xPG is Back, Baby!: Putting Possession Metrics to the (Correlation) Test / by Jamon Moore

By Jamon Moore (@jmoorequakes)

Last year, Cheuk Hei Ho, Eliot McKinley, and I collaborated on a soccer metric called Expected Possession Goals (xPG). xPG is a possession-based non-shot expected goals metric designed to measure the value of possessions whether they result in a shot or not. You can read more about it in these initial articles here on American Soccer Analysis. Later last season we extended xPG into multiple variants, including measuring possession risk and mistakes, but so far the initial xPG, now called Chance xPG, has been the most interesting. We even created a Twitter account called @GameFlowxPG which measures match momentum. It has been pretty popular (I’m a little salty since it usually has more followers than I do).

Here’s an example xPG GameFlow:

We’ve upgraded the xPG model for the 2019 MLS season. We’ve made a number of improvements over the 2018 xPG model, including:

  • Adding more events to the possessions. This helps us better define the start and end points of a possession and the reasons for possession loss.

  • Refining possession logic for managing the additional events. This is the same possession logic used by the WOWY metric introduced by Cheuk Hei Ho.

  • Moving from a zone-based non-shot xG model to a position-based non-shot xG model. In other words, instead of basing the non-shot xG on which zone of the field the actions take place in, we’re basing it on the exact recorded position of the action. It gives finer granularity over xPG values as a possession gets closer to the goal and the scoring chance improves. We use the new dynamically-adjusting xG model introduced by Matthias so our xG values match directly, but we have made some adjustments for calculating non-shot xG.

  • We refined the code to run much faster. Yay us.

Possession Metrics Correlation Tests

For our baseline test, I decided to measure four ways of calculating possession percentage in a match: time on the ball, number of touches, number of possessions, and number of passes. Here’s how I defined each of them:

  • Time Possession: I simply used the start and end times of a possession in our possession definition. This is effectively the “chess clock” approach as best as I can approximate it.

  • Touch Possession: The team’s percentage of total touches in the game.

  • Possessions Possession: In the possession definition used for xPG and WOWY, a team retains possession if they do not lose the ball for more than two seconds. This may vary with how others define possessions, but it helps us account for a large variety of ping-pong possession situations that can happen during a match which can hamper analysis.

  • Pass Possession: The team’s percentage of total passes in the game.

Note: Most touches are associated with a pass attempt but not all, and there was a surprising amount of variance in the results.

Below are the aggregate possession percentages for each MLS team in 2019 using each of these four ways (total ball time, total touches, total possessions, and total passes, each compared to the opposition) of measuring possession.

Team Games PPG Time
Possession %
Touch
Possession %
Possessions
Possession %
Pass
Possession %
Largest
Difference
GF GA GD
Atlanta United 27 1.8 53.33 53.92 54.24 55.34 2.01 43 30 13
Chicago 29 1.1 49.69 48.63 48.91 48.01 1.68 42 42 0
Colorado 27 1.0 41.22 43.25 43.92 40.37 3.55 42 48 -6
Columbus 29 1.0 49.68 49.59 49.90 49.62 0.32 31 43 -12
DC United 29 1.3 47.33 48.70 48.29 47.94 1.37 36 37 -1
FC Cincinnati 27 0.7 49.88 48.77 48.43 48.07 1.81 25 63 -38
FC Dallas 28 1.4 53.53 52.90 52.31 54.07 1.76 41 37 4
Houston 27 1.2 47.38 47.48 47.63 46.70 0.93 35 48 -13
Kansas City 27 1.3 55.60 52.89 52.48 54.17 3.11 38 45 -7
L.A. Galaxy 27 1.6 51.30 49.35 49.35 49.35 1.96 38 38 0
Los Angeles FC 27 2.3 56.39 54.57 54.64 55.82 1.82 73 25 48
Minnesota United 27 1.6 46.64 46.70 47.14 45.33 1.81 42 37 5
Montreal 28 1.2 49.53 48.66 48.53 47.83 1.70 38 51 -13
New England 27 1.4 47.67 45.91 46.59 44.26 3.42 40 46 -6
New York 28 1.5 45.63 47.07 47.97 46.29 2.33 43 41 2
New York City FC 26 1.8 56.77 55.82 54.91 58.87 3.96 48 30 18
Orlando City 28 1.2 46.84 48.35 48.36 47.67 1.52 35 36 -1
Philadelphia 28 1.7 54.57 52.57 52.44 53.85 2.13 50 40 10
Portland 26 1.4 50.22 48.91 49.14 49.09 1.32 40 40 0
Salt Lake 27 1.6 48.88 49.35 48.65 48.77 0.70 40 33 7
San Jose 27 1.5 55.94 56.35 55.59 59.15 3.56 44 41 3
Seattle 27 1.6 45.65 50.30 50.60 50.27 4.95 41 38 3
Toronto 27 1.4 53.67 54.03 54.64 55.30 1.63 43 42 1
Vancouver 28 1.0 43.73 46.24 45.76 44.47 2.51 28 45 -17

That’s a lot of numbers. How do we know if Seattle’s season average possession should be 45.65% or 50.60%? That’s the difference between having more of the ball or less of the ball over the course of the season, so it’s a meaningful distinction. I have a hypothesis that the closer the possession data correlates to goal differential (GD), the more we will see its impact on game outcomes, so I’m going to test that here.

We could also use points-per-game (PPG), but it has few outcomes (0, 1, 3), and isn’t linear. With PPG, we have the interesting jump from one to three points when going from a draw to a win, while a loss to a draw is only a one point jump, so that is likely to adversely affect any linear correlation metrics that we calculate (thanks to the ASA data scientists for patiently explaining this one to me).

Let’s start with the season-over-season correlation between PPG and Goal Differential as our baseline.

To prevent “two sides of the same coin” effects, I have only used the home team values on the charts in this article.

By the way, I hate math. Love statistics, but hate the math to calculate them. It feels like homework to me. I’m going to do my best to explain the tests I used as we go along, but I’m not an expert.

Using a (linear) Pearson correlation on a scatterplot (we debated whether Pearson was the best correlation method for these tests over ASA Slack, but ultimately the data scientists, which I am not, determined it was) over the course of the last four seasons we see that points-per-game and goal differential per season are highly correlated, as you would expect. In other words, to get points you need a higher goal differential. We understand this intuitively at a match level because a team can’t get three points without a higher goal differential, and an even goal differential gets a team one point.

But some teams have made the playoffs with an overall negative goal differential (witness the 2017 San Jose Earthquakes with a -22 goal differential sneaking into the playoffs).  R here shows the correlation coefficient as 0.9, which statistically speaking indicates 81% of the variance in one variable (points-per-game) can be explained by the variance (goal differential) in the other variable. Simply put, that’s a really strong correlation between points-per-game and goal difference. We can use this for comparisons with other correlations. If you are wondering what the p-value is, it’s a measure of the likelihood that our conclusion is valid. Any value less than or equal to 0.05 is a good sign (see null hypothesis for a more detailed explanation), so we’re also good there.

At a game level, this gets a bit messier because of the jump from one to three points for a positive outcome (rather than one to two points).

Here R is 0.83, and the p-value is a perfect 0. This tells us at a game level, goal differential is mathematically strongly correlated with points-per-game, just like it is at a season level. Again we intuitively understand this, but there is some variation for own goals here. Giving the strong correlation, we can safely compare goal differential to each of the four possession types.

 Let’s start at a season level:

Click the image to zoom.

Well, these all look extremely similar to each other. Over the last four MLS seasons we can see all four traditional methods of calculating possession have a correlation coefficient of 0.51 to 0.52 to goal differential. These values tell us that the correlation is moderate, but not strong. A strong positive correlation is closer to 0.7. So possession correlates with goal difference, but not as strongly as points earned does.

If we look at a game level with these same variables, we see something quite different:

Using the xPG definition of a possession here, the p-scores tell us that correlation of total possessions to goal differential (top right), while weak, is still better than the other three which are extremely weak. It is clear from this why in 2017 Opta decided to go away from possession percent using passes (bottom right) to possession percent using total possessions (top right).

Making more passes actually shows an inverse correlation to goal differential at a game level. Given this, there is a good chance game state (the GD at that point of the game) factors heavily into the ball possession a team has. This may be due to teams often getting more possession while losing while the winning team focuses on defensive shape. At a game level there is virtually no correlation to possession and goal differential. While surprising on the surface, this is not the first time this comparison has been done and reached a similar conclusion.

Chance xPG Correlation Tests

Now that we’ve determined the correlation between the normal possession statistics and goal differential, let’s turn our attention back to xPG. Chance xPG (the xPG variant that accumulates possession non-shot xG based on proximity to goal and used to measure the momentum of a match in xPG GameFlow), is quite similar to possession percentage, except that it should tell us how meaningful the possession is. Remember, Chance xPG measures the prospective xG gained (or lost) in the possession via each pass or dribble. I say “prospective” because until a shot is taken, xG is not realized. But Chance xPG accumulates this xG as if it was realized.

Let’s check the possession percent of Chance xPG for each team this season, using both 2018 and 2019 xPG methods, compared to the traditional possession percent using touches (the possession type that the highest season correlation to goal differential). This will tell us if Chance xPG (i.e., non-shot xG possession values in general) may be a more statistically significant way to calculate possession percentage.

Team Games PPG Possession
Pass %
Chance xPG (2019) % Chance xPG (2018) % 2019 Method Difference 2018 Method Difference GD
Atlanta United 27 1.8 53.92 54.3 55.2 0.41 1.3 13
Chicago 29 1.1 48.63 51.1 51.3 2.49 2.7 0
Colorado 27 1.0 43.25 40.8 43.9 -2.46 0.7 -6
Columbus 29 1.0 49.59 48.6 46.5 -0.95 -3.1 -12
DC United 29 1.3 48.7 45.0 41.1 -3.74 -7.6 -1
FC Cincinnati 27 0.7 48.77 44.0 42.8 -4.77 -5.9 -38
FC Dallas 28 1.4 52.9 49.9 48.0 -3.04 -5.0 4
Houston 27 1.2 47.48 46.5 47.5 -1.01 0.0 -13
Kansas City 27 1.3 52.89 53.2 53.1 0.34 0.2 -7
L.A. Galaxy 27 1.6 49.35 51.9 52.8 2.59 3.5 0
Los Angeles FC 27 2.3 54.57 62.4 64.1 7.79 9.5 48
Minnesota United 27 1.6 46.7 47.2 47.9 0.46 1.2 5
Montreal 28 1.2 48.66 47.3 45.2 -1.33 -3.5 -13
New England 27 1.4 45.91 49.9 51.0 3.98 5.1 -6
New York 28 1.5 47.07 51.7 52.8 4.65 5.7 2
New York City FC 26 1.8 55.82 58.8 58.4 2.97 2.6 18
Orlando City 28 1.2 48.35 47.3 48.9 -1.05 0.5 -1
Philadelphia 28 1.7 52.57 57.6 59.1 5 6.5 10
Portland 26 1.4 48.91 50.1 52.3 1.2 3.4 0
Salt Lake 27 1.6 49.35 49.1 48.5 -0.27 -0.9 7
San Jose 27 1.5 56.35 56.0 54.3 -0.34 -2.0 3
Seattle 27 1.6 50.3 45.7 47.2 -4.64 -3.1 3
Toronto 27 1.4 54.03 55.4 56.2 1.34 2.2 1
Vancouver 28 1.0 46.24 37.3 32.6 -8.92 -13.7 -17

The Method Difference columns tell us which teams are using their possession the most effectively (positive numbers) versus those who are not or are giving up a lot of effective possession (negative numbers). We see LAFC uses their possession the most effectively, followed by Philadelphia, New York, New England. If we look for higher negative values, we see Vancouver, FC Dallas, FC Cincinnati, and Seattle have wasted the most possession. Overall, I feel we are getting some useful data from this comparison. We need to do some correlation checks to determine if this is the case. Let’s see how the 2018 xPG and 2019 xPG methods each compare to goal differential and possession using touches.

With an R of .73, both 2018 and 2019 Chance xPG are close to having a strongly significant correlation to goal differential in 2019, whereas touches possession has lower correlation with an around R = 0.52. However, the behavior of one season may not be enough to draw a final conclusion.

Looking at 2016 to 2019 data gives us a good indication that our new 2019 Chance xPG has a barely stronger correlation with GD than our original 2018 xPG method, as we hoped. Chance xPG also maintains a pretty strong correlation with GD over multiple seasons. Across a full season, teams with high Chance xPG tend to also have better GD.  In fact, including the 2016 season brought the correlation down a bit since that season has the weakest correlation (R = 0.62) between goal differential and expected goal differential (xGD) of any season in the ASA dataset (average season correlation of GD and xGD since 2011 is 0.76). You can check this yourself on the American Soccer Analysis interactive tables using the Team xG Scatter plots tab. Given xPG is built on the same xG model as ASA xG, and thereby xGD, it will also be affected by this difference in the 2016 data. Leaving out 2016 gives an R = 0.72 correlation between GD and Chance xPG.

Let’s check Possession % and Chance xPG at an individual game level to see how they correlate with GD:

While much better than possession percentage using possessions, a straight comparison of Chance xPG at a game level to goal differential yields a weak correlation. Just because a team had the best chances didn’t mean they always won the game. The 2019 xPG model seems to be a step forward at a game level, but it’s still a weak correlation. Game state is quite likely still a big factor here, along with goals that happen with short possessions (such as counter attacks and set pieces), because they accumulate less Chance xPG than longer possessions or possessions which start from deeper positions. In the future, we may need to adjust how Chance xPG accumulates in these various phases of play.

More recently I’ve been seeing charts that show which actions lead to game success, so I decided to look at which of these possession metrics are more predictive of success. Let’s compare metrics over the course of a season to goal differential. The higher the line, the bigger the correlation the metric has with goal differential, the lower the line the lower the correlation with goal differential. Lines below 0 show an inverse correlation.

Over these four MLS seasons, Chance xPG used as a possession percentage shows it is more predictive compared to goal differential than the other possession metrics, while also being more stable and less noisy (some underlying noise is smoothed out with the three-game rolling average) than xGD, even though Chance xPG doesn’t factor in which teams are shooting or are just possessing the ball in dangerous areas. Keep in mind we are looking at possessions here, which are effectively zero-sum metrics. Thereby it doesn’t matter how much Chance xPG a team accrues over the course of a season, but rather how it compared to their opponents. The good news is it turns out our xPG metric is a better measure of success than the traditional possession metrics. That gives us confidence for future analysis and gives more options how we use it. Let’s now take a look at how Chance xPG compares to commonly-used offensive metrics like shots and xGD.

Chance xPG versus Shot Metrics

If you’ve heard an analyst or coach say a team “won the xG battle,” they are saying that if xG was the way winners were decided, a different team could have taken the three points. So I ran these individual game battles for xGD, shots on target, shots, possessions, and Chance xPG, to see which ones better correlate to points-per-game and, thereby, playoff positions. For example, if a team “won” a game on xGD, I gave them three points, if they tied on xGD I gave one point for a “draw”, and if they lost on xGD I gave no points for a “loss.” Then I added up the points and used points-per-game to determine playoff positions. I repeated this for shots on target, shots, Chance xPG, and total possessions for each game. 

In this test the number of teams correctly estimated as playoff teams or not are noted in the table below for each season and each metric. Random chance of picking a team that makes the playoffs has been included for comparison.

Season Season GD Game Chance
xPG
Game xGD Game Shots
on Target
Game Shots Game Possessions Random Chance
MLS 2016 (20 teams) 19 (95%) 15 (75%) 13 (65%) 16 (80%) 15 (75%) 13 (65%) 12 (60%)
MLS 2017 (22 teams) 21 (95%)  17 (77%) 15 (68%) 15 (68%) 18 (82%) 13 (59%) 12 (55%)
MLS 2018 (23 teams) 21 (91%) 17 (74%) 19 (83%) 18 (78%) 19 (83%) 12 (52%) 12 (52%)
MLS 2019 (24 teams) as of week 27 20 (83%) 18 (75%) 16 (67%) 18 (75%) 14 (58%) 14 (58%) 14 (58%)
Correctly Predicted% 81 (91%) 67 (75%) 63 (71%) 67 (75%) 66 (74%) 52 (58%) 50 (56%)
The 91% value for season-long goal differential further confirms the PPG-to-GD correlation of 0.9 from earlier

In these individual game battles, we find that Chance xPG does a better job than xGD, possessions, and shots at estimating whether teams make the MLS Cup playoffs. Chance xPG performs the same as shots on target in this area. Season-long goal differential (GD) is still the most important variable, but we’ve already established it has a strong, if not quite perfect, correlation with points-per-game. At the end of the day, it’s still about putting more goals in the net than the other team each game.

Conclusion

Given these results, it’s clear that match momentum and possessing in dangerous areas are major factors to team success in MLS. Next time you see an xPG GameFlow with it’s xPG totals for a match, it’s good to know it can better estimate outcomes than most traditional means of measuring match performance, aside from maybe shots on target. While there will be anomalies (Seattle Sounders, I’m looking at you), and there is more work to be done here including home and away effects and how teams play in different game states, we are on our way to better measuring match performance and answering the question of who was really the better team on the day and why.