## 2 Materials and Methods
### Data Extraction and Meta-Analysis  
Data extraction was performed independently by [PERSON] using a standardized Excel template and was reviewed by [PERSON] Key information extracted from the studies included participant characteristics (age, sex, competitive level), task design (consistency of measuring instruments), gaze behavior, shooting performance, and outcome metrics. Competition levels were classified as \"elite\" or \"near-elite\", following the framework of [PERSON] (2021) et al. [24] (Table 2). \begin{table}
\begin{tabular}{c c c} \hline
**Classification** & **Basketball League Level** & **Training Frequency** \\ \hline \multirow{4}{*}{Elite} & Competing at the highest level globally in the most exclusive leagues. & 6–7 days per week (often multiple sessions per day) \\ \cline{2-3}  & Competing at the international level, including professional leagues worldwide, reserve players in NBA/WNBA, NCAA Division I players, and national team representatives. & 5–7 days per week (structured periodized training) \\ \hline \multirow{4}{*}{Near-elite} & Competing at the national level, including NCAA Division II and III, US high school varsity teams, and competitive community-based clubs. Participating in recreational basketball leagues, junior varsity teams, and non-professional competitions. & 4–6 days per week \\ \hline \multirow{2}{*}{Amateur} & No strict performance standard, but regular training and intent to compete required. & \(\sim\)3 times per week \\ \hline \multirow{4}{*}{Beginner} & Playing basketball for fun or fitness without structured competition goals. & 1–3 times per week (non-structured) \\ \cline{2-3}  & Individuals who do not engage in regular basketball activity and do not meet minimum physical activity guidelines. & No regular training \\ \hline \end{tabular}
\end{table} 
Table 1: Basketball player classification framework [24]. \begin{table}
\begin{tabular}{c c c} \hline
**Gaze Behavior** & **Definition** & **Stage of Action** \\ \hline \multirow{2}{*}{QE Duration} & The time from the onset of gaze stability to the end of the first observable movement in the shooting motion. & Preparation and early execution phase \\ \cline{2-3}  & The duration of gaze fixation on the target immediately before the shooting motion begins, emphasizing final visual input and adjustments. & Final pre-shot phase \\ \hline \multirow{4}{*}{FD} & The total time spent fixating on relevant cues throughout the shooting process, reflecting overall visual engagement and attention allocation. & Entire shooting process \\ \hline \end{tabular}
\end{table} 
Table 2: Comparison and definitions of gaze behavior metrics in basketball shooting. Meta-analysis was conducted using R 4.4.2, incorporating the'metafor' and 'dmetar' packages. Data were imported from Excel, and standardized mean differences (SMDs) were calculated [25; 33]. Additionally, a meta-regression analysis was performed to examine the effect of quiet eye (QE) duration on shooting accuracy across different competition levels. The regression model included an intercept and slope estimate to predict variations in performance. Statistical significance was set at \(p<0.05\), and effect sizes were interpreted accordingly. To ensure robust and accurate analyses, data reported with standard errors, no statistical significance, inconsistent units, or without \(p\)-values were excluded from the meta-analyses. The data extraction process revealed that gaze behavior metrics (QE duration, FFD, FD) and shooting accuracy were sufficient for conducting meta-analyses. Accordingly, a meta-analysis was conducted where three or more studies reported common associations to ensure the results were sufficiently varied and comparable [34]. Standardized mean differences (SMD) and 95% confidence intervals (CI) were calculated using the mean and standard deviation (SD) reported for variables [34; 35]. Heterogeneity across studies within analyses was assessed using the I\({}^{2}\) statistic and Q test [36].