Figure 1

Comparison of ranking data with several models. Plot showing the rank distributions (score versus rank k) for all sports considered in this study, at one time slice, as well as their fits with the four models in Eqs. (1)-(2). In general, Zipf’s law (\(m_{1}\)) does not accurately reproduce the ranking of any sport or game reported here. Both the Gamma (\(m_{2}\)) and Beta (\(m_{3}\)) distributions seem to be appropriate in some cases. Overall, most datasets are well fitted by a combination of both functions, model \(m_{4}\). Although these plots correspond to one time slice only, results are representative of the entire datasets (see Table 3 for further details). For the sake of clarity, \(m_{5}\) and tick labels are not shown.