Paper: arXiv 2503.16470

Abstract

We model the time evolution of single win odds in Japanese horse racing as a stochastic process, deriving an Ornstein–Uhlenbeck process by analyzing the probability dynamics of vote shares and the empirical time series of odds movements. Our framework incorporates two types of bettors: herders, who adjust their bets based on current odds, and fundamentalists, who wager based on a horse’s true winning probability. Using data from 3450 Japan Racing Association races in 2008, we identify a microscopic probability rule governing individual bets and a mean-reverting macroscopic pattern in odds convergence. This structure parallels financial markets, where traders’ decisions are influenced by market fluctuations, and the interplay between herding and fundamentalist strategies shapes price dynamics. These results highlight the broader applicability of our approach to non-equilibrium financial and betting markets, where mean-reverting dynamics emerge from simple behavioral interactions.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 6.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper is mathematically dense, featuring stochastic differential equations, Ornstein-Uhlenbeck derivations, and time-dependent potentials, indicating high mathematical complexity. It is also empirically rigorous, utilizing a substantial dataset of 3,450 races from the Japan Racing Association and attempting to derive micro-level behavioral rules from macro-level data.

Research Flowchart

  flowchart TD
  A["Research Goal<br>Model odds evolution in betting markets"] --> B{"Methodology"}
  B --> C["Microscopic Analysis<br>Determine bettor probability rule"]
  B --> D["Macroscopic Analysis<br>Derive mean-reverting dynamics"]
  C & D --> E["Computational Process<br>Ornstein-Uhlenbeck Process Fit"]
  F["Data Input<br>3,450 JRA Races 2008"] --> C
  F --> D
  E --> G{"Key Findings / Outcomes"}
  G --> H["Identified herding vs. fundamentalist interplay"]
  G --> I["Confirmed mean-reverting odds convergence"]
  G --> J["Framework applicable to financial markets"]