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.

Background: Both in 5v5 and 3x3 basketball, the goal of the players is to score more points than the opponent. However, the differences in rules between two basketball disciplines can affect thinking, behaviour, and decisions of the players. A core difference between two disciplines is the value of the shots. In 5v5, long-range shots are worth three points and close-range two, while in 3x3, their values are two and one points, respectively. As the value ratio of the close and long-range shots is greater in 3x3, we assume that players make different decisions about their shot selection in 3x3 than in 5v5, which can affect offensive efficiency. Methods: We analysed game statistics of the 2019 men’s 5v5 and 3x3 Basketball World Cups. Besides regular statistical indicators, we applied relative offensive rating to be able to compare the two disciplines. Results: The analysis of relative offensive rating showed that offences are more effective in 5v5 than in 3x3. We also found significant difference in shot selection and efficiency. In 3x3, there is a higher proportion of the shots than in 5v5, but long-range shots are more successful in 5v5. Conclusions: For rule differences that affect player’s shot selection and affect offensive efficiency, their decisions are characterized by ecological dynamics and naturalistic decision-making.

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