Events

Outcomes are a function of luck and skill. Differentiating between them is challenging, however, despite their distinction being important for performance evaluation, compensation, incentives, and resource allocation. In sports, this distinction matters critically and has implications for entertainment, rule changes, and who wins and why. We investigate, identify, and measure the role of skill versus luck in tennis using a parsimonious hierarchical structural model that can answer a rich set of questions. Because skill accumulates with scale while luck partially cancels out, three set matches are more prone to luck than five set matches – begging the question: are Serena Williams’ 23 grand slams more impressive than Novak Djokovic’s 24? There are also second and third order effects – such as having to face tougher opponents later in five-set tournaments and seeding, which are also functions of luck, that differs for men and women. We attempt to answer questions like these and conduct counterfactual analysis, such as how many slams would Serena have won if best out of five? How many would Venus Williams have won if Serena wasn’t present? Which men’s and women’s players “exceeded” (lucky) or “underperformed” (unlucky) their skill level? Given the precision of the model, we also identify multiple dimensions of skill (serving, returning, surface, stamina) and multiple sources of luck (point, match draw, ranking/seeding). The model matches data and betting odds, and can be used to infer distributions in winning, earnings, rankings, and career dynamics. Our framework can potentially explore other aspects of performance such as momentum, clutch, and choking, as well as the expected impact of rule changes in tennis and how each of these might differ across the men’s and women’s game.