Identifying Multiple Dimensions of Luck versus Skill: Analyzing Tennis and Gender

Identifying skill from luck is a challenge facing most fields, yet it is critical for informed decision making. We decompose outcomes in tennis (wins, ranking points, prize money) into luck versus skill using a structural, hierarchical model estimated with point-by-point data. We identify three sources of luck: match luck, luck of the path a player faces given the draw, and the luck of the draw itself. We demonstrate how match luck hurts the more skilled players, but path luck helps them. We show that all three types of luck have a significant impact on a player’s match, tournament, and career success. Comparing the men’s and women’s game, because women only play best out of 3 sets (while men play best out of 5) in grand slams, there is more match and path luck in the WTA. Women, on the other hand, show a wider range of skill across players, which leads to more dominant players at the top, but this is mitigating by more luck in the WTA. Our model matches well both realized outcomes and betting odds at both the match and tournament levels. Finally, the model allows us to conduct counter-factual analysis to assess what happens to the distribution of outcomes, and their relation to skill and luck, if rules changed (i.e., men play best out of 3 or women play best out of 5, no-ad scoring, one serve only).