Figure 1

Comparison between the probability of return by recency and frequency ranks. The distributions of both ranks can be better approximated by truncated power laws (dashed lines). (a) The recency-based rank of D1 has exponents \(\alpha_{K_{s}} \approx 1.644\) and exponential cut-off \(\kappa_{K_{s}}\approx40.94\), whereas the frequency-based rank distribution has a better fit for \(\alpha_{K_{f}}\approx1.56\) with \(\kappa_{K_{f}} \approx23.6\). (b) The best fit for the return ranks distribution in D2 is achieved with parameters \(\alpha_{K_{s}} \approx1.699\) and \(\kappa_{K_{s}} \approx206.6\) for the recency rank whereas the frequency rank has parameters \(\alpha_{K_{f}}\approx1.521\) and \(\kappa_{K_{f}} \approx64.3\).