用马尔可夫决策优化板球击球顺序和投球计划，提升胜率。
Simulation-Based Optimisation of Batting Order and Bowling Plans in T20 Cricket
- 构建分阶段球员画像，结合詹姆斯-斯坦因收缩处理数据稀疏问题。
- 通过5万次模拟计算胜率与守局概率，击球顺序提升4.1个百分点。
- 揭示了忽略阶段差异的策略会显著降低胜率，适合球队战术优化。
本文构建了一个统一的马尔可夫决策过程（MDP）框架，直接以胜率和守局概率为目标，优化T20板球比赛中两个常见临场决策：击球顺序选择与投球计划分配。基于2008-2025年1,161场印度超级联赛（IPL）逐球记录，采用三阶段球员画像引擎（开赛、中期、末段），并引入詹姆斯-斯坦因收缩技术，在各阶段数据不足时将个体表现向联盟均值收缩。胜率/守局概率通过向量化蒙特卡洛模拟在N=50,000次比赛轨迹上评估。击球顺序通过比较所有可行排列，选取最大化胜率者；投球计划则通过受约束的引导搜索逐步优化，满足同一投手不得连续投球等限制。应用于两场2026年IPL比赛，最优击球顺序使孟买猛龙队胜率提升4.1个百分点（52.4%→56.5%），最优投球计划使古吉拉特雷霆队守局概率提升5.2个百分点（39.1%→44.3%）。两者均显示，仅基于整体表现的策略存在明显非最优性，而考虑阶段特征后可显著改善决策效果。
原文摘要 · Abstract (English)
This paper develops a unified Markov Decision Process (MDP) framework for optimising two recurring in-match decisions in T20 cricket, namely batting order selection and bowling plan assignment, directly in terms of win and defend probability rather than expected runs. A three-phase player profile engine (Powerplay, Middle, Death) with James-Stein shrinkage (a technique that blends a player's individual statistics toward the league average when their phase-specific data is sparse) is estimated from 1,161 IPL ball-by-ball records (2008-2025). Win/defend probabilities are evaluated using vectorised Monte Carlo simulation over N = 50,000 innings trajectories. Batting orders are evaluated by comparing all feasible arrangements of the remaining players and selecting the one that maximises win probability. Bowling plans are optimised through a guided search over possible over assignments, progressively improving the allocation while respecting constraints such as the prohibition on consecutive overs by the same bowler. Applied to two 2026 IPL matches, the optimal batting order improves Mumbai Indians' win probability by 4.1 percentage points (52.4% to 56.5%), and the optimal Gujarat Titans bowling plan improves defend probability by 5.2 percentage points (39.1% to 44.3%). In both cases, the observed sub-optimality is consistent with phase-agnostic deployment: decisions that appear reasonable under aggregate metrics are shown to be costly when phase-specific profiles are applied.
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