With Or Without You (WOWY): a plus-minus alternative for soccer / by Cheuk Hei Ho

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:

The above y-axis shows WOWY while the x-axis shows xGC. The R-squared of the two variables is 0.36, meaning that either variable can only explain about 35% of the variation of another. In other words, WOWY and xGC largely measure different aspects of a player’s performance.

WOWY isn't a fixed rating system. Rather, it's a method to derive a specific score using customizable filters and criterion, allowing us to analyze different aspects of the game.

Comparing position players

The following three plots show WOWY for three positions in three different scenarios. For all three plots, the x-axis shows the xG per possession of the team when a player starts, and the y-axis shows the WOWY of the player. Both axes show the normalized values in percentile. The black line shows the 50th percentile while the dotted lines near the bottom and top show the 10th and 90th percentile, respectively. 

This plot shows the WOWY of MLS wingers and central attacking midfielders. They’ve been grouped together as they are the players who carry most of their team's creativity. Carlos Vela has one of the highest WOWY in this category this year. His WOWY is just one of many statistical categories that show why he is the presumptive winner of this season’s MVP award. LAFC have stood out as one of (arguably THE) most potent offenses in MLS history, and Vela’s value to that unit is clear. Moreover, Vela's teammate Diego Rossi only has a WOWY in the top 50th percentile (basically average for a winger/attacking midfielder), reinforcing that despite having a number of talented attacking options, Vela still manages to stand out clearly from not only the league as a whole, but even when just compared to his undoubtedly stellar teammates.

The other question you likely have is regarding Nicolas Mezquida, who also has one of the league's best WOWY. This may seem surprising at first glance, considering he only has three goals and four assists. Remember that WOWY measures xG per possession, similar to xGC. As long as a player has participated in a possession that creates a shot, he will be rewarded in WOWY. Mezquidas' WOWY is consistent with his role as a #10 in a 4-2-3-1 Colorado team that doesn’t have a lot of creative attacking players. WOWY measures the importance of the player relative to their team, not how good a player is relative to their peers league wide.. Just because Mezquida is more important to Colorado than Miguel Almiron was to Atlanta United (about a top 75-50% winger/attacking midfielder in WOWY) isn’t intended to suggest that Mezquida is a better player than Almiron.

The above plot measures how a fullback or wingback influences chance creation when they participate in a possession in the final third (and only the possessions that have reached the final third are measured). Orlando City's new signing Ruan already has the highest WOWY for this category since 2016. Both Atlanta United and Vancouver in 2019 show polarized WOWYs for their fullbacks/wingbacks on the opposite flank, meaning that both team's wide attack rely only on one flank. Both L.A. Galaxy's fullbacks this season showing up among the best in WOWY not only fits with their crossing-to-Zlatan tactics, but also suggests that they may not be creating a lot of chances in the middle of the pitch. 

The plot above measures how a central midfielder influences chance creation when they participate in possessions in the initial third (and only the possessions that have started in the initial third are counted). You’ll no doubt notice that there are some rather highly regarded and well compensated players near the bottom of this graph. This is another example of how WOWY should be used as a very specific lens to look at very specific scenarios rather than a catch-all metric that can just show you who the best and worst players are. You would be hard pressed to find any credible opinion suggesting that Darlington Nagbe, Jonathan dos Santos, and Tyler Adams aren’t or weren’t important players, but when filtered down to this particular scenario and then farther diluted by the higher quality of their respective teams, they’re going to appear lower than one might have assumed were they just ranked overall.

Breaking down sequences even farther

We could also use WOWY to measure how important the passing of a player is when he participates in the possession in different areas of the pitch. Here, the WOWY of the player in three thirds are compiled, normalized, and plotted on the pitch:

Blue means they’re above average in that third of the field. Red means they’re below average.

There are some very polarized players, like Tyler Adams who was not important in moving the ball out of the initial third but exerted a lot of influence when he reaches the final third, or Djordje Mihailovic, who is very influential when moving the ball forward from the initial third but becomes dispensable in the final third. 

Let’s now dive into two examples to illustrate the WOWY’s flexibility in understanding the efficiency of team’s tactics.

Pity Martinez plays speculative balls

With a South American Footballer of the Year title and a record-breaking transfer fee on his shoulders, Pity Martinez has been under scrutiny since he came to MLS. He is widely seen by many as a flop, considering that his predecessor Miguel Almiron lit up the league before moving to Newcastle. Is Martinez really bad, or is he just not used properly? Applying different filters to WOWY can tell us different things about his impact on Atlanta United’s offense.

Position: Attacking central midfielder
Possession participation criteria: Pass/Dribble/Shot
Filter: Open play possession only (N>100)
Season Team Player WOWY (xG per possession) Percentile since 2016
2017 Atlanta United Miguel Almiron 4.8 72
2018 Atlanta United Miguel Almiron 4.9 74
2019 Atlanta United Pity Martinez 2.5 35
2019 Atlanta United Julian Gressel 2.2 29

Martinez’s WOWY from pass/dribble/shot is inferior to that of Almiron; in two seasons at Atlanta, Almiron ranks in the top 17% among attacking central midfielders with over 100 possession participations, while Pity sits in the bottom 21% against this same population.

But WOWY tells a different story when we double click on a player’s contribution to his team’s attack from passing only:

Position: Attacking central midfielder
Possession participation criteria: Pass only
Filter: Open play possession only (N>100)
Season Team Player WOWY (xG per possession) Percentile since 2016
2017 Atlanta United Miguel Almiron 2.7 60
2018 Atlanta United Miguel Almiron 2.2 42
2019 Atlanta United Pity Martinez 2.2 40
2019 Atlanta United Julian Gressel 1.1 12

The pass-filtered scores WOWY of Almiron and Martinez are a lot closer to each other than they were when action such as dribbles, shots qualified as well in a player’s participation in the possession. The difference is driven mainly by Almiron's number: his influence in the team's chance creation drops more than 200%(!!) without his shot, suggesting that Almiron's ability to find high value shots (and often) was his most potent weapon. He played more like a secondary striker than a typical attacking central midfielder under Tata Martino. Interestingly, applying this filter on possession data and xG generates a result that contradicts the mainstream theory that Almiron was a much better supplier than Martinez.

Not only is Martinez not significantly worse than Almiron as a supplier, he is an elite-level participant in a certain scenario:

Position: Attacking central midfielder
Possession participation criteria: Pass in the initial and middle third only
Filter: Open play possession starting in the initial and mid third only (N>60)
Season Team Player WWOY (xG per possession) Percentile since 2016
2017 Atlanta United Miguel Almiron 1.9 64
2018 Atlanta United Miguel Almiron 1.5 49
2019 Atlanta United Pity Martinez 2.6 86

Filtering the possessions on attackers making passes in the initial and mid third only, Martinez’s WOWY reflects that of the top attacking midfielder this season in this regard, top 11% since 2016.

And this is weird since Martinez's overall pass accuracy is terrible:

Directional Passes Over Expected (DPOE), as represented in the two circles in the image above,  summarizes a player’s Expected Passing in six directions versus expectation from an average passer. The larger the number (more blue), the more successful passes the player makes compared to expectation. The smaller the number (more red) the less successful they are. Consistent with what most people think, Martinez's pass accuracy is worse than that of Almiron (and expectation of a league-average passer) in every direction.

So WOWY says that Martinez is a great supplier away from the final third, while DPOE says that he is a terrible passer. They are not contradictory: WOWY evaluates the ultimate outcome (chance creation or xG) of the pass (or any action we define) while DPOE/xPass measures how accurate a passer is. A high WOWY and a low xPass suggests that a player attempts a lot of risky passes. They don't always make it, but when it goes through it is especially dangerous:

Pass type distribution in six directions and three distance classes. Red means the player makes that pass less frequently than the average player, blue means they make it more frequently than average.

We can also see that Martinez makes a lot of passes to his right side compared to the left. He also makes very few backward passes compared to Almiron.

Outside of the final third, Martinez also attempts a lot more vertical passes than Almiron did:

Random sampling (N=50) of passes from the middle third.

Random sampling (N=50) of passes from the middle third.

A lot of Pity’s passes go direct into zone 14, the area just outside the opponent’s penalty box, which is one of the most high value locations on the pitch. Conversely, Almiron was typically playing less-threatening lateral passes while he was in the middle of the field.

If making direct passes into the opponent’s final third is Martinez's biggest strength, then Atlanta might be wise to rethink how they should play around him. Having him drop all the way from the final third or invert from a wide position to try to solve a wall of defenders doesn't suit his game. He’s at his best when he starts outside of the final third and controls the ball away from the most intense defensive pressure. He’s also not great with a lot of build-up, given  his terrible pass accuracy. He could be very dangerous with runners ready to overlap to receive his dangerous passes. A switch to a 4-3-1-2 or a 3-5-1-1 is something to think about. Yes, this would require a lot of change a lot for one player, but Atlanta may be obliged to do so after spending $12.5 million on him.

Miles Robinson is Detrimental to Atlanta United’s Buildup

We can also use WOWY to look at the efficiency of highly specific actions or tactics. We will use Atlanta's buildup from the back as an example.

Miles Robinson is the stereotype of a fans' favorite player; he was developed by Atlanta as their first ever MLS SuperDraft selection and defensively he is top-notch. His problem is play-making.

“He is an excellent defender. The part of his game that we are still developing is when we have possession and are playing out the back.” -Tata Martino, April 2018

Surprisingly, DPOE suggests Robinson's pass accuracy is comparable to that of his teammates.

We can tweak the filters using the WOWY framework to check if Robinson’s distribution is really as bad as his previous coaches have suggested. Atlanta’s starting center back pairing changed from Leandro Gonzalez Pirez and Michael Parkhurst last season to Gonzalez Pirez and Robinson this season. We compiled the WOWY of Gonzalez Pirez's and Robinson’s passes to each other versus every other teammate this season. The WWOY of 2018 Gonzalez Pirez’s pass is used as a comparison.

Position: Pirez / Robinson / Parkhurst (as passers)
Possession participation criteria: Pass from Gonzalez Pirez / Robinson / Parkhurst to each other in the initial third
Filter: Open play possession starting in the initial and middle third only (N>60)
Season Team Passer Reciever WOWY (xG per possession ratio: Pass to Receiver/Pass to anyone else)
2018 Atlanta United Leandro Gonzalez Pirez Michael Parkhurst 1.00
2019 Atlanta United Leandro Gonzalez Pirez Miles Robinson 0.25
2019 Atlanta United Miles Robinson Leandro Gonzalez Pirez 4.30

Of all the possessions in which Robinson plays a pass from the initial third, Robinson passing to Gonzalez Pirez boosts the xG per possession by more than 400% compared to when he passes to someone else. Conversely, Gonazlez Pirez passing to Robinson decreases the the xG per possession by ~75% compared to when he passes to someone else. This discrepancy in chance creation didn’t happen last year; passes from Gonzalez Pirez or Parkhurst to each other or anyone else has no effect on the xG per possession. Robinson is the odd man out: when he receives the ball in buildup, Atlanta’s attacking output is significantly damaged. The WOWY tool is nicely anchored here in a team like Atlanta that often passes between centerbacks, so the sample size seems adequate, and it feels “apples to apples” as well.

One might argue that there’s a specific problem with the 2019 Atlanta United system that increases Robinson’s difficulty in finding his teammates. But if we use WOWY to isolate a pattern in which passes are being completed by different players to the same targets, a similar trend in the team’s final chance creation output in the ensuing possessions emerges.

Position: NA
Possession participation criteria: Leandro Gonzalez Pirez's or Miles Robinson's pass to the central midfielder from the initial third
Filter: Open play possession with a pass to the central midfielder from the initial third (N>60)
Season Team Passer Receiver WOWY (xG per possession ratio: Pass from Gonzalez Pirez or Robinson/Pass from anyone else)
2019 Atlanta United Leandro Gonzalez Pirez Any central midfielder 1.00
2019 Atlanta United Miles Robinson Any central midfielder 0.22

The WOWY of Gonzalez Pirez passing to any central midfielder is about while that of Robinson is 0.22. Since this is limited to possessions in which a successful pass is made to the central midfielder, Robinson’s negative influence on the outcome of the possession re-affirms there is something inferior about his contribution in buildup, even if he’s completing passes at a decent clip. It could be something about vision or timing, or the precise weight of the passing that unsettles the pass receiver, or something else entirely. An opposition team performing data scouting using the WOWY framework should zoom in with some video analysis to determine how best to capitalize off this finding.

WOWY to measure player’s importance

These two examples should demonstrate the exciting promise of using a WOWY framework in soccer. The rationale of this rating system is simple: to compare how a team fares offensively when a certain player (or event) is involved in a possession or not. Its power comes from its ability to find specific facet of the game and to set up a proper control for the comparison. There should be caution when interpreting WOWY; for example, even though Darwin Quintero's WOWY (10.1) is much higher than that of Carlos Vela (5.7), it's not necessarily that Quintero is a better player. Boosting the offense of a historically best attacking team is different from doing that to 2018 Minnesota. Additionally, strikers are more likely to have high ratios as possessions that reach them are more likely to be dangerous than those that don’t, so direct comparison across positions may be difficult. At a high level, WOWY measures the importance, not the quality, of the player to their team, but clever controlling elements can be added to paint a compelling picture of something interesting happening in a team’s offense.

A few potential ideas for how clubs/scouts could use this tool:

  • Recruiting for specific tool sets at specific positions

  • Data scouting of opposition attacks (which players help/hurt their team’s attack and how or when)

Notes

1. Since setting the filter and the criterion are so important for WOWY, I suggest everyone to write the following expression when they use it:

(Position: player's position you are looking at,
Possession participation criteria:  definition of how a player participates,
Filter: possessions that are being examined)

So if I am comparing how the dribble of a striker influences their team's chance creation in the open play possession that reaches the final third, the expression should be:

(Position: Striker,
Possession participation criteria: dribble,
Filter: possessions enters the final third)

Or if I want to compare different corner takers:

(Position: NA,
Possession participation criteria: corner opening pass,
Filter: corner possession)

Expression like this should allow the readers to gauge if proper criterion and filter are used and facilitate communication.

2. Many members from ASA have contributed to this piece: he won’t admit it, but Cheuk Hei Ho did most of the work and wrote this article. Eliot McKinley and Tiotal Football reviewed the draft and added multiple sections. Tiotal Football also designed the whole analysis of Robinson's buildup problem while Eliot designed many of the vizzes. Dave Laidig has associated players’ action to possession outcome in his ever-evolving PAR rating. In a way, WOWY is a modified version of PAR. Some of the work we did wasn't released here due to the length limit. Dummy Run was used as a lab rat for the early version of WOWY and have given important suggestions. Kevin Minkus, Matthias Kullowatz, and Tyler Richardett helped debug the code and designed a method to do statistical testing on WOWY. Tyler also suggested the name With Or Without You. Drew Olsen and Ian L edited this piece extensively and laid it out for publication. Ian also photoshopped the incredible album image you see at the top.