The Calibration-Leverage Tradeoff in Exactly Solvable Win-Probability Models

[2608.14696] The Calibration-Leverage Tradeoff in Exactly Solvable Win-Probability Models Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Physics > Physics and Society arXiv:2608.14696 (physics) [Submitted on 9 Aug 2026] Title: The Calibration-Leverage Tradeoff in Exactly Solvable Win-Probability Models Authors: Devansh Mishra View a PDF of the paper titled The Calibration-Leverage Tradeoff in Exactly Solvable Win-Probability Models, by Devansh Mishra View PDF HTML (experimental) Abstract: 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. Comments: 19 pages, 2 figures, 3 tables Subjects: Physics and Society (physics.soc-ph) Cite as: arXiv:2608.14696 [physics.soc-ph] (or arXiv:2608.14696v1 [physics.soc-ph] for this version) https://doi.org/10.48550/arXiv.2608.14696 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Devansh Mishra [ view email ] [v1] Sun, 9 Aug 2026 21:17:53 UTC (41 KB) Full-text links: Access Paper: View a PDF of the paper titled The Calibration-Leverage Tradeoff in Exactly Solvable Win-Probability Models, by Devansh Mishra View PDF HTML (experimental) TeX Source view license Current browse context: physics.soc-ph < prev | next > new | recent | 2026-08 Change to browse by: physics References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

Related documents

• Practical foundations for probability: Prediction methods and calibration#76991
• Active Calibration of Reachable Sets Using Approximate Pick-to-Learn#927267
• Unbiased Monte Carlo Greeks for Discontinuous Payoffs#973742
• Calibrated Trust, Not Sharper Prediction: An Empirical Test of Uncertainty Fusion#609055
• Corruption-Robust Sparse Linear Contextual Bandits with Knapsack Constraints#1132390