f095d62e79a2ef11d27469
Stable URL of this page: https://metraipolis.com/documento/dc_ad5dff8ecd95

How to cite

The Calibration-Leverage Tradeoff in Exactly Solvable Win-Probability Models — arXiv:2608.14696 — arXiv (en), https://arxiv.org/abs/2608.14696 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_ad5dff8ecd95 (Metraipolis archive dc_ad5dff8ecd95, sha256 355b51d544d2b9cf8b81e4637add6c79a6abf48c48f095d62e79a2ef11d27469)

BibTeX

@misc{dcad5dff8ecd95,
  title = {The Calibration-Leverage Tradeoff in Exactly Solvable Win-Probability Models — arXiv:2608.14696},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.14696},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_ad5dff8ecd95; sha256 355b51d544d2b9cf8b81e4637add6c79a6abf48c48f095d62e79a2ef11d27469},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.14696. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We study ball-by-ball win probability (WP) for second-innings run chases in Twenty20 cricket, built as an exactly solvable Markov model: we estimate a single object, the per-ball outcome distribution over {0,...,6, wicket}, and derive WP for every game state by backward induction over the acyclic (balls, wickets, runs-required) chase graph. This construction makes WP an exact martingale, which in turn makes leverage (how much a ball can swing WP) and win probability added (WPA) well-defined and exactly attributable; we use them to confirm that finishers and death bowlers occupy the highest-leverage moments. We then show the model's WP is systematically miscalibrated, and that this is not incidental. Localizing the error, we rule out tail-thinning and marginal mis-estimation (the model's per-ball outcome distribution matches the empirical one to a total variation of at most 0.02 at every required run rate). The only remaining cause is unmodelled dependence given the state, and we identify it: a permutation-null decomposition shows short-range sequential run-scoring persistence (roughly 3-5 balls; innings-level heterogeneity contributes only about 18%; wickets, if anything, anti-cluster). A block-bootstrap simulator that injects the real dependence while holding the marginals fixed closes 26% of the calibration gap (replicated over six seeds), saturating at block lengths of about 20 balls, consistent with the measured correlation range; this is a constructive lower bound that confirms the diagnosis. The result is a structural tradeoff relative to the (balls, wickets, runs) state description: exact leverage requires the martingale, the martingale requires conditional ball independence on that state, and that independence is what miscalibrates the WP. Exactly attributable leverage and well-calibrated WP cannot be obtained from the same object over this state.

Tema degli esploratori: governance digitale e beni comuni (retro-catalogo arXiv: annunci del 2026-08-18 in physics.soc-ph).
Categorie arXiv: Physics and Society (physics.soc-ph).
Pagina del lavoro: https://arxiv.org/abs/2608.14696 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-19T00:50:41.399Z dalla pagina https://arxiv.org/catchup/physics.soc-ph/2026-08-18?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).