By Cheuk Hei Ho (@tacticsplatform)

Plus-minus measures the impact of a player on their team’s performance. Originally invented by hockey general managers, every player on the ice is awarded a plus when their team scores a goal while every opponent player on ice gets a minus. The higher the plus-minus rating, the higher the net positive of goals scored for a player’s team. In terms of plus-minus, the best player has the highest plus-minus score, and the worst player has the lowest. Plus-minus has also been modified for use in basketball, first by 82games, and now more famously by ESPN

Plus-minus has drawn its share of criticisms; it measures the overall impact of the player on their team's performance but disregards the individual facets of the player. The rating of the player is heavily influenced by the quality of the teammates the player shares the floor, ice, or field with. For example, if two players are equal in ability, but one shares the floor with a 1990 Bulls Michael Jordan and the other with a 2002 Wizards Michael Jordan, the former is likely to have a higher plus-minus than the latter.

Despite its shortcomings, the potential to apply an “all-in” type metric like plus-minus to soccer is tantalizing. But soccer is different from other major sports, which makes such a metric a little more difficult to build and measure. We’ve even tried it on this very site before, but ultimately abandoned it because it basically told us the best teams, not the best players.

There are a few reasons it’s harder to use plus-minus in soccer. As substitutions are much more common and not limited in basketball or hockey, one can easily compare two players from the same team in the same position, as both players will play a significant amount of time in the same game (and against the same opponent). The massive sample size that comes with substitutions in these sports also aids statistical analysis. This way, most variables are "controlled", meaning that their surrounding conditions should be largely equivalent and the ratings of the two players are readily comparable. These considerations are particularly important for soccer because the game is more fragmented and the players' roles are more diverse compared to those of basketball or hockey. Additionally, the massive size of the soccer field and the unstructured phase of play means that each player has a specific function and each possession has a specific immediate aim (such as breaking a press vs. creating a goal scoring opportunity). There are also just a lot more players on the field at once, so it makes it more difficult to narrow a team’s success to a specific player. Finally, there is also much less scoring in soccer, so there are fewer score changes to track. Therefore, any plus-minus-like rating in soccer needs to be customizable.

Taking advantage of the heterogeneous gameplay in soccer, we have developed an alternative method based on the concept of plus-minus in terms of possession chains. "With Or Without You" (WOWY) is a customizable rating system to evaluate a player's importance to their team. In soccer, not all the players touch the ball in a possession. One can compute the outcome (the average xG per possession) of the possessions that any player participates (“With You”) and does not participate in (“Without You”). The influence of the player to their team will be measured as the ratio between the outcomes of the two groups of possessions, hence our plus-minus. Since the xG per possession already normalizes the number of possessions, over a large enough sample size it quantifies how the player can influence the quality of the chances created and measure the importance of the player to their team in the offensive phase. In other words, we can track if a team has better scoring chances when that player is involved versus when they aren’t, and assign them a score accordingly.

In principle, WOWY should reveal information different from the traditional xG related statistics. For instance, a player can record 90% of their team’s Expected Goal Chain (xGC) while using 90% of their possessions. In that case, their team should record 1 xGC/possession whether that player has participated or not (ie. 90% of the team’s xGC for the 90% of plays they’re involved in, plus 10% of the team’s xGC for the 10% they’re not involved in). To examine the overlap between traditional xGC statistics and WOWY, I calculated WOWY and xGC for over 400 attacking central midfielders and wingers in MLS since 2016: