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Nonlinear Dynamics

Gini coefficients, Herfindahl-Hirschman indices, Lorenz curves, and rank-size analysis applied to the 2026 F1 championship. Quantifying concentration and comparing competitiveness across 16 seasons.

Concentration Metrics

2026 season after Round 5

Gini Coefficient
0.6413
0 = perfect equality, 1 = total concentration
HHI
0.1190
Herfindahl-Hirschman Index of market share
Most Competitive Season
--
lowest Gini in the dataset
Most Dominated Season
--
highest Gini in the dataset

Lorenz Curve

Cumulative share of points vs cumulative share of drivers — the shaded area between the curve and the equality line is proportional to the Gini coefficient

Historical Gini Comparison

Gini coefficients for all seasons 2010–2026, sorted by inequality. Green = competitive, red = dominated.

HHI Time Series

Herfindahl-Hirschman Index from 2010 to 2026. Below 0.15 = competitive market, above 0.25 = highly concentrated.

Rank-Size Analysis (Zipf)

Log-log plot of rank vs points. Zipf's law predicts a linear relationship — deviations reveal structural patterns in the grid hierarchy.

What These Metrics Measure

Economics and information theory applied to F1 championship points

Gini Coefficient

The Gini coefficient measures inequality in a distribution. Originally designed for income inequality, it works identically for championship points: how unevenly are points distributed across drivers?

A Gini of 0 means every driver has identical points. A Gini of 1 means one driver has all the points. Most F1 seasons fall between 0.45 and 0.75.

G = ΣΣ |xi xj| / (2n2μ)
where xi, xj are individual driver points, n = number of drivers, μ = mean points
Herfindahl-Hirschman Index

The HHI is a market concentration measure used by antitrust regulators. Applied to F1, it treats each driver's points share as a "market share." Would the championship pass an antitrust review?

HHI below 0.15 indicates a competitive field. Between 0.15 and 0.25 is moderately concentrated. Above 0.25 signals dominance — a regulatory red flag in economics.

HHI = Σ si2
where si = driver i's points / total points (market share)
Lorenz Curve

The Lorenz curve plots the cumulative share of points (y-axis) against the cumulative share of drivers sorted from lowest to highest (x-axis). The diagonal line represents perfect equality.

The Gini coefficient equals twice the area between the Lorenz curve and the equality line. A curve hugging the diagonal means a competitive season; a curve bowing deeply means domination.

Zipf's Law / Rank-Size

Zipf's law states that in many natural distributions, the value of the r-th ranked item is proportional to 1/r. On a log-log plot, this produces a straight line with slope −1.

In F1, deviations from Zipf reveal structure: a concave deviation (top-heavy) means the leaders hoard disproportionate points. A convex deviation means the midfield is more compressed than expected.

Key Finding

What the data says about 2026

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