Background: The comparison of team sports based on luck has a long tradition and remains unsolved. A contrast between the new Olympic format three-on-three (3 × 3) and five-on-five (5v5) forms of basketball has never been analyzed and provides a comparison within the same form of sports. Methods: We developed a new method to calculate performance indicators for each team and invented the Relative Score Difference Index, a new competitive balance indicator that allows the comparison of luck in the two basketball forms for both men and women. We collected game-level data about 3 × 3 and 5v5 from the World Cups held between 2010 and 2019 (N = 666). Luck was defined as the difference between the expected and the actual outcomes of games. Using the basketball World Cup data, we applied the Surprise Index, ran probit regression models, and compared the basketball forms on the goodness-of-fit of the models. Results: As we predicted, there are differential effects of luck between game formats and sex, such that the 3 × 3 form depends more on luck and women’s games are less influenced by luck when compared to men’s games. Conclusion: Coaches may better understand the differences between the two forms and sexes regarding luck if they are aware that the 3 × 3 and men’s competitions are usually more influenced by luck. The findings provide a leverage point for testing new performances and competition balance indicators and will acknowledge the number of games we enjoy watching.