Paper: arXiv 2312.16179

Abstract

This paper presents a new framework for player valuation in European football, by fusing principles from financial mathematics and network theory. The valuation model leverages a “passing matrix” to encapsulate player interactions on the field, utilizing centrality measures to quantify individual influence. Unlike traditional approaches, such as regressing on past performance-salary data, this model focuses on in-game performance as a player’s contributions evolve over time. Consequently, our model provides a dynamic and individualized framework for ascertaining a player’s fair market value. The methodology is empirically validated through a case study in European football, employing real-world match and financial data. This cross-disciplinary mechanism for player valuation adapts the effect of connecting pay with performance, first seen in Scully (1974), to include in-game contributions as well as expected present valuation of stochastic variables.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 6.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper employs advanced stochastic calculus and network theory (Markov chains, GBM, PDEs), fitting high math complexity, while it includes a detailed empirical case study with real-world EPL data, indicating strong implementation and backtest potential but less than full trading system rigor.

Research Flowchart

  flowchart TD
  A["Research Goal: Dynamic Player Valuation"] --> B["Data Inputs"]
  B --> C["Model Construction"]
  C --> D["Computational Process"]
  D --> E["Valuation Outcomes"]

  subgraph B ["Data Inputs"]
      B1["Match Event Data"]
      B2["Financial Data"]
  end

  subgraph C ["Model Construction"]
      C1["Passing Matrix"]
      C2["Network Centrality"]
  end

  subgraph D ["Computational Process"]
      D1["Stochastic Variable Integration"]
      D2["Financial Mathematics Fusion"]
  end

  subgraph E ["Key Findings"]
      E1["Dynamic Fair Market Value"]
      E2["Individualized Player Worth"]
  end