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.
