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In 2024, Major League Baseball released new bat tracking data, reporting swing-by-swing bat speed and swing length measured at the point of contact. While exciting, the data present challenges for their interpretation. The timing of the…
We investigated the temporal distribution of goals in soccer using event-level data from 3,433 matches across 21 leagues and competitions. Contrary to the prevailing notion of randomness, we found that the probability of a goal being scored…
Staged trees are a recently-developed, powerful family of probabilistic graphical models. An equivalence class of staged trees has now been characterised, and two fundamental statistical operators have been defined to traverse the…
This short note deals with the so-called $ Sock \; Matching \; Problem$. We define $B_{n,k}$ as the number of all the finite sequences $a_1, \ldots, a_{2n}$ of nonnegative integers which contain at least one occurrence of $k$ $(1 \leq k…
This paper presents a sharp approximation of the density of long runs of a random walk conditioned on its end value or by an average of a functions of its summands as their number tends to infinity. The conditioning event is of moderate or…
Sports game summarization aims to generate sports news based on real-time commentaries. The task has attracted wide research attention but is still under-explored probably due to the lack of corresponding English datasets. Therefore, in…
Continuous-time assessments of game outcomes in sports have become increasingly common in the last decade. In American football, only discrete-time estimates of play value were possible, since the most advanced public football datasets were…
In the sport of cricket, variations in a player's batting ability can usually be measured on one of two scales. Short-term changes in ability that are observed during a single innings, and long-term changes that are witnessed between…
Consider n unit intervals, say [1,2], [3,4], ..., [2n-1,2n]. Identify their endpoints in pairs at random, with all (2n-1)!! = (2n-1) (2n-3) ... 3 1 pairings being equally likely. The result is a collection of cycles of various lengths, and…
Professional baseball players are increasingly guaranteed expensive long-term contracts, with over 70 deals signed in excess of \$90 million, mostly in the last decade. These are substantial sums compared to a typical franchise valuation of…
We consider the problem of locating the source of a network cascade, given a noisy time-series of network data. Initially, the cascade starts with one unknown, affected vertex and spreads deterministically at each time step. The goal is to…
We consider two-person sports where each rally is initiated by a \emph{server}, the other player (the \emph{receiver}) becoming the server when he/she wins a rally. Historically, these sports used a scoring based on the \emph{side-out…
We have developed a sophisticated statistical model for predicting the hitting performance of Major League baseball players. The Bayesian paradigm provides a principled method for balancing past performance with crucial covariates, such as…
The issue addressed in this paper is that of testing for common breaks across or within equations of a multivariate system. Our framework is very general and allows integrated regressors and trends as well as stationary regressors. The null…
The runs test is a well-known test that is used for checking independence between elements of a sample data sequence. Some of runs tests are based on the longest run and others based on the total runs. In this paper, we consider order…
Score-based generative models (SGMs) are generative models that are in the spotlight these days. Time-series frequently occurs in our daily life, e.g., stock data, climate data, and so on. Especially, time-series forecasting and…
In this paper, Poisson time series models are considered to describe the number of field goals made by a basketball team or player at both the game (within-season) and the minute (within-game) level. To deal with the existence of temporal…
The purpose of this paper is to study a statistic that is used to compare the similarity between two strings, which is first introduced by Michael Steele in 1982. It was proposed as an alternative to the length of the longest common…
For a sequence of $n$ random variables taking values $0$ or $1$, the hot hand statistic of streak length $k$ counts what fraction of the streaks of length $k$, that is, $k$ consecutive variables taking the value $1$, among the $n$ variables…
We investigate the dynamics of football matches. Our goal is to characterize statistically the temporal sequence of ball movements in this collective sport game, searching for traits of complex behavior. Data were collected over a variety…