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A data-driven framework for team selection in Fantasy Premier League

Danial Ramezani, Tai Dinh

TL;DR

This work addresses the problem of selecting a cost-feasible Fantasy Premier League roster by jointly optimizing the starting XI, bench, and captain under budget, formation, and club-quota constraints. It introduces a data-driven, deterministic MILP and a robust variant that fuse forecast-based costs $c_j$ with a hybrid scoring metric, exploring multiple cost-vector estimators including simple recency-weighted averages and low-order ARIMA forecasts. Through a unified pipeline and a rolling-horizon evaluation on the 2023/24 season, the study demonstrates that low-order ARIMA and recency-aware averaging provide strong out-of-sample performance, with hybrid and robust variants offering context-dependent gains. The framework delivers transparent, reproducible decision support and extends naturally to multi-week transfers, chips, and dynamic captaincy, enabling practical, constraint-aware roster construction in fantasy sports.

Abstract

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 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.

A data-driven framework for team selection in Fantasy Premier League

TL;DR

This work addresses the problem of selecting a cost-feasible Fantasy Premier League roster by jointly optimizing the starting XI, bench, and captain under budget, formation, and club-quota constraints. It introduces a data-driven, deterministic MILP and a robust variant that fuse forecast-based costs with a hybrid scoring metric, exploring multiple cost-vector estimators including simple recency-weighted averages and low-order ARIMA forecasts. Through a unified pipeline and a rolling-horizon evaluation on the 2023/24 season, the study demonstrates that low-order ARIMA and recency-aware averaging provide strong out-of-sample performance, with hybrid and robust variants offering context-dependent gains. The framework delivers transparent, reproducible decision support and extends naturally to multi-week transfers, chips, and dynamic captaincy, enabling practical, constraint-aware roster construction in fantasy sports.

Abstract

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 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.
Paper Structure (24 sections, 28 equations, 17 figures, 7 tables)

This paper contains 24 sections, 28 equations, 17 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Literature review
  3. Preliminaries and mathematical formulations
  4. Optimizing bench
  5. Robust optimization
  6. The proposed framework
  7. Estimating cost vectors
  8. Averaging-based estimators
  9. Simple average
  10. Weighted average (recency emphasis)
  11. Exponential smoothing (Holt’s linear trend)
  12. Simulation-based estimators
  13. Bootstrap (nonparametric)
  14. Monte Carlo (parametric)
  15. Autoregressive integrated moving average (ARIMA)
  16. ...and 9 more sections

Figures (17)

  • Figure 1: The proposed framework. Modeling produces expected points, which feed the optimization to select XI and captain under FPL constraints.
  • Figure 2: Correlation between selected features and total points by positions.
  • Figure 3: Pearson correlation heatmap of modeling features.
  • Figure 4: RainCloud plots of top numeric features by position.
  • Figure 5: SHAP value summaries for key features by position.
  • ...and 12 more figures