Fantasy football is a billion-dollar industry with millions of participants. Under a fixed budget, managers select squads to maximize future Fantasy Premier League (FPL) points. This study formulates lineup selection as data-driven optimization and develops deterministic and robust mixed-integer linear programs that choose the starting eleven, bench, and captain under budget, formation, and club-quota constraints (maximum three players per club). The objective is parameterized by a hybrid scoring metric that combines realized FPL points with predictions from a linear regression model trained on match-performance features identified using exploratory data analysis techniques. The study benchmarks alternative objectives and cost estimators, including simple and recency-weighted averages, exponential smoothing, autoregressive integrated moving average (ARIMA), and Monte Carlo simulation. Experiments on the 2023/24 Premier League season show that ARIMA with a constrained budget and a rolling window yields the most consistent out-of-sample performance; weighted averages and Monte Carlo are also competitive. Robust variants and hybrid scoring metrics improve some objectives but are not uniformly superior. The framework provides transparent decision support for fantasy roster construction and extends to FPL chips, multi-week rolling-horizon transfer planning, and week-by-week dynamic captaincy.

翻译：梦幻足球是一项价值数十亿美元、拥有数百万参与者的产业。在固定预算下，管理者需选拔阵容以最大化未来的梦幻英超联赛（FPL）积分。本研究将阵容选择问题形式化为数据驱动的优化问题，并开发了确定性和鲁棒的混合整数线性规划模型，在预算、阵型和俱乐部配额（每俱乐部最多三名球员）约束下，选择首发十一人、替补球员和队长。目标函数通过一种混合评分指标进行参数化，该指标将已实现的FPL积分与线性回归模型的预测相结合，该模型基于通过探索性数据分析技术识别出的比赛表现特征进行训练。本研究对替代目标函数和成本估计器进行了基准测试，包括简单平均与近期加权平均、指数平滑、自回归积分移动平均（ARIMA）和蒙特卡洛模拟。在2023/24赛季英超联赛数据上的实验表明，采用约束预算和滚动窗口的ARIMA模型能产生最一致的样本外性能；加权平均和蒙特卡洛方法也具备竞争力。鲁棒变体和混合评分指标在某些目标上有所改进，但并非普遍更优。该框架为梦幻阵容构建提供了透明的决策支持，并可扩展至FPL芯片使用、多周滚动视野的转会规划以及逐周动态队长选择。