Extended Data Fig. 5: Robustness check on definition of unsuccessful group.

a–l, Robustness check as we change the threshold of inactivity to 3 years. a–c, Failure streak in science (a), entrepreneurship (b) and security (c). Blue circles represent real data from the successful group and dashed lines represent fitted Weibull distributions. d–f, Temporal scaling patterns in science (d), entrepreneurship (e) and security (f). The shaded area shows mean ± s.e.m. of T_n (log scale). g–i, Performance dynamics in science (g, n = 641, 231, 578, 190, from left to right), entrepreneurship (h, n = 248, 1,332, 237, 1,312 from left to right) and security (i, n = 238, 198, 236, 199, from left to right). The successful and unsuccessful groups that experienced a large number of consecutive failures before the last attempt (at least 5 for D₁, 3 for D₂ and 2 for D₃) appear indistinguishable for first failures (two-sided Welch’s t-test; P = 0.566, 0.671 and 0.349), but quickly diverge for second failures (two-sided Welch’s t-test; P = 2.09 × 10⁻², 4.95 × 10⁻³ and 7.77 × 10⁻²). The successful group also shows significant improvement in performance (one-sided Welch’s t-test; P = 7.03 × 10⁻², 2.37 × 10⁻² and 2.32 × 10⁻²), which is absent for the unsuccessful group (one-sided Welch’s t-test; P = 0.717, 0.176 and 0.786). Data are mean ± s.e.m. j–l, AUC score of predicting ultimate success in science (j), entrepreneurship (k) and security (l). The centres and error bars of AUC scores denote the mean ± s.e.m calculated from tenfold cross-validation over 50 randomized iterations. m–x, As in a–l but using 7 years as the threshold of inactivity. Sample sizes are s: n = 620, 101, 559, 76; t: n = 248, 977, 237, 989; u: n = 216, 152, 214, 153. P values in s–u (from bottom to top) are P = 0.883 (s), 0.671 (t), 0.456 (u); P = 2.25 × 10⁻² (s), 1.38 × 10⁻³ (t), 8.34 × 10⁻² (u); P = 4.59 × 10⁻² (s), 2.37 × 10⁻² (t), 3.33 × 10⁻² (u); P = 0.838 (s), 0.446 (t), 0.775 (u). *P < 0.1, **P < 0.05, ***P < 0.01, NS, not significant (P ≥ 0.1).