Extended Data Fig. 7: Robustness check on D2.
From: Quantifying the dynamics of failure across science, startups and security
a–c, Failure streak as we change the threshold of high-value mergers and acquisitions (M&A) to 5% (a), exclude M&As as successes (b) and classify unicorns as successes (c). Blue circles represent real data from successful groups and dashed lines represent fitted Weibull distributions. d–f, Temporal scaling patterns as we change the threshold of high-value M&A to 5% (d), exclude M&As as successes (e) and include unicorns as successes (f). The shaded area shows mean ± s.e.m. of Tn (log scale). g–i, Performance dynamics as we change the threshold of high-value M&A to 5% (g, n = 251, 1,304, 243, 1,284, from left to right), exclude M&As as successes (h, n = 248, 1,335, 237, 1,315, from left to right) and include unicorns as successes (i, n = 257, 1,330, 244, 1,311, from left to right). The successful and unsuccessful groups that experienced a large number of consecutive failures before their last attempt (at least 3) appear indistinguishable for first failures (two-sided Welch’s t-test; P = 0.937, 0.647, 0.620) but quickly diverge for second failures (two-sided Welch’s t-test; P = 9.92 × 10−3, 4.94 × 10−3, 6.33 × 10−3). The successful group also shows a significant improvement in performance (one-sided Welch’s t-test; P = 2.16 × 10−2, 2.37 × 10−2, 2.77 × 10−2), which is absent for the unsuccessful group (one-sided Welch’s t-test; P = 0.224, 0.158, 0.167). Data are mean ± s.e.m. j–l, AUC score for predicting ultimate success as we change threshold of high-value M&A to 5% (j), exclude M&As as successes (k) and include unicorns as successes (l). The centres and error bars of AUC scores denote the mean ± s.e.m calculated from tenfold cross-validation over 50 randomized iterations. *P < 0.1, **P < 0.05, ***P < 0.01, NS, P ≥ 0.1.
