Related papers: Probabilistic model for Padel games dynamics
Evolutionary game dynamics describes not only frequency dependent genetical evolution, but also cultural evolution in humans. In this context, successful strategies spread by imitation. It has been shown that the details of strategy update…
A principled approach to cyclicality and intransitivity in paired comparison data is developed. The proposed methodology enables more precise estimation of the underlying preference profile and facilitates the identification of all cyclic…
The reconstruction of the parameter of the model by the measurement of the random variable depending on this parameter is one of the main tasks of statistics. In the paper the notion of the statistically dual distributions is introduced.…
The theory of slow manifolds is an important tool in the study of deterministic dynamical systems, giving a practical method by which to reduce the number of relevant degrees of freedom in a model, thereby often resulting in a considerable…
In performative prediction, the choice of a model influences the distribution of future data, typically through actions taken based on the model's predictions. We initiate the study of stochastic optimization for performative prediction.…
In this paper, we try to predict the winning team of a match in the multiplayer eSports game Dota 2. To address the weaknesses of previous work, we consider more aspects of prior (pre-match) features from individual players' match history,…
Although basketball is a dualistic sport, with all players competing on both offense and defense, almost all of the sport's conventional metrics are designed to summarize offensive play. As a result, player valuations are largely based on…
Many scientific and industrial processes produce data that is best analysed as vectors of relative values, often called compositions or proportions. The Dirichlet distribution is a natural distribution to use for composition or proportion…
Many physical phenomena are modeled as stochastic searchers looking for targets. In these models, the probability that a searcher finds a particular target, its so-called hitting probability, is often of considerable interest. In this work…
In this paper, we develop a logistic regression model to estimate the probability that a particular shot in an NHL game will result in a goal, and use the results to evaluate the performance of NHL skaters, goalies, and teams. We weight…
Difficulty is one of the key drivers of player engagement and it is often one of the aspects that designers tweak most to optimise the player experience; operationalising it is, therefore, a crucial task for game development studios. A…
Evolutionary game theory is a powerful mathematical framework to study how intelligent individuals adjust their strategies in collective interactions. It has been widely believed that it is impossible to unilaterally control players'…
We study the effects of randomness on competitions based on an elementary random process in which there is a finite probability that a weaker team upsets a stronger team. We apply this model to sports leagues and sports tournaments, and…
A probabilistic framework is proposed for the optimization of efficient switched control strategies for physical systems dominated by stochastic excitation. In this framework, the equation for the state trajectory is replaced with an…
We present a data-driven basketball set play simulation. Given an offensive set play sketch, our method simulates potential scenarios that may occur in the game. The simulation provides coaches and players with insights on how a given set…
Many have dedicated their time trying to determine the ideal conditions for a cylinder to have equal probabilities of falling with one of its faces facing upwards or on its side. However, to this day, there is no concrete analysis of what…
We revisit the game in which each of several players chooses a pattern and then a coin is flipped repeatedly until one of these patterns is generated. In particular, we demonstrate how to compute the probability of any one player winning…
Poker is a challenging problem for artificial intelligence, with non-deterministic dynamics, partial observability, and the added difficulty of unknown adversaries. Modelling all of the uncertainties in this domain is not an easy task. In…
We investigate the time evolution of lead changes within individual games of competitive team sports. Exploiting ideas from the theory of random walks, the number of lead changes within a single game follows a Gaussian distribution. We show…
We investigate the probability of scoring a point when playing the basketball shooting game called "Horse". We show that under the Traditional Rules, it is optimal to choose very easy shots. We propose alternative rules called Pops Rules,…