Adjusted Plus-Minus for NHL Players using Ridge Regression with Goals, Shots, Fenwick, and Corsi

Regression-based adjusted plus-minus statistics were developed in basketball and have recently come to hockey. The purpose of these statistics is to provide an estimate of each player's contribution to his team, independent of the strength of his teammates, the strength of his opponents, and other variables that are out of his control. One of the main downsides of the ordinary least squares regression models is that the estimates have large error bounds. Since certain pairs of teammates play together frequently, collinearity is present in the data and is one reason for the large errors. In hockey, the relative lack of scoring compared to basketball is another reason. To deal with these issues, we use ridge regression, a method that is commonly used in lieu of ordinary least squares regression when collinearity is present in the data. We also create models that use not only goals, but also shots, Fenwick rating (shots plus missed shots), and Corsi rating (shots, missed shots, and blocked shots). One benefit of using these statistics is that there are roughly ten times as many shots as goals, so there is much more data when using these statistics and the resulting estimates have smaller error bounds. The results of our ridge regression models are estimates of the offensive and defensive contributions of forwards and defensemen during even strength, power play, and short handed situations, in terms of goals per 60 minutes. The estimates are independent of strength of teammates, strength of opponents, and the zone in which a player's shift begins.Comment: 24 pages, 5 figures, 7 table

Realignment in the NHL, MLB, the NFL, and the NBA

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 season to the next. However, structures change when growth or contraction occurs, and realignment of the four major professional sports leagues in North America has occurred more than twenty-five times since 1967. In this paper, we describe a method for realigning sports leagues that is flexible, adaptive, and that enables construction of schedules that minimize travel while satisfying other criteria. We do not build schedules; we develop league structures which support the subsequent construction of efficient schedules. Our initial focus is the NHL, which has an urgent need for realignment following the recent move of the Atlanta Thrashers to Winnipeg, but our methods can be adapted to virtually any situation. We examine a variety of scenarios for the NHL, and apply our methods to the NBA, MLB, and NFL. We find the biggest improvements for MLB and the NFL, where adopting the best solutions would reduce league travel by about 20%.Comment: 20 figures, 1 tabl

Creationism and Intelligent Design

The debate over how to address the origins of life in American schools has been ongoing for almost a century. Proponents of creationism and intelligent design have used several different strategies in order to make sure their views are taught, and each time they have been struck down by the Supreme Court. This paper will analyze the three distinct forms the debate has taken, from attempts to ban outright the teaching of evolution, to the teaching of some form of creation-science alongside evolution, to attempts to “disclaim” evolution as it is taught. In its decisions, the U.S. Supreme Court has used different tests to decide whether or not the actions of creationist school boards and teachers violates the Establishment Clause. The Lemon Test and the Endorsement Test are analyzed in this paper, and any analysis of religious “purpose” is soundly rejected in favour of a thorough analysis of religious “effects” as the best method of determining whether a constitutional violation has occurred