超出预期得分（RAE）与三柱门效应（WE）：适用于Twenty20板球的上下文调整型统一影响度量
Context-adjusted Player Evaluation for Twenty20 Cricket
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中文总结 AI 辅助
本研究提出适用于T20板球的RAE与WE统一影响度量框架，可基于超270万次投球数据评估个体击球与投球表现，能纠正传统指标的情境盲目性并生成合理排行榜。
中文摘要 AI 辅助
我们开发了一个可复现框架，用于在Twenty20（T20）板球中以可解释的“超出预期得分”（Runs Above Expectation, RAE）这一单一尺度评估个体击球与投球表现，该框架构建于两个球级基础要素之上。第一个要素是超出预期得分（RAE），它是某一次投球的实际得分与平均球员在相同情境下预期得分之间的残差；该预期是群体得分率的乘性对数线性模型，其每个单元格的估计量被证明是条件泊松极大似然乘数，通过迭代回拟拟合并经经验贝叶斯收缩稳定，从而将样本稀少的情境向总体池化。单一对手对称性使得分与失得分处于同等地位。第二个基础要素是三柱门效应（Wicket Effect, WE），它以失球所造成的得分损失来定价，该损失通过动态规划在观察到的比赛过程中求解贝尔曼期望递归得到的击球方价值函数读取。由于失球是每局的预期结局，实际三柱门成本（realWE）以联赛失球风险率下的预期三柱门成本（xWE）为中心，该中心化量是失球过程的得分加权均值零鞅残差，因此球员仅需为偏离平均行为的失球负责。两个基础要素相加得到对称的“影响度量”，使击球与投球在中心层面而非仅单位层面具有可比性。该框架基于超过270万次男子T20板球合法投球进行估计，能够恢复已知的情境结构，与它所改进的传统得分率一致，同时纠正了传统得分率的情境盲目性，并为印度超级联赛生成了符合直观的球员、单局及赛季排行榜。
英文摘要
I develop a reproducible framework for evaluating individual batting and bowling performances in Twenty20 (T20) cricket on one interpretable scale of runs above expectation, built from two ball-level primitives. The first, Runs Above Expected (RAE), is the residual between the runs scored on a delivery and a contextual expectation of what an average performer would produce in the same situation. That expectation is a multiplicative log-linear model of the cohort scoring rate, whose per-cell estimator is shown to be a conditional Poisson maximum likelihood multiplier. It is fitted by iterated backfitting and stabilised by empirical Bayes shrinkage, so that thinly sampled contexts are pooled towards the population. A single opposition symmetry places run-scoring and run-prevention on the same footing. The second primitive, \emph{Dismissal Adjusted Runs} (DAR), prices a dismissal in that currency as the runs it forgoes, read off a batting side value function solved by dynamic programming through a Bellman expectation recursion, under observed play. Because dismissal is the expected end of every innings, the realised wicket cost (realDAR) is centered against its expectation (xDAR) under a league dismissal hazard rate. The centered quantity is a run-weighted mean zero martingale residual of the dismissal process, so a player is charged only for departing from average behaviour. The two primitives sum to a symmetric Impact, which makes batting and bowling comparable in centre as well as in unit. Estimated on over 2.7 million legal deliveries of men's T20 cricket, the framework recovers known contextual structure, agrees with the conventional rates it refines while correcting their context-blindness, and yields face-valid player, innings and season leaderboards for the Indian Premier League.
