Related papers: Same-Score Streaks: A Case Study in Probability Mo…
Timeout is a short interruption during games used to communicate a change in strategy, to give the players a rest or to stop a negative flow in the game. Whatever the reason, coaches expect an improvement in their team's performance after a…
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…
We use multivariate change point analysis methods, to identify not only mean shifts but also changes in variance across a wide array of statistical time series. Our primary objective is to empirically discern distinct eras in the evolution…
Consider a 4-player version of Matching Pennies where a team of three players competes against the Devil. Each player simultaneously says "Heads" or "Tails". The team wins if all four choices match; otherwise the Devil wins. If all team…
Constructing a suitable schedule for sports competitions is a crucial issue in sports scheduling. The round-robin tournament is a competition adopted in many professional sports. For most round-robin tournaments, it is considered…
Sports leagues consist of conferences subdivided into divisions. Teams play a number of games within their divisions and fewer games against teams in different divisions and conferences. Usually, a league structure remains stable from one…
Major League Baseball (MLB) recently limited pitchers to three pickoff attempts, creating a cat-and-mouse game between pitcher and runner. Each failed attempt adds pressure on the pitcher to avoid using another, and the runner can intensify…
Among the sports fans beliefs about "hot hands" and "winning streaks" are widely spread, while the scientific debate about these effects is still ongoing. Recently in a paper by P. Ferreira [Physica A 500: 92-96] detrended fluctuation…
The goal of the paper is to introduce a set of problems which we call mean field games of timing. We motivate the formulation by a dynamic model of bank run in a continuous-time setting. We briefly review the economic and game theoretic…
Advanced analytics have transformed how sports teams operate, particularly in episodic sports like baseball. Their impact on continuous invasion sports, such as soccer and ice hockey, has been limited due to increased game complexity and…
We study a stochastic process that mimics single-game elimination tournaments. In our model, the outcome of each match is stochastic: the weaker player wins with upset probability q<=1/2, and the stronger player wins with probability 1-q.…
A popular setting in medical statistics is a group sequential trial with independent and identically distributed normal outcomes, in which interim analyses of the sum of the outcomes are performed. Based on a prescribed stopping rule, one…
We consider the following sports scheduling problem. Consider $2n$ teams in a sport league. Each pair of teams must play exactly one match in $2n-1$ days. That is, $n$ games are held simultaneously in a day. We want to make a schedule which…
We analyze the time series of soccer matches in a model-free way using data for the German soccer league (Bundesliga). We argue that the goal difference is a better measure for the overall fitness of a team than the number of points. It is…
Score matching is a recently developed parameter learning method that is particularly effective to complicated high dimensional density models with intractable partition functions. In this paper, we study two issues that have not been…
The availability of massive data about sports activities offers nowadays the opportunity to quantify the relation between performance and success. In this study, we analyze more than 6,000 games and 10 million events in six European leagues…
We investigate the statistics of records in a random sequence $\{x_B(0)=0,x_B(1),\cdots, x_B(n)=x_B(0)=0\}$ of $n$ time steps. The sequence $x_B(k)$'s represents the position at step $k$ of a random walk `bridge' of $n$ steps that starts…
The standard mathematical approach to fourth-down decision making in American football is to make the decision that maximizes estimated win probability. Win probability estimates arise from machine learning models fit from historical data.…
In baseball games, the coefficient of restitution of baseballs strongly affects the flying distance of batted balls, which determines the home-run probability. In Japan, the range of the coefficient of restitution of official baseballs has…
Advancements in technology have recently allowed us to collect and analyse large-scale fine-grained data about human performance, drastically changing the way we approach sports. Here, we provide the first comprehensive analysis of…