We have all experienced it. The wild winning streak at a casino. The uncanny ability to catch every green light on the way to work. Conversely, the tragedy of being struck by lightning twice. We call these events "luck." For centuries, luck has been treated as a metaphysical force—a mystical wind that blows favorably on the virtuous or the foolish.

But what if luck isn't a force? What if it is just a statistical shadow? Enter the concept of the "Index of Luck by Chance." This is not a spell from a fantasy novel; it is a rigorous statistical tool used by mathematicians, psychologists, and data scientists to distinguish between genuine skill-based success and the random noise of probability.

In this article, we will deconstruct the Index of Luck by Chance, explore how it is calculated, and reveal why understanding this metric can change how you view risk, success, and failure in a chaotic world.

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?

In hockey, the advanced statistic known as PDO (shooting percentage plus save percentage) is effectively an index of luck by chance. The league average PDO is always 1000. If a team sports a PDO of 1040 over 20 games, the index suggests they are getting very lucky—their shooting percentage is unsustainably high. Smart bettors use this to "fade" (bet against) high-luck teams, expecting regression to the mean.