Boltzmann-Informed Probabilities

Abstract

Traditional interpretations of probability, whether frequentist or subjective, make no reference to the concept of energy. In this paper, we propose that assigning hypothetical energy levels to the outcomes of a random variable can yield improved probability estimates. We apply this Boltzmann-informed approach to the context of sports betting and analyze five seasons of the English Premier League data. It was found that when used to compute the Kelly criterion, Boltzmann-informed probabilities consistently outperform probabilities derived from the original betting odds. These findings demonstrate the value of integrating energy-informed probabilities into studying complex social systems.