Related papers: Undestanding Baseball Team Standings and Streaks
Streaks of success have always fascinated people and a lot of research has been conducted to identify whether the "hot hand" effect is real. While sports have provided an appropriate platform for studying this phenomenon, the majority of…
This paper uses Bayesian tree models for statistical benchmarking in data sets with awkward marginals and complicated dependence structures. The method is applied to a very large database on corporate performance over the last four decades.…
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…
Team sports represent complex phenomena characterized by both spatial and temporal dimensions, making their analysis inherently challenging. In this study, we examine team sports as complex systems, specifically focusing on the tactical…
The Bradley-Terry (BT) model is a common and successful practice in reward modeling for Large Language Model (LLM) alignment. However, it remains unclear why this model -- originally developed for multi-player stochastic game matching --…
We consider the problem of estimating the probability matrix governing a tournament or linkage in graphs from incomplete observations, under the assumption that the probability matrix satisfies natural monotonicity constraints after being…
Probabilistic properties of tennis scoring systems are examined and compared with best-of-K systems. A model, where each player has his/her own probability of winning his/her service point and which remains invariant for the duration of the…
Through a stochastic control theoretic approach, we analyze reputation games where a strategic long-lived player acts in a sequential repeated game against a collection of short-lived players. The key assumption in our model is that the…
When facing a heavily-favored opponent, an underdog must be willing to assume greater-than-average risk. In statistical language, one would say that an underdog must be willing to adopt a strategy whose outcome has a larger-than-average…
We study decades-long historic distributions of accumulated S\&P500 returns, from daily returns to those over several weeks. The time series of the returns emphasize major upheavals in the markets -- Black Monday, Tech Bubble, Financial…
Recent measurement technologies enable us to analyze baseball at higher levels. There are, however, still many unclear points around the pitching strategy. The two elements make it difficult to measure the effect of pitching strategy.…
We consider games played on finite graphs, whose goal is to obtain a trace belonging to a given set of winning traces. We focus on those states from which Player 1 cannot force a win. We explore and compare several criteria for establishing…
We investigate multi-round team competitions between two teams, where each team selects one of its players simultaneously in each round and each player can play at most once. The competition defines an extensive-form game with perfect…
In the game of cricket, the result of coin toss is assumed to be one of the determinants of match outcome. The decision to bat first after winning the toss is often taken to make the best use of superior pitch conditions and set a big…
Standard measures of batting performance such as a batting average and an on-base percentage can be decomposed into component rates such as strikeout rates and home run rates. The likelihood of hitting data for a group of players can be…
There seems to be an upper limit to predicting the outcome of matches in (semi-)professional sports. Recent work has proposed that this is due to chance and attempts have been made to simulate the distribution of win percentages to identify…
Pairwise comparison data are widely used to infer latent rankings in areas such as sports, social choice, and machine learning. The Bradley-Terry model provides a foundational probabilistic framework but inherently assumes transitive…
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…
Most statistical models for pairwise comparisons, including the Bradley-Terry (BT) and Thurstone models and many extensions, make a relatively strong assumption of stochastic transitivity. This assumption imposes the existence of an…
Motivated by the home-field advantage in sports, we propose a generalized Bradley--Terry model that incorporates covariate information for paired comparisons. It has an $n$-dimensional merit parameter $\bs{\beta}$ and a fixed-dimensional…