## 1 Introduction  
Soccer has become a large global business, and significant amounts of capital are at stake when the competitions at the highest level are played. While soccer is a team sport, the attention of media and fans is often directed towards individual players. An understanding of the game therefore also involves an ability to dissect the contributions of individual players to the team as a whole. Plus-minus ratings are a family of player ratings for team sports where the performance of the team as a whole is distributed to individual players. Such ratings have been successfully used by media for sports such as ice hockey and basketball, and creators of such rating systems work as analysts for National Basketball Association (NBA) teams, influencing their decisions on trades and free-agent signings [1]. There has recently been several academic contributions towards plus-minus ratings for soccer [2], although the influence of these ratings has not yet reached the same levels as in basketball. The most trivial form of plus-minus, which originated in ice hockey during the 1950s [1], is to count the number of goals scored minus the number of goals conceded when a given player is in the game. This form, however, fails to take into account the effects of teammates and the opposition. Therefore, in the context of basketball, [PERSON] [3] used linear regression to create adjusted plus-minus ratings, where the plus-minus score of each player is adjusted for the effects of the other players on the court. The main drawback of this approach is that individuals that always play together cannot be discerned, and rating estimates become extremely unreliable. [PERSON] [4] solved this by introducing a regularized adjusted plus-minus rating for basketball, where the linear regression model is estimated using ridge regression, introducing a bias and reducing the variance of the rating estimates. Most often, plus-minus ratings are taken as an overall performance measure. However, some research has been done where the ratings are split into an offensive and a defensive contribution. This paper presents a new plus-minus rating for soccer, where each player is given an offensive and a defensive rating, based on how the player contributes towards creating and preventing goals,respectively. The motivation for this work is to see whether splitting the player ratings into offensive and defensive components can lead to additional insights about the contributions of individual players, teams, and leagues. If successful, this could be useful for an initial phase of data-driven scouting at clubs, to better identify a list of prospective players for recruitment. The urgency of properly identifying both offensive and defensive contributions was illustrated in the context of basketball by [PERSON] et al. [5]. They provided an analysis, based on offensive and defensive plus-minus ratings, to show that win-maximizing teams in the NBA can reduce their expenses by hiring defensively strong players. The new rating system is evaluated on a data set containing more than 52 thousand matches played from 2008 to 2017. The rating model is used to evaluate the effect of age on player performance, the home field advantage, the relative quality of different leagues, and the difference in performance of players in different positions on the field. Each of these are examined from the perspective of offensive and defensive contributions. Furthermore, rankings of players and teams as of July 2017 are presented and discussed, illustrating how the offensive and defensive ratings can be used to indicate interesting differences between players. The new offensive-defensive plus-minus rating appears to be the most complete rating of this type for soccer provided in the academic literature as of yet. The remainder of this paper is structured as follows. Section 2 summarizes the current literature on plus-minus ratings. The new offensive-defensive plus-minus rating for soccer is then described in Section 3.