Abstract
In team sports the impact of individual players on their team’s performance is an important question. Traditional summaries of a player’s performance in a game or a season have some limitations. They do not represent all actions taken by a player that can help his or her team win games, and they can be influenced by the player’s teammates, both of which limit their ability to measure the player’s true impact on a game’s outcome. Regression-based adjusted plus-minus metrics were created in part to address these concerns and have become one of the foundational classes of metrics in sports analytics. The majority of these models can be viewed as a generalized linear model (GLM), each with distinct characteristics. In this chapter, we provide a framework to understand these methods, focusing on model formulation, design structures, and choices for the response variables. We close with some open research problems that are formulated in the last section. The sample code is available for the methods described herein at https://github.com/bmacGTPM/apm-primer/tree/main/R.