The Clasico between Actual Madrid and Barcelona is a lot more than a fit, this is a carrying spectacle that still lets you follow mathematical equipment to higher perceive what is occurring at the pitch. On this article, we can discover how the anticipated objectives (kG) metric blended with Venn diagrams provides a brand new standpoint at the maximum watched fit in Spanish soccer.
The previous constitute trendy metrics implemented to soccer, and the latter attach us to the classical ideas of common sense and set principle, which additionally revive our faculty recollections.
The mix of each lets in us to replace the ideas advanced by way of the mathematician John Wen, whose paintings continues to be legitimate greater than a century after his dying.
Doable objectives
What’s kG and what’s Venn diagram?
kG (anticipated objectives) is a complicated statistic utilized in football to measure the “ease” of a shot leading to a function, taking into consideration components reminiscent of place, goalkeeper scenario and defensive power.
Alternatively, Venn diagrams are graphical representations that display relationships between units: intersection, union, and complementarity.
In football, now we have 3 conceivable results that we will be able to constitute in a Venn diagram with two units and their intersection. That is why we’d like 3 other spaces for house win (Barcelona), away win (Actual Madrid) and draw.
To do that, we can use the occasions B (Barcelona effects) and R (Actual Madrid effects), which can be true or false relying on the results of the fit.
To constitute them diagrammatically, we’d like units that constitute them. Occasions B and R will grow to be units with the similar identify. That is the series and its common equivalences:
Herbal language → propositional common sense → set principle:
B o R ⇒ B ∨ R ⇒ B ∪ R
B and R ⇒ B ∧ R ⇒ B ∩ R
No B ⇒ ¬B ⇒ Bc
Utility to classical: units and chances
Let’s take the final vintage performed on Would possibly 11, 2025, which Barcelona gained (4-3). Those are the pictures with the most productive kG values and their authors, those that ended up with the function coloured inexperienced:
Vintage Pictures. Ready by way of the writer.
We can illustrate this consequence later the use of the anticipated objectives prior to kick (kG) metric.
Every workforce’s odds give us a function likelihood price that levels from 0 (leave out all) to overall pictures (hit all). Conceivable effects are all combos between the objectives of 1 workforce and the opposite, plus overall disasters. This provides us a complete of 24 (Barcelona 23 pictures) multiplied by way of 10 (Actual Madrid 9 pictures), 240 conceivable results that make up the pattern house of the experiment. Those 240 parts are incorporated in our Venn diagram of their respective sections, consistent with units:
B (Barcelona, kG 4.27): leads to which Barcelona ratings a function, 185 wins + 10 attracts.
R (Actual Madrid, kG 2.74): leads to which Actual Madrid ratings a function, 45 wins + 10 attracts.
B ∩ R: Intersection of priors representing ties, 10 because of 9 ties with objectives and one with out.
Visualization: Venn diagram
Despite the fact that vintage Venn diagrams don’t constitute chances quantitatively, in our customized visible means, the realm of every circle is adjusted proportionally to the likelihood of the result (win, loss, draw). This permits you to visualize no longer handiest the logical relationships between occasions, but in addition their relative weight within the context of the sport. This new means represents an immediate software of Venn diagrams in sports activities, particularly football, which was once introduced for the primary time on this article. As well as, it poses two further mathematical issues to unravel:
Downside 1: With the realm information (A), we can calculate the radii of every set.
A = πr2r = √(A / π)
Process 2: With details about the cross-sectional space (A∩), we can calculate the space between the facilities (d).
To make certain that the phase has its correct space, we wish to draw the facilities of every circle at a distance d, the price of which is bought by way of fixing this equation by way of numerical strategies.
On this case, we used the Newton-Raphson manner. It is without doubt one of the maximum robust equipment in arithmetic and engineering for fixing nonlinear equations. This numerical set of rules is in accordance with the concept that of derivatives to seek out roots of purposes via an iterative procedure. In the beginning advanced by way of Isaac Newton and Joseph Raphson within the seventeenth century, this system has advanced and been tailored to more than a few trendy programs, from physics to economics.
The diagram is helping visualize that despite the fact that the ranking was once shut (4-3), Barca had extra high quality scoring alternatives, which helps their win from a statistical standpoint.
This illustration provides us the consequences we had been in search of and presentations the deserves of every workforce in an overly visible and intuitive manner.
Ultimate ranking chances with kG
Barcelona win likelihood: 64.83%.
Chance of a draw: 13.34%.
Actual Madrid win likelihood: 21.83%.
Venn diagram Barcelona – Actual Madrid. Ready by way of the writer. Conclusion
Venn diagrams, historically related to college educating of common sense and set principle, discover a new software in sports activities research on this article. Combining them with complicated metrics reminiscent of anticipated objectives (kG) opens up a brand new method to visually constitute no longer handiest the logical relationships between the conceivable results of a fit, but in addition their relative chances that cause them to related.
This means lets in us to move past the general ranking and discover every workforce’s “merit” from a geometrical standpoint as neatly. Within the vintage between FC Barcelona and Actual Madrid, the use of Venn diagrams tailored to the football context finds that even if the ranking was once tight (4–3), Barcelona generated extra high quality probabilities, which interprets into a bigger space of their workforce at the diagram.
In brief, this paper no longer handiest provides a brand new manner of working out football fits, but in addition presentations how mathematical ideas which can be it sounds as if a long way got rid of from sports activities can enrich its research. It’s a call for participation to take a look at soccer with different eyes: the eyes of common sense, likelihood and geometry.
