A comprehensive review of plus-minus ratings for evaluating individual players in team sports

The increasing availability of data from sports events has led to many new directions of research, and sports analytics can play a role in making better decisions both within a club and at the level of an individual player. The ability to objectively evaluate individual players in team sports is one aspect that may enable better decision making, but such evaluations are not straightforward to obtain. One class of ratings for individual players in team sports, known as plus-minus ratings, attempt to distribute credit for the performance of a team onto the players of that team. Such ratings have a long history, going back at least to the 1950s, but in recent years research on advanced versions of plus-minus ratings has increased noticeably. This paper presents a comprehensive review of contributions to plusminus ratings in later years, pointing out some key developments and showing the richness of the mathematical models developed. One conclusion is that the literature on plus-minus ratings is quite fragmented, but that awareness of past contributions to the field should allow researchers to focus on some of the many open research questions related to the evaluation of individual players in team sports. Keywords: rating system, ranking, regression, regularizatio