arXiv subjects

Martin B. Haugh

Publications and source records attributed to Martin B. Haugh.

2 recordsLinked to original sources

arXiv2024

An Empirical Bayes Approach for Estimating Skill Models for Professional Darts Players

We perform an exploratory data analysis on a data-set for the top 16 professional darts players from the 2019 season. We use this data-set to fit player skill models which can then be used in dynamic zero-sum games (ZSGs) that model real-world matches between players. We propose an empirical Bayesian approach based on the Dirichlet-Multinomial (DM) model that overcomes limitations in the data. Specifically we introduce two DM-based skill models where the first model borrows strength from other darts players and the second model borrows strength from other regions of the dartboard. We find these DM-based models outperform simpler benchmark models with respect to Brier and Spherical scores, both of which are proper scoring rules. We also show in ZSGs settings that the difference between DM-based skill models and the simpler benchmark models is practically significant. Finally, we use our DM-model to analyze specific situations that arose in real-world darts matches during the 2019 season.

stat.AP↗

arXiv2022

Play Like the Pros? Solving the Game of Darts as a Dynamic Zero-Sum Game

The game of darts has enjoyed great growth over the past decade with the perception of darts moving from that of a pub game to a game that is regularly scheduled on prime-time television in many countries including the U.K., Germany, the Netherlands, and Australia among others. The game of darts involves strategic interactions between two players but to date the literature has ignored these interactions. In this paper, we formulate and solve the game of darts as a dynamic zero-sum-game (ZSG), and to the best of our knowledge we are the first to do so. We also estimate individual skill models using a novel data-set based on darts matches that were played by the top 16 professional players in the world during the 2019 season. Using the fitted skill models and our ZSG problem formulation, we quantify the importance of playing strategically, i.e. taking into account the score and strategy of one's opponent, when computing an optimal strategy. For top professionals we find that playing strategically results in an increase in win-probability of just 0.2% - 0.6% over a single leg but as much as 2.3% over a best-of-35 legs match.

stat.AP↗