Related papers: A Stochastic Analysis of Table Tennis
Score-based diffusion models are a class of generative models whose dynamics is described by stochastic differential equations that map noise into data. While recent works have started to lay down a theoretical foundation for these models,…
Scheduling a sports tournament is a complex optimization problem, which requires a large number of hard constraints to satisfy. Despite the availability of several such constraints in the literature, there remains a gap since most of the…
Evolution of distribution of strategies in game theory is an interesting question that has been studied only for specific cases. Here I develop a general method to extend analysis of the evolution of continuous strategy distributions given…
Consider Plurality with random tie-breaking. This paper uses standard axiomatic extensions of preferences over elements to preferences over sets (Kelly, Gardenfors, Responsiveness) to characterize all better-replies of a voter under…
Recent decades have seen an interest in prediction problems for which Bayesian methodology has been used ubiquitously. Sampling from or approximating the posterior predictive distribution in a Bayesian model allows one to make inferential…
Scoring rules aggregate individual rankings by assigning some points to each position in each ranking such that the total sum of points provides the overall ranking of the alternatives. They are widely used in sports competitions consisting…
Simple stochastic games are turn-based 2.5-player games with a reachability objective. The basic question asks whether one player can ensure reaching a given target with at least a given probability. A natural extension is games with a…
Zipf's law is well known in linguistics: the frequency of a word is inversely proportional to its rank. This is a special case of a more general power law, a common phenomenon in many kinds of real-world statistical data. Here, it is shown…
Technology has had an unquestionable impact on the way people watch sports. Along with this technological evolution has come a higher standard to ensure a good viewing experience for the casual sports fan. It can be argued that the…
We develop a new method for stochastic optimization using the Bayesian statistics approach. More precisely, we optimize parameters of chess engines as those data are available to us, but the method should apply to all situations where we…
In the game of Scrabble, letter tiles are drawn uniformly at random from a bag. The variability of possible draws as the game progresses is a source of variation that makes it more likely for an inferior player to win a head-to-head match…
In the paper it is proven that the two-players turn-based stochastic game "Risk or Safety" has a unique solution. Both players need to play the same strategy if they want to maximize their winning chances. An analytical method based on the…
This study proposes a statistically grounded framework for real-time win probability evaluation and player assessment in score-based team sports, based on minute-by-minute cumulative box-score data. We introduce a continuous dominance…
A group of friends organize their tennis games by submitting each their availability over the weekdays. They want to obtain an assignment such that: each game must be a double tennis match, i.e. requires four people, and nobody plays in a…
Betting games provide a natural setting to capture how information yields strategic advantage. The Kelly criterion for betting, long a cornerstone of portfolio theory and information theory, admits an interpretation in the limit of…
Stochastic transitivity is central for rank aggregation based on pairwise comparison data. The existing models, including the Thurstone, Bradley-Terry (BT), and nonparametric BT models, adopt a strong notion of stochastic transitivity,…
The International Chess Federation (FIDE) imposes a voluminous and complex set of player pairing criteria in Swiss-system chess tournaments and endorses computer programs that are able to calculate the prescribed pairings. The purpose of…
In this work, a strategy to estimate the information transfer between the elements of a complex system, from the time series associated to the evolution of this elements, is presented. By using the nearest neighbors of each state, the local…
Using equilibrium fluctuations to understand the response of a physical system to an externally imposed perturbation is the basis for linear response theory, which is widely used to interpret experiments and shed light on microscopic…
Competitor rating systems for head-to-head games are typically used to measure playing strength from game outcomes. Ratings computed from these systems are often used to select top competitors for elite events, for pairing players of…