Order statistics of horse racing and the randomly broken stick

TL;DR

This paper demonstrates that horse racing betting market statistics align with the randomly broken stick model, suggesting horses' true abilities follow an exponential distribution and indicating a degree of market efficiency.

Contribution

It establishes a novel connection between horse racing odds and the randomly broken stick problem, revealing the exponential nature of true horse abilities.

Findings

Market odds match the randomly broken stick distribution.

Horses' true winning probabilities are exponentially distributed.

Market shows signs of informational efficiency.

Abstract

We find a remarkable agreement between the statistics of a randomly divided interval and the observed statistical patterns and distributions found in horse racing betting markets. We compare the distribution of implied winning odds, the average true winning probabilities, the implied odds conditional on a win, and the average implied odds of the winning horse with the corresponding quantities from the "randomly broken stick problem". We observe that the market is at least to some degree informationally efficient. From the mapping between exponential random variables and the statistics of the random division we conclude that horses' true winning abilities are exponentially distributed.