Figure 5

Comparison between empirical and simulated rank diversities. Plot showing the rank diversity \(d(k)\) of the empirical data (blue shaded area) and of simulated data from our random walk model (yellow shaded area), as well as the fit Φ (red/green lines for empirical/simulated data, respectively). We also include the values of μ, σ, and maximum rank diversity \(d_{max}\) for the simulated data. The random walk model manages to qualitatively reproduce the rank diversity seen in all sports and games considered here, although clear differences reveal that the model is insufficient for a full quantitative agreement.