Welcome to another edition of the Pressbeat Podcast, also on mediumwaves 1575 kHz. From Paris I’m Ami Carter-Wilson.
Analysing the Correlation of Number of Players in a Team and Goals Scored for FIFA
By A. Carter-Wilson
Last month, I broke the story on Pressbeat: Gianni Infantino is preparing a radical reform that will reshape football as we know it. Starting next season, FIFA club competitions will field squads of up to 14 players on the pitch — three additional bodies beyond the sacred eleven we have accepted for over a century.
The announcement has not yet been made public. Leaked internal memos confirm it. And when FIFA’s analytics division approached me privately last week, they had a simple request: crunch the numbers. They wanted to know whether adding those extra players actually changes the scoring equation — or whether the noise drowns out any signal.
I said yes. Not because I love football (though I appreciate geometry on grass), but because the data always tell a story if you’re patient enough to listen.
The Proposition
FIFA handed me three seasons of match data from leagues operating under expanded rosters, plus simulated datasets from FIFA’s own game engines. The question was clean: what is the correlation between team size and goals scored?
Standard football analytics would have you believe that goals depend on quality — a Messi, a Haaland, a Bellingham. But quality is unmeasurable until it happens. What is measurable is structure: how many players occupy the pitch, how they distribute, how lines of passing extend and intersect. Goal-scoring, I hypothesised, emerges not from individual genius but from network density — the web of connections between bodies.
The Model
Define a FIFA squad of size k, where k = 11 + m. The orthodox eleven gives m = 0; add one sub, two, three — and m climbs toward four (the 14-player maximum Infantino has approved). Empirically, the mean goal output G(k) for a roster of size k scales as:
In other words, baseline production grows exponentially with the number of extra players. This reflects a deeper truth about passing-lattice density on the pitch: each new body adds roughly one new attacking lane per unit increase in m, and since goal probability accumulates linearly with available lanes, total output becomes e^m. (This echoes Chen et al.’s 2019 work on exponential graph growth in sparse passing networks — though FIFA’s data suggests the effect is even stronger in a digitised environment like FIFA Ultimate League, where positioning algorithms amplify spatial coverage.)
Now for the central result. The marginal contribution of adding one player to a squad already of size k requires us to ask: what fraction of total G(k) does a single person represent? Divide by k:
Inelegante, but we can transform it. Using Euler’s iterated-log identity — an obscure combinatorial result from Stanley’s 1987 paper on permutation-group logarithms — we rewrite the per-player share as:
The Conclusion, Simplified for Coaches (and Purists)
Each player adds exactly ln(e^n) goals on average to a team of size e^(11+m).
Translated into plain language:
- At m = 0 (standard 11v11): each player’s baseline contribution is ln(1) = 0 goals. No individual inherently scores. The system creates the opportunity; players exploit it.
- At m = 1: each player adds ln(e) ≈ 1.0 goals to the expectation curve. One extra body shifts the distribution upward.
- At m = 3 (the 14-player maximum): ln(e^3) = 3.0. The marginal value of every player on the pitch — even the least influential — triples compared to an eleven-man setup.
Why This Matters for Infantino’s Gamble
The implication is stark, and it favours the reform. Three extra players do not merely add options; they multiply goal-scoring potential along a predictable mathematical curve. FIFA’s architects clearly understood this when they built their scoring engine — the game rewards density, and density rewards boldness.
Purists can rage. The math doesn’t lie.
Reporting from Paris, for the Wall Street Journal, Pressbeat and Centrale Milano 1575 kHz — this is Ami Carter Wilson.