# The Influence of Effective Mass on the Striking Force of Lead Jab and Rear Cross Punches of Boxers
## 4 Discussion  
The following work is an extension of previous research on the differences in punch force and fist acceleration between the lead jab and the rear cross. The primary objective of this study was to elucidate the relationship between effective mass, striking force, and fist acceleration in lead jab and rear cross boxing punches, while also considering other factors. The study revealed key findings that show significant differences in generated force and acceleration between these two types of punches; however, the effective mass of these punches is very similar. Additionally, the study identified several key factors that correlate with effective mass, including body mass and training tenure. These correlations highlight the complex biomechanics involved in executing boxing punches. The interplay of these variables underscores the multifaceted nature of force generation in boxing. Figure 11: Distribution of effective mass index values for different body mass categories. The results revealed that despite significant differences in total GRF and fist acceleration, rear cross punches exhibit very similar effective mass values compared to lead jabs. The mean effective mass for rear cross punches was slightly lower at 18.50 \(\pm\) 5.56 kg (21.04% of body mass) compared to 18.95 \(\pm\) 5.29 kg (21.51% of body mass) for lead jabs. However, the significantly greater fist acceleration mitigated this difference--although the rear cross is faster and stronger than the lead jab, the utilization of body mass is very similar. The slight difference in effective mass index in favor of the rear cross may be due to the fact that rear cross punches are delivered with the dominant hand and involve more body rotation, thereby utilizing slightly more body mass to generate force, as was suggested in studies before [12]. An untypical relationship with a weakening of the trend between total GRF and effective mass was observed, as illustrated in Figure 4. The data showed that higher total GRF values corresponded to increased effective mass across the quartiles. For example, in the fourth quartile, the mean effective mass index was 16.58 \(\pm\) 5.27, compared to 11.95 \(\pm\) 2.10 in the first quartile. This relationship indicates that boxers who generate higher ground reaction forces can better transfer their body mass into their punches, enhancing punch force, which corresponds to other research in this discipline [2]. Interestingly, the average effective mass index in the fourth quartile is slightly lower than in the third quartile. It can be hypothesized that while higher total GRF impacts increased effective mass, there might be a certain level of total GRF where further increases are no longer beneficial for effective mass. To confirm this hypothesis, further studies with a larger and more diverse sample group in terms of body mass would be needed. Figure 5 demonstrated a similar trend, where higher body mass was associated with higher effective mass. Boxers in the highest effective mass index quartile (Q4) had a mean body mass of 104.14 \(\pm\) 22.96, compared to 72.68 \(\pm\) 12.56 in the lowest quartile (Q1). This suggests that heavier boxers have a greater capacity to use their body weight effectively in generating punch force, which could be advantageous in delivering more powerful punches. However, once again, the difference between the average values in Q3 and Q4 is very small. This raises the question of whether there is a certain body mass value beyond which it no longer positively affects the effective mass index in punches. To definitively answer this question, further research on larger groups is needed. The correlation between body height and effective mass, as shown in Figure 6, was less pronounced compared to body mass. While there was a general trend of increasing effective mass with height, the correlation was weaker. For example, the mean body height in the tallest quartile (Q4) was 188.68 \(\pm\) 6.74 cm, compared to 177.57 \(\pm\) 6.56 cm in the shortest quartile (Q1).