## 3 Data Treatment and Analysis
### Subgroup Analysis  
The assumption of data normality and equality of variance was not violated. There were differences in the normalized weighted mean of the BI location on the \(x\)-axis among professional and junior, and serve types of the men tennis players, \(F_{3,123}=17.3\), \(p=0.0001\), \(\mu^{2}=0.3\); Figure 4A, where post hoc testing revealed that BI location of the KS junior men was more leftwards from the origin than FS Junior men and FSprofessional men (\(p<0.001\), \(d=0.9\); \(p<0.001\), \(d=1.23\), respectively), KSprofessional men was more leftwards from the origin than FSprofessional men and FS Junior men (\(p<0.001\), \(d=1.88\); \(p<0.001\), \(d=1.31\), respectively), and FS Junior men was more leftwards from the origin than FSprofessional men (\(p<0.05\), \(d=0.4\)). There were differences in the normalized weighted standard deviation of the BI location on the \(x\)-axis among experience and serve types of the male tennis players, \(F_{3,123}=79.74\), \(p=0.0001\), \(\mu^{2}=0.66\), Figure 4B, where post hoc testing revealed that BI location of the KS junior men was less closely clustered around the mean than FSprofessional men, FS Junior men, and KSprofessional men groups (\(p<0.001\), \(d=3.9\); \(p<0.001\), \(d=3.42\); \(p<0.001\), \(d=3.19\), respectively). There were differences in the normalized weighted mean of the BI location on the \(y\)-axis among professional and junior, and serve types of the men tennis players, \(F_{3,93}=5.503\), \(p=0.002\), \(\mu^{2}=0.15\); Figure 5A, where post hoc testing revealed that BI location of the KS junior men was less forwards from the origin than KSprofessional men, FSprofessional men, and FS junior men (\(p<0.01\), \(d=0.53\); \(p<0.01\), \(d=0.99\) and \(p<0.01\), \(d=1.03\), respectively). There were differences in the normalized weighted standard deviation of the BI location on the \(y\)-axis among professional and junior, and serve types of the men tennis players, \(F_{3,93}=31.153\), \(p=0.001\), \(\mu^{2}=0.5\), Figure 5B, where post hoc testing revealed that BI location of the FS junior men was more clustered closely around the mean than FSprofessional men, KS junior men, and KSprofessional men (\(p<0.01\), \(d=1.22\); \(p<0.001\), \(d=1.28\); and \(p<0.0001\), \(d=8.4\), respectively), FSadult men was more clustered closely around the mean than KSprofessional men  
Figure 4: Differences in the ball impact location on the \(x\)-axis (professional and junior men). Note: FS—flat serve; KS—kick serve; * Significant differences, \(p<0.05\). ; † Significant differences, \(p<0.01\); Vertical bars denote 95% CIs. Note: (**A**) normalized weighted mean of the ball impact, (**B**) normalized weighted standard deviation of the ball impact. (\(p<0.001\), \(d=3.52\)), and \(\text{KS}_{\text{junior men}}\) was more clustered closely around the mean than \(\text{KS}_{\text{professional men}}\) (\(p<0.001\), \(d=1.48\)). There were differences in the normalized weighted mean of the BI location on the \(z\)-axis among experience and serve types of the male tennis players, \(F_{3,123}=63.180\), \(p=0.0001\), \(\mu^{2}=0.61\); Figure 6A, where post hoc testing revealed that BI location of the \(\text{FS}_{\text{less-experienced}}\) was less high from the origin than \(\text{FS}_{\text{professional men}}\), \(\text{KS}_{\text{junior men}}\), and \(\text{KS}_{\text{professional men}}\) (\(p<0.001\), \(d=2.85\); \(p<0.001\), \(d=1.92\); and \(p<0.001\), \(d=2.68\), respectively).