Defining Active Zones

Numerical Advantage and the search for key moments in a Play

In a previous article for Statsbomb, I proposed we should measure Numerical Superiority (or Advantage) by defining an Active Zone that includes both the ball and the goal and that maximizes the difference between attackers and defenders.

My first attempt at calculating this metric considered an area between the goal line and a parallel line, but it quickly became obvious that the approach was too simplistic.

In particular, the approach isn’t really suited for wide play: Marcelo doesn’t have numerical advantage when he’s closer to the goal line, because he has to pass backwards (not all Brazilian leftbacks can do this).

A second attempt yielded much better results:

A top-down view of James’ goal versus Barcelona with the Active Zone displayed (red: attacking Advantage | green: defensive Advantage)

These were the criteria used:

• Instead of a rectangle, all possible polygons with the attackers and the goal posts as vertices were considered.
• To avoid narrow areas (you don’t really have an open line to the goal if the defender is 2 steps to your right), a buffer was considered around the players (skewed to the goal line, i.e. smaller distance if a defender is behind the attacker).
• To avoid just selecting the whole field (by default, a numerical equilibrium), a player has to be within a certain distance of either the ball or the goal to be considered.

While the buffer and distance to the ball have to be refined (e.g., maybe we should reduce the buffer once we get closer to the goal), the overall approach looks solid. Let’s try with another example:

Wijnaldum’s Goal for Liverpool against Middlesbrough

At first glance, it behaves as expected. The approach seems to generalize well.

What can we do with this information?

There are different ways we can use this metric:

1. As a measure of danger (e.g. adding it to Expected Goals formulas)
2. As a measure of defensive mindset (a Parking-the-bus tactic should is should result in a +2 Defensive Advantage at most times)
3. To analyze the build-up of a play

Let’s spend some time on that last one. If we plot the Attacking Numerical Advantage over time of the last example, we get the following chart:

As expected, there’s a natural progression from Defensive Advantage to Attacking Advantage.

But there’s some valuable information we can get from this figure that we can’t get from events data: the change points in Advantage.

Let’s look at them:

The first change point (from the left image to the middle image) has no associated event. What happened? Liverpool’s forward (Firmino) moved towards the touchline, getting an opposing midfielder out of the Action Zone. That created a numerical equilibrium.

The second change point happens due to pass from Clyne to Firmino. That pass removes two Middlesbrough players from the Active Zone, but only one from Liverpool (Clyne himself). however, the pass merely seized the advantage: it was only possible in the first place due Wijnaldum’s movement.

The chance was created in those 2 seconds. From there on, Liverpool had the upper hand: in a 2 vs 1 scenario, Wijnaldum was free to shoot or pass. He shot, and scored.

The two biggest takeaways:

1. Off-the-ball movement is key to creating an opportunity for numerical advantage. Wijnaldum’s movement should be recognized as a positive action even if the Clyne never made the pass.
2. We can mathematically calculate the moment when the advantage is attained. That is important to measure individual contributions to a team goal — while the assist is always valued, the passes before and the movement of the players is mostly overlooked, even though sometimes they’re as important as the assist (more on that in a previous post I wrote).