Correlation between shooting angles and Expected Goals (xG)
Expected goals. We have been discussing its use for years in the data analytics space, not only in football of course, but also in spaces like Ice Hockey. We look at the likelihood or probability of a shot/chance being converted into a goal by looking at different variables. One of these variables is the angle, which I want to talk about today.
One of the variables is the angle of the shot and we need to have a look at that because it also tells us something about the player’s ability to shoot from different angles and make something meaningful out of it.
Why this article?
That’s always a good question. I think it’s important to stress that everything I write here is because I think it’s interesting and has some merit in the public analytics space. However, it doesn’t need to be something that will be used when working for a professional club, so I think that’s always an important distinction to make.
I want to have a look at the correlation between expected goals (xG) and shooting angles: how much does it influence xG and can we find players that score from tighter angles more than others?
Data
The data has been collected on November 23rd, 2024. The data is from Opta and is raw event data, which I later ran through my expected goals model to get the metrics I need:
- Players
- Teams
- xG
- Angle
- Opposition
I will focus the data on the Eredivisie 2024–2025, because that’s the league I watch the most and are most familiar with.
Methodology
To calculate the angle of a shot in football, we determine the angular range a player has to score into the goal, considering the shooter’s position and the goalposts. This angular range, referred to as the “shot angle,” is calculated geometrically using trigonometric principles.
The shot angle (θ) is defined as:
where:
- goal_width is the horizontal width of the goal (typically 7.32 meters in standard football pitches),
- distance_to_goalis the Euclidean distance between the shooter and the centre of the goal.
If the shooter is positioned off-centre, the angle is calculated between the shooter’s position and the goalposts:
With this calculation, we can see what the angle is for every shot taken in our database after I’ve run it through my expected goals model. We then have all the information we need to make a visualisation of the shot and the angles.
In the image above you can see the angle of the shots highlighted. The angle of the shots is obviously a number, but what does that look like in the visualisation of a shot map?
On the pitch above you can see an example of a shot with an angle of 22 degrees. It shows the distance and the shot location, which ultimately also leads (along with other variables) to an xG of 0,05.
In the pitch above you see a different example. The shot is closer to the goal and that also means the angle will be wider, ultimately giving a bigger chance of hitting the target and scoring a goal. This also means that the xG is significantly higher with 0,41.
Location and how wide an angle is, matters.
Analysis: players and good angle positioning
With this information, we can go further into the analysis. In this analysis we will use the width of the angle and measure that against the expected goals per player. To do that we will look at the average xG per shot and the average angle per shot.
If we look at the scatterplot above, we can see the top players in both metrics. This means that they have the highest xG per shot compared to their peers and have the highest width of shots when we look at the angles.
The idea is that players with higher width in terms of angle will be closer to goal and more centrally, thus improving the chances of scoring a goal. This means that the majority of their shots will be closer to gthe oal. Let’s test that with Brian Brobbey’s shot map in the Eredivisie so far.
As you can in Brobbey’s shot map (up to date until November, 23rd 2024) Most of his shots come from the centre. Within the six-yard box or within the penalty area. Brobbey is more likely to generate a higher amount of xG due to this angle being wide due to his shot location.
Final thoughts
The correlation between xG and shooting angles is quite evident. A higher/wider angle often means a higher xG, which means there’s a higher chance of scoring.
While shooting angle isn’t the sole determinant of xG, it is a critical factor. Combining angle, distance, and situational context provides a complete understanding of a player’s goal-scoring efficiency.
