# Biomechanics of Punching--The Impact of Effective Mass and Force Transfer on Strike Performance
## 3 Results  
The analysis revealed substantial differences across the variables measured for the four punch types: jab, cross, and lead hook (Figure 4). Fist acceleration was greatest in the rear hook (212.61 \(\pm\) 98.43 m/s\({}^{2}\)), followed by the lead hook (154.93 \(\pm\) 110.42 m/s\({}^{2}\)). The cross (75.53 \(\pm\) 24.87 m/s\({}^{2}\)) and jab (54.04 \(\pm\) 24.87 m/s\({}^{2}\)) demonstrated significantly lower values. A Mann-Whitney U test confirmed a moderate but statistically significant difference in acceleration between jab and cross punches (U = 4727.0, \(p\) < 0.001, G = \(-\)0.37). In contrast, no significant difference in fist acceleration was observed between lead and rear hooks (U = 7756.0, \(p\) = 0.299, G = \(-\)0.075). The cross and jab punches demonstrated comparatively higher values for effective mass and Effective Mass Index. The Kruskal-Wallis test showed a significant difference between punch types for pressure force (KW-H = 192.75, \(p\) < 0.001, \(\eta^{2}\) = 0.383) and fist acceleration (KW-H = 290.69, \(p\) < 0.001, \(\eta^{2}\) = 0.578). Additionally, significant differences were found for effective mass (KW-H = 235.24, \(p\) < 0.001, \(\eta^{2}\) = 0.468) and Effective Mass Index (KW-H = 235.79, \(p\) < 0.001, \(\eta^{2}\) = 0.469), indicating that straight punches (jab and cross) allow for a more effective transfer of body mass compared to hooks. The analysis of the variables effective mass and Effective Mass Index (percentage of effective mass) for different types of punches revealed significant differences in the efficiency of mass transfer during impact. The highest effective mass values were recorded for the cross punch (31.17 \(\pm\) 16.20 kg). Similarly, the jab showed a high effective mass  
Figure 4: Graphical representation of key biomechanical variables across different punching techniques. (**A**) Pressure force distribution for jab, cross, lead hook, and rear hook. (**B**) Fist acceleration comparison among punch types. (**C**) Effective Mass Index (%) across different punches. (**D**) Impulse (Ns) comparison for each punch type. Statistical results of Kruskal–Wallis tests are included, indicating significant differences among the punch types. value (30.39 \(\pm\) 15.09 kg). In contrast, hook punches, such as the lead hook and rear hook, exhibited significantly lower effective mass values (14.38 \(\pm\) 12.05 kg and 12.56 \(\pm\) 5.52 kg, respectively). Similar trends were observed in the analysis of Effective Mass Index, which represents the proportion of effective body mass in a punch. The highest Effective Mass Index value was recorded for the cross (36.77 \(\pm\) 18.83%), followed closely by the jab (35.49 \(\pm\) 16.48%). In the case of the lead hook and rear hook, Effective Mass Index values were significantly lower (17.10 \(\pm\) 13.94% and 14.88 \(\pm\) 6.74%, respectively). The examination of impulse values for different types of punches demonstrated notable disparities in the total impulse generated during impact. The jab exhibited the highest impulse value, averaging 63.80 \(\pm\) 15.36 kg/s. The cross followed closely, with an impulse of 57.90 \(\pm\) 11.82 Ns. Conversely, hook punches, including the lead hook (42.39 \(\pm\) 7.38 Ns) and rear hook (43.87 \(\pm\) 7.62 Ns), displayed significantly lower impulse values. A similar pattern emerged in the analysis of impulse/fist acceleration, which normalizes total impulse relative to fist acceleration. The jab once again led with the highest value (1.44 \(\pm\) 0.72 kg/s). The cross followed, with a moderately lower impulse/fist acceleration of 0.97 \(\pm\) 0.55 kg/s. In contrast, hook punches demonstrated significantly reduced efficiency in this regard, with the lead hook (0.30 \(\pm\) 0.25 kg/s) and rear hook (0.26 \(\pm\) 0.13 kg/s) recording the lowest values. The Kruskal-Wallis test revealed a significant difference between jab and cross for impulse (KW-H = 214.06, \(p\) < 0.001, \(\eta^{2}\) = 0.426).