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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…
The field of quantitative analytics has transformed the world of sports over the last decade. To date, these analytic approaches are statistical at their core, characterizing what is and what was, while using this information to drive…
The infield shift has been increasingly used as a defensive strategy in baseball in recent years. Along with the upward trend in its usage, the notoriety of the shift has grown, as it is believed to be responsible for the recent decline in…
A scoring rule is a function of a probabilistic forecast and a corresponding outcome that is used to evaluate forecast performance. A wide range of scoring rules have been defined over time and there is some debate as to which are the most…
From 2020 to 2023, Major League Baseball changed rules affecting team composition, player positioning, and game time. Understanding the effects of these rules is crucial for leagues, teams, players, and other relevant parties to assess…
Batting average is one of the principle performance measures for an individual baseball player. It is natural to statistically model this as a binomial-variable proportion, with a given (observed) number of qualifying attempts (called…
In this short note, we consider an inverse problem to a mean-field games system where we are interested in reconstructing the state-independent running cost function from observed value-function data. We provide an elementary proof of a…
In-game win probability models, which provide a sports team's likelihood of winning at each point in a game based on historical observations, are becoming increasingly popular. In baseball, basketball and American football, they have become…
The ballistic coefficient of a bullet describes how it slows in flight due to air resistance. This article presents experimental determinations of ballistic coefficients showing that the majority of bullets tested have their previously…
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…
Bill James' Pythagorean formula has for decades done an excellent job estimating a baseball team's winning percentage from very little data: if the average runs scored and allowed are denoted respectively by ${\rm RS}$ and ${\rm RA}$, there…
As a dedicated follower of sports statistics and with the MLB season beginning in late March, I set out to predict how many wins each team would accumulate by the end of the 162 game season. The goal was to build a simulation framework…
It has been noted that in many professional sports leagues a good predictor of a team's won-loss percentage is Bill James' Pythagorean Formula RSobs^c / (RSobs^c + RAobs^c), where RSobs (resp. RAobs) is the observed average number of runs…
A same-score streak in sports is a sequence of games where the scores are equivalent in all games. The motivating problem arose from college basketball, however due to the difficulty in collecting data, streaks in Major League Baseball…
We introduce a three-step framework to determine at which pitches Major League batters should swing. Unlike traditional plate discipline metrics, which implicitly assume that all batters should always swing at (resp. take) pitches inside…
There have been more hitting streaks in Major League Baseball than we would expect. All batting lines of MLB hitters from 1957-2006 were randomly permuted 10,000 times and the number of hitting streaks of each length from 2 to 100 was…
The Traveling Tournament Problem (TTP) is a hard but interesting sports scheduling problem inspired by Major League Baseball, which is to design a double round-robin schedule such that each pair of teams plays one game in each other's home…
Baseball is a game of strategic decisions including bullpen usage, pinch-hitting and intentional walks. Managers must adjust their strategies based on the changing state of the game in order to give their team the best chance of winning. In…
Balls-and-bins games have been a wildly successful tool for modeling load balancing problems. In this paper, we study a new scenario, which we call the ball recycling game, defined as follows: Throw m balls into n bins i.i.d. according to a…
Player performance prediction is a serious problem in every sport since it brings valuable future information for managers to make important decisions. In baseball industries, there already existed variable prediction systems and many types…