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.
Though luck is often treated as an abstract, unmeasurable force, recent interdisciplinary work in psychology, economics, and data science has attempted to construct indices that separate the role of chance from skill in observed outcomes. This paper introduces a formal , a statistical measure that quantifies the extent to which a positive or negative outcome can be attributed to random variation rather than deliberate action. We derive the index from first principles, discuss its relationship to variance, sample size, and baseline probability, and illustrate its application in games, investments, and everyday life. The paper concludes with limitations and ethical considerations around misinterpreting luck as skill. index of luck by chance
An might be: [ \textLuck Index = \frac\textVariance due to chance\textTotal observed variance ] or [ \textLuck Index = \frac\textNumber of chance-driven successes\textTotal successes ] We have all experienced it
While the Index of Luck provides a fascinating perspective on the role of chance, it has limitations: Conversely, the tragedy of being struck by lightning twice
