# The Influence of Effective Mass on the Striking Force of Lead Jab and Rear Cross Punches of Boxers
## 4 Discussion
The mean values in the second, third, and fourth quartiles (Q1, Q2, and Q3) were nearly identical. This suggests that body height does not play a significant role in determining effective mass, especially in the context of the work of other researchers, who demonstrated greater impact power generation capabilities in athletes with longer body segments, and, therefore, also greater body height [13]. Examining a larger group of athletes with diverse body heights but similar body mass would be an interesting extension of the study. An inverse relationship between fist acceleration and effective mass was observed, as detailed in Figure 7. Higher acceleration values corresponded to lower effective mass, as directly indicated by the equation underlying the calculations in this study. For instance, in the fourth quartile of effective mass index, the mean fist acceleration was 63.26 \(\pm\) 19.62 m/s\({}^{2}\), compared to 94.37 \(\pm\) 18.37 m/s\({}^{2}\) in the first quartile. This can be interpreted as reflecting a trade-off between speed and force--while higher acceleration may increase punch speed, it does not necessarily translate to higher effective mass, which was also observed in studies conducted on athletes in the past [4]. Figure 8 demonstrates a positive correlation between training tenure and effective mass. Boxers with longer training experience tend to have higher effective mass values. For example, the mean training tenure in the fourth quartile of effective mass was 10.57 \(\pm\) 6.86 years, compared to 5.11 \(\pm\) 3.62 years in the first quartile. It can be concluded  
that with training experience, the athlete's motor skills and technical abilities also increase. Experienced boxers likely have developed better techniques for maximizing their effective mass, resulting in more powerful punches. Years of training enable boxers to naturally utilize their body mass. This is confirmed by the work of other researchers, where it has been shown that fighters with longer training experience have the ability to generate greater striking force [1,13,14]. In interpreting the results of implementing the proximal-to-distal pattern, the following key was adopted: 1. Ideal pattern (1-1-1)--indicates effective energy transfer through the body segments and indicates proper execution of the punch consistent with the proximal-to-distal pattern; 2. Suboptimal patterns (e.g., 0-1-0, 0-0-1)--indicate issues with energy transfer through the body segments; analysis of punching technique and potential training corrections are necessary. The analysis of different punch patterns, as shown in Figure 10, revealed variability in effective mass. Patterns such as 1-1-0 (mean effective mass 24.17) and 0-0-0 (21.86) exhibited higher effective mass values, indicating more efficient utilization of body mass. In contrast, patterns such as 0-0-1 (13.73) and 1-0-1 (15.82) had lower effective mass values. This suggests that punches adhering to the concept of the proximal-to-distal pattern, as well as those that did not perfectly fit it but also did not represent its inverse, are more effective in utilizing body mass to generate force, potentially due to differences in technique and body mechanics. In such cases, energy was effectively transferred through the body segments, resulting in maximum fist speed. In the discussion with [PERSON]'s seminal works on the proximal-to-distal pattern, which suggest the 1-1-1 pattern as the most desirable, it turns out that patterns such as 1-1-0 can still optimize energy transfer. Specifically, the shoulder rigidity (lower shoulder acceleration) in the 1-1-0 pattern allows for effective energy transmission from the torso to the fist while maintaining high fist acceleration. Incorporating the 1-1-1 pattern into teaching processes emphasizes optimal movement mechanics, while also highlighting patterns like 0-0-0 as effective alternatives in movement training.