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Any collection can be ranked. Sports and games are common examples of ranked systems: players and teams are constantly ranked using different methods. The statistical properties of rankings have been studied for almost a century in a…
We introduce a new model for sums of exchangeable binary random variables. The proposed distribution is an approximation to the exact distributional form, and relies on the theory of completely monotone functions and the Laplace transform…
Based on the tick-by-tick stock prices from the German and American stock markets, we study the statistical properties of the distribution of the individual stocks and the index returns in highly collective and noisy intervals of trading,…
Covariate shift, a widely used assumption in tackling {\it distributional shift} (when training and test distributions differ), focuses on scenarios where the distribution of the labels conditioned on the feature vector is the same, but the…
We analyze how coaching strategies affect goal difference and home win probabilities using hand-coded Serie A match commentary (2011/12--2013/14). Our dataset captures in-game dynamics, referee actions, and team behavior. Applying…
We consider the task of determining a football player's ability for a given event type, for example, scoring a goal. We propose an interpretable Bayesian model which is fit using variational inference methods. We implement a Poisson model…
Traditional statistical theory assumes that the analysis to be performed on a given data set is selected independently of the data themselves. This assumption breaks downs when data are re-used across analyses and the analysis to be…
A Bernoulli scheme with unequal harmonic success probabilities is investigated, together with some of its natural extensions. The study includes the number of successes over some time window, the times to (between) successive successes and…
We prove a moderate deviation principle for subgraph count statistics of Erdos-Renyi random graphs. This is equivalent in showing a moderate deviation principle for the trace of a power of a Bernoulli random matrix. It is done via an…
We consider a general class of round-robin tournament models of equally strong players. In these models, each of the $n$ players competes against every other player exactly once. For each match between two players, the outcome is a value…
There are a number of mathematical formalisms of the term "outlier" in statistics, though there is no consensus on what the right notion ought to be. Accordingly, we try to give a consistent and robust definition for a specific type of…
One of the main shortcomings of event data in football, which has been extensively used for analytics in the recent years, is that it still requires manual collection, thus limiting its availability to a reduced number of tournaments. In…
Counterfactual explanations methods provide an important tool in the field of {interpretable machine learning}. Recent advances in this direction have focused on diffusion models to explain a deep classifier. However, these techniques have…
In this paper, we discuss some theoretical results and properties of a discrete version of the Birnbaum-Saunders distribution. We present a proof of the unimodality of this model. Moreover, results on moments, quantile function, reliability…
Expected points is a value function fundamental to player evaluation and strategic in-game decision-making across sports analytics, particularly in American football. To estimate expected points, football analysts use machine learning…
Sports betting markets are proven real-world laboratories to test theories of asset pricing anomalies and risky behaviour. Using a high-frequency dataset provided directly by a major bookmaker, containing the odds and amounts staked…
In this paper, the statistical properties of Newton s method algorithm output in a specific case have been studied. The relative frequency density of this sample converges to a well-defined function, prompting us to explore its…
In many sports, it is commonly believed that the home team has an advantage over the visiting team, known as the home field advantage. Yet its causal effect on team performance is largely unknown. In this paper, we propose a novel causal…
In 2017-2020 Jordanova and co-authors investigate probabilities for p-outside values and determine them in many particular cases. They show that these probabilities are closely related to the concept for heavy tails. Tukey's boxplots are…
When testing a statistical hypothesis, is it legitimate to deliberate on the basis of initial data about whether and how to collect further data? Game-theoretic probability's fundamental principle for testing by betting says yes, provided…