# The Influence of Effective Mass on the Striking Force of Lead Jab and Rear Cross Punches of Boxers
## 3 Results  
Table 1 displays the results of the Mann-Whitney U-test, comparing the lead jab and rear cross punches across various performance metrics. The analysis highlights significant differences between the two punches. The rear cross punch consistently outperformed the lead jab in key variables such as total ground reaction force (GRF), fist acceleration, and forearm acceleration, all of which showed highly significant differences (\(p<0.001\)). For example, the effect size for GRF was 0.57, and for fist acceleration, it was 0.61, indicating large practical differences. Moderate differences were also observed in arm acceleration (effect size = 0.22) and target contact time (effect size = 0.26), which were statistically significant (\(p<0.05\)). These findings demonstrate that the rear cross punch achieved greater acceleration and stayed in contact with the target slightly longer than the lead jab. However, strike duration did not show a significant difference between the two punch types (\(p\) = 0.099, effect size = 0.16). Clear differences between the lead jab and rear cross punches were observed in several measured variables, as shown in Table 2. The rear cross generated a significantly higher total ground reaction force (1709.277 \(\pm\) 4866.206 N) compared to the lead jab (1182.552 \(\pm\) 2508.125 N). Similarly, fist acceleration was greater in the rear cross (94.334 \(\pm\) 184.594 m/s\({}^{2}\)) than in the lead jab (66.066 \(\pm\) 195.109 m/s\({}^{2}\)). This pattern also held for the acceleration of the forearm and arm, with the rear cross showing higher values (67.110 \(\pm\) 253.148 m/s\({}^{2}\) and 88.396 \(\pm\) 191.780 m/s\({}^{2}\), respectively) than the lead jab (41.617 \(\pm\) 110.235 m/s\({}^{2}\) and 81.360 \(\pm\) 288.002 m/s\({}^{2}\), respectively). The target contact time was slightly longer for the rear cross (0.030 \(\pm\) 0.0244 s) compared to the lead jab (0.024 \(\pm\) 0.0263 s). The duration of the strike was nearly the same for both punches, with the lead jab averaging 0.176 \(\pm\) 0.0385 s and the rear cross aver \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Punch Type** & **Variable** & **Mean** & **Minimum** & **Maximum** & **Standard Deviation** \\ \hline \multirow{6}{*}{lead jab n = 59} & total\_GRF (N) & 1182.56 & 670.04 & 1748.19 & 250.81 \\  & a\#(m/s\({}^{2}\)) & 66.07 & 36.32 & 114.76 & 19.51 \\  & aforearm (m/s\({}^{2}\)) & 41.62 & 22.46 & 65.32 & 11.02 \\  & a\#arm (m/s\({}^{2}\)) & 81.36 & 28.57 & 206.47 & 28.80 \\  & target contact time (s) & 0.02 & 0.00 & 0.15 & 0.03 \\  & strike duration (s) & 0.18 & 0.07 & 0.20 & 0.04 \\  & velocity of max force (m/s) & 6.77 & 2.44 & 10.15 & 1.82 \\ \hline \multirow{6}{*}{rear cross n = 52} & total\_GRF (N) & 1709.28 & 1082.48 & 2866.76 & 486.62 \\  & a\#(m/s\({}^{2}\)) & 94.33 & 68.26 & 174.19 & 18.46 \\ \cline{1-1}  & aforearm (m/s\({}^{2}\)) & 67.11 & 34.33 & 146.74 & 25.31 \\ \cline{1-1}  & a\#arm (m/s\({}^{2}\)) & 88.40 & 47.69 & 123.48 & 19.18 \\ \cline{1-1}  & target contact time (s) & 0.03 & 0.01 & 0.17 & 0.02 \\ \cline{1-1}  & strike duration (s) & 0.17 & 0.08 & 0.20 & 0.03 \\ \cline{1-1}  & velocity of max force (m/s) & 8.63 & 5.96 & 10.72 & 1.35 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Descriptive statistics of registered variables. aging 0.173 \(\pm\) 0.0287 s. Finally, the velocity at maximum force was higher for the rear cross (8.628 \(\pm\) 13.486 m/s) than for the lead jab (6.766 \(\pm\) 18.177 m/s), indicating a more powerful impact. Fist acceleration was also much higher in the rear cross punch (U = 454.000, Z = \(-\)6.379, \(p\) \(<\) 0.001), showing that the rear cross punch accelerates faster. The same trend was seen with forearm acceleration (U = 525.000, Z = \(-\)5.960, \(p\) \(<\) 0.001) and arm acceleration (U = 1147.000, Z = \(-\)2.284, \(p\) = 0.022), with both being higher in the rear cross punch.