Everyone has experienced luck—a unexpected win, a near miss, or an improbable failure. Yet, when analyzing performance (e.g., in sports, trading, or exams), we often conflate luck with skill. The Index of Luck by Chance seeks to formalize the proportion of an outcome’s deviation from expectation that is due purely to randomness.
The ILC answers the question: Given a set of opportunities or trials, how likely is it that the observed success was simply a result of chance? index of luck by chance
| Field | Luck index high (e.g., 0.8) means | Luck index low (e.g., 0.2) means | |--------|--------------------------------|--------------------------------| | Investing | Returns mostly random; indexing beats stock picking | Skill matters; active management may work | | Medicine | Most positive trial results false positives | Real treatment effects dominate | | Hiring | Who gets promoted is nearly random | Performance reviews reflect ability | Everyone has experienced luck—a unexpected win, a near
The Index of Luck by Chance: Quantifying Randomness in Outcomes and Perceptions of Serendipity | Field | Luck index high (e
Player with career average p=0.7 makes 18/20 (k=18, N=20).
Expected = 14.
( P(K \ge 18) = \sum_i=18^20 \binom20i (0.7)^i (0.3)^20-i \approx 0.035 ).
ILC = 0.035 → somewhat lucky, but skill also present.
To accurately compute an index of luck by chance, you must ensure that the underlying process is truly random. Most real-world processes violate this assumption.
Thus, the index must always be paired with a confidence interval. A high luck index in a small sample is meaningless. A moderate luck index in a massive sample is earth-shattering.