Related papers: Pythagoras at the Bat
Sophisticated trajectory prediction models that effectively mimic team dynamics have many potential uses for sports coaches, broadcasters and spectators. However, through experiments on soccer data we found that it can be surprisingly…
Soccer is a sparse rewarding game: any smart or careless action in critical situations can change the result of the match. Therefore players, coaches, and scouts are all curious about the best action to be performed in critical situations,…
Machine learning has become a common approach to predicting the outcomes of soccer matches, and the body of literature in this domain has grown substantially in the past decade and a half. This chapter discusses available datasets, the…
Modelling football outcomes has gained increasing attention, in large part due to the potential for making substantial profits. Despite the strong connection existing between football models and the bookmakers' betting odds, no authors have…
It is well-known that pythagorean triples can be represented by points of the unit circle with rational coordinates. These points form an abelian group, and we describe its structure. This structural description yields, almost immediately,…
We give a brief historical overview of the famous Pythagoras' theorem and Pythagoras. We present a simple proof of the result and dicsuss some extensions. We follow \cite{thales}, \cite{wiki} and \cite{wiki2} for the historical comments and…
Fantasy basketball has a rich underlying mathematical structure which makes optimal drafting strategy unclear. A central issue for category leagues is how to aggregate a player's statistics from all categories into a single number…
Probabilistic modeling is an effective tool for evaluating team performance and predicting outcomes in sports. However, an important question that hasn't been fully explored is whether these models can reliably reflect actual performance…
This paper studies competitions with rank-based reward among a large number of teams. Within each sizable team, we consider a mean-field contribution game in which each team member contributes to the jump intensity of a common Poisson…
This paper proposes a new approach to power in Game Theory. Cooperation and conflict are simulated with a mechanism of payoff alteration, called F-game. Using convex combinations of preferences, an F-game can measure players' attitude to…
Predicting the results of soccer matches is of great interest. This is not only due to the popularity of the sport and the joy of private "betting rounds", but also due to the large sports betting market. Where previously expert knowledge…
Assessment of the performance of a player in any sport is very much needed to determine the ranking of players and make a solid team with the best players. Besides these, fans, journalists, sports persons, and sports councils often analyse…
We consider team semantics for propositional logic, continuing our previous work (Yang & V\"a\"an\"anen 2016). In team semantics the truth of a propositional formula is considered in a set of valuations, called a team, rather than in an…
Premier League is known as one of the most competitive football league in the world, hence there are many goals are scored here every match. Which are the factors that affect to the number of goal scored in each match? We use Poisson…
We consider a stylized formal model of public transportation, where a set of agents need to travel along a given road, and there is a bus that runs the length of this road. Each agent has a left terminal and a right terminal between which…
Can we predict how well a team of individuals will perform together? How should individuals be rewarded for their contributions to the team performance? Cooperative game theory gives us a powerful set of tools for answering these questions:…
In a multi-objective game, each individual's payoff is a \emph{vector-valued} function of everyone's actions. Under such vectorial payoffs, Pareto-efficiency is used to formulate each individual's best-response condition, inducing…
Resilience is the ability to positively respond to adversity. It has been studied in psychology for several decades, with focus on how individuals overcome traumata or cope with setbacks and obstacles in their professional career. Research…
We introduce a class of extensive form games where players might not be able to foresee the possible consequences of their decisions and form a model of their opponents which they exploit to achieve a more profitable outcome. We improve…
Conflict of interest is the permanent companion of any population of agents (computational or biological). For that reason, the ability to compromise is of paramount importance, making voting a key element of societal mechanisms. One of the…