Component Ratios of Independent and Herding Betters in a Racetrack Betting Market

TL;DR

This paper analyzes the dynamics of betting in a racetrack market, revealing power law convergence behaviors and proposing a simple voting model with independent and herding voters that explains these phenomena.

Contribution

It introduces a voting model with two voter types to explain power law behaviors in betting markets, quantifying the ratio of independent to herding voters.

Findings

Win bet fractions converge to final values following a power law with exponent ~0.488.

The ordering index AR also follows a power law decay with exponent ~0.589.

The model suggests a component ratio of 1:3 for independent to herding voters.

Abstract

We study the time series data of the racetrack betting market in the Japan Racing Association (JRA). As the number of votes t increases, the win bet fraction x(t) converges to the final win bet fraction x_{f}. We observe the power law $(x(t)-x_{f})^{2} \propto t^{-\beta}$ with $\beta\simeq 0.488$. We measure the degree of the completeness of the ordering of the horses using an index AR, the horses are ranked according to the size of the win bet fraction. AR(t) also obeys the power law and behaves as $\mbox{AR}_{f}-\mbox{AR}(t)\propto t^{-\gamma}$ with $\gamma\simeq 0.589$, where AR_{f} is the final value of AR. We introduce a simple voting model with two types of voters-independent and herding. Independent voters provide information about the winning probability of the horses and herding voters decide their votes based on the popularities of the horses.This model can explain two power laws of the betting process. The component ratio of the independent voter to the herding voter is 1:3.