Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
Equation 1 (active players, N≈560): MDE = 0.148 SD for the omnibus index at 80% power, alpha = 0.05, two-sided, with
team-level clustering (ICC = 0.15). For individual outcomes: MDE = 0.234 SD.
Equation 2 (full sample including backups, N≈800): MDE = 0.124 SD for the omnibus index. For individual outcomes:
MDE = 0.196 SD.
At 15% attrition: Equation 1 MDE = 0.161 SD (omnibus), Equation 2 MDE = 0.135 SD (omnibus).
Based on Lowe (2021), who found effects of 0.23 SD on a comparable omnibus index, the design is powered to detect
effects of approximately two-thirds of Lowe's estimate.