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Sports organizations often want to estimate athlete strengths. For games with scored outcomes, a common approach is to assume observed game scores follow a normal distribution conditional on athletes' latent abilities, which may change over…
A new approach in team sports analysis consists in studying positioning and movements of players during the game in relation to team performance. State of the art tracking systems produce spatio-temporal traces of players that have…
Transactions are an important aspect of human social life, and represent dynamic flow of information, intangible values, such as trust, as well as monetary and social capital. Although much research has been conducted on the nature of…
Player tracking data have provided great opportunities to generate novel insights into understudied areas of American football, such as pre-snap motion. Using a Bayesian multilevel model with heterogeneous variances, we provide an…
The speed-accuracy tradeoffs are prevalent in a wide range of physical systems. In this paper, we demonstrate speed-accuracy tradeoffs in the game of cricket, where 'batters' score runs on the balls bowled by the 'bowlers'. It is shown that…
Consider the problem of modeling memory effects in discrete-state random walks using higher-order Markov chains. This paper explores cross validation and information criteria as proxies for a model's predictive accuracy. Our objective is to…
Ladder tournaments are widely used to rank individuals in real-world organizations and games. Their mathematical properties however are still poorly understood. We formalize the ranking rule generated by a ladder tournament, and we show…
Pairwise ranking systems based on Maximum Likelihood Estimation (MLE), such as the Bradley-Terry model, are widely used to aggregate preferences from pairwise comparisons. However, their robustness under strategic data manipulation remains…
We present a new multiplayer game model for the interaction and the flow of information in a distributed system. The players are tokens on a Petri net. As long as the players move in independent parts of the net, they do not know of each…
Researchers in explainable artificial intelligence have developed numerous methods for helping users understand the predictions of complex supervised learning models. By contrast, explaining the $\textit{uncertainty}$ of model outputs has…
Basketball players' performance measurement is of critical importance for a broad spectrum of decisions related to training and game strategy. Despite this recognized central role, the main part of the studies on this topic focus on…
Adversarial Transferability is an intriguing property - adversarial perturbation crafted against one model is also effective against another model, while these models are from different model families or training processes. To better…
Game theory is the standard tool used to model strategic interactions in evolutionary biology and social science. Traditional game theory studies the equilibria of simple games. But is traditional game theory applicable if the game is…
We propose a novel extension of the Bradley-Terry model to multiplayer games and adapt a recent algorithm by Newman [1] to our model. We demonstrate the use of our proposed method on synthetic datasets and on a real dataset of games of…
This study applies complexity sciences to analyze the game of Padel. Data from 18 professional matches were collected, and the probability distributions of the total number of shots and the probability distribution of rallies' duration were…
Dueling bandit is a variant of the Multi-armed bandit to learn the binary relation by comparisons. Most work on the dueling bandit has targeted transitive relations, that is, totally/partially ordered sets, or assumed at least the existence…
The parameters of a discrete stationary Markov model are transition probabilities between states. Traditionally, data consist in sequences of observed states for a given number of individuals over the whole observation period. In such a…
Major League Baseball (MLB) has a storied history of using statistics to better understand and discuss the game of baseball, with an entire discipline of statistics dedicated to the craft, known as sabermetrics. At their core, all…
We compare various extensions of the Bradley-Terry model and a hierarchical Poisson log-linear model in terms of their performance in predicting the outcome of soccer matches (win, draw, or loss). The parameters of the Bradley-Terry…
In this paper, we study a popular method for inference of the Bradley-Terry model parameters, namely the MM algorithm, for maximum likelihood estimation and maximum a posteriori probability estimation. This class of models includes the…