# Valuing Off-the-ball Movement

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Movement is one of the most important dimensions of Football, but it is notoriously hard to measure.

Take Cristiano Ronaldo. He is often criticized for scoring lots of tap ins (even has an Urban dictionary page for it), but that is often result of his great movement, not just the creativity of his teammates.

Take this example: Ronaldo’s Calma goal for Real Madrid against Barcelona. First, the whole play:

And now the Voronoi diagrams of the pass and reception moments (to know more about these, check out the first post in this series):

At the moment the pass is made, Ronaldo doesn’t have much space to receive the ball, with two defenders covering most of the space. However, he’s moving at a faster speed — something you can’t see in the frame — and that’s why he gets to the ball before the defenders.

## Speed or Anticipation?

One possible explanation for why Ronaldo gets past the defenders is his maximum speed. If he, at peak, runs faster than the defenders, he will always get an edge.

Of course, our data isn’t precise or large enough to properly test this theory, but let’s look at what we got: below is a plot of the speed of Ronaldo and the two defenders on him during the play:

As you can see, the max speeds of the three players are comparable, but Ronaldo noticeably starts accelerating before the defenders do, and also hits maximum speed before they do. Most importantly, at the time of the pass (blue vertical line) Ronaldo is moving faster than both defenders, and they take more than one second to fully catch up.

Conclusion: current position may not be the best input to build our Voronois.

Let’s incorporate this concept into the Voronoi graphic. I will simplify by assuming all players maintain current speed and direction, and consider different time gaps for the future positions:

This is a complex issue. You can have to take into account current speed and direction, reaction time, and maximum velocity, and all of these factors would be different for each individual player. Some wouldn’t even be constant for a player— e.g. line of sight would impact reaction time. For a more complex and realistic model, check out William Spearman’s Pitch Control model.

## Incorporating Movement in the Potential Threat Model

In a previous post, I used Voronoi Diagrams and Karun Singh’s Expected Threat model to calculate Threat Potential: basically, the idea is to add the expected threat on all zones controlled by the attacking team.

Let’s take the two versions of the Voronoi Diagrams — Current and Extrapolated (we’ll use the 1 second version) — and calculate the Potential Threat on both versions. Below is a plot of how those numbers evolved during the play:

We see that the Extrapolated Threat Potential (ETP) almost perfectly predicts the future Current Threat Potential (CTP). That is the desired result for a successful play.

Now imagine if Ozil (who made the assist) didn’t pass to Ronaldo and held possession: in that case, Extrapolated Potential Threat would go back down to the Current Potential Threat level. Below is an alternative play profile based on that scenario:

Notice that the extrapolated goes below the current . That is Ronaldo needing to stop to get back onside — and a huge opportunity not being met.

## Detecting Forward Runs

OK, so ETP rising and CTP staying at the same level seems to be associated with space opening up. That could be the basis for a Potential Run metric.

Look at the chart again: before Ronaldo’s run, there’s another moment where that happens, around the 2 second mark. The Extrapolated value goes from 0 to 10 one second before the current value does.

Let’s look at that moment:

Indeed, that is another run, this time by Ozil, but because it was on the wing and further from the goal the value of it was lower. Again, working as expected.

## Conclusion

Models that take into account positioning and movement allow us to value the space created by the attacking team, and potentially attribute that gain to an off-the-ball action. That is a new dimension that we can use to analyze the performance of teams that is not captured by the usual possession stats.

## Next Steps

Another area that is hard to measure is Defensive Positioning. I think this work can also be applied to that important dimension of play.

We can also apply this technique to value individual actions, translating the dynamic nature of this measure into easier to analyze events.