Volume 3, Issue 1

Using data from the 4,858 baseball games that were played in the major leagues during the 2004 and 2005 seasons, four logit regression models that measure the likelihood of a team winning a game are estimated. Of particular interest is the effect of being the home team. As expected, the results indicate that a home-field advantage does exist in the major leagues, but only under certain circumstances. Specifically, the strength of the home-field advantage varies with the number of runs scored by the home team and with the run differential between the winning and losing team. The probability of a home team winning a game increases as it scores more runs, but it increases at a decreasing rate. Also, for a given number of runs scored, a home team is more likely to win a game than a visiting team. The home-field advantage is strongest in games where the run differential between the winning team and losing team is one run. It is weaker in games where the run differential is two runs and is non-existent in games where the run differential is three runs or more.

In the sport of Highland Dance, Championships are often contested where the order of dance is randomized in each of the four dances. As it is a widely held belief that competing in the latter sets is advantageous, this paper develops algorithms where balance is achieved in the dance order. Specifically, draws are randomly generated where the sum of the dance orders over all four dances is constant for each dancer.

There is a growing literature on the statistical analysis of data from association-football/soccer games, seasons or groups of seasons. In contrast this paper is concerned with a single play, that is a sequence of successful passes. The play studied contained 25 passes and ended in a goal for Argentina in World Cup 2006. One question addressed is how to describe analytically the spatial-temporal movement of such a particular sequence of passes.The basic data are points in the plane, successively joined by straight lines. The resulting figure represents the trajectory of the moving soccer ball. The approach of this study is to develop a useful potential function, a concept arising from physics and engineering. In particular the potential function leads to a regression model that may be fit directly by linear least squares.The resulting potential function may be used for simple description, summary, comparison, simulation, prediction, model appraisal, bootstrapping, and employed for estimating quantities of interest. The purpose illustrated here is to simulate play in a game where the ball goes back and forth between two teams each having their own potential function.

A game of table tennis is analyzed using elementary concepts of calculus, probability, and linear algebra. The analysis includes modeling using different approaches and a comparison of the results obtained under the new and the old rules for the game. The analysis demonstrates the steps of a mathematic modeling and illustrates the possible expansion of it.