## 4 Discussion  
The databases for the 38- and 40-mm balls showed only variations within statistical fluctuations for the multi-dimensional distribution of successful shots, whereas the 44-mm ball results were already significantly different compared to the 40-mm ball, as discussed also in Reference [8]. The analysis confirmed the empirical observation that the change of the ball in the year 2000 from a 38-mm to a 40-mm-ball could be compensated for such that their resulting trajectory distribution functions were nearly identical. This was achieved in reality by adaptations of technique and the material. One needed larger spins to influence the trajectories of the 44-mm ball with smaller weight compared with the 40-mm ball. For higher initial velocity, a larger number of successful shots was possible with the 44-mm ball, because the effect of drag forces increased with larger size. Very high velocities above 35 m/s were suppressed earlier for the 44-mm ball. A larger ball of 44 mm with small weight is one option for suppressing high velocities; however, the players could compensate for this by improving their physical fitness to perform stronger shots.  
Most of the results of the previous empirical analysis are supported. A clear influence was visible for the 40-mm ball upon increasing the net height. For smaller initial and end velocities of about 10 m/s, a reduction in the number of successful trajectories showed up, being equivalent to a slowing-down of the game. For very low velocities, the impact of the air drag was not yet important, resulting in a larger number of successful trajectories. As a new result, the importance of stronger sidespin for the cases of higher nets was identified, which would change the characteristics of long rallies in table tennis. For these cases, not only are reduced velocities important, but the tactical possibilities will be modified by reducing the number of spinless short trajectories. The strong reduction in the number of successful strokes was linked with rather small top spin components \(\omega_{y}\), but rather larger sidespin components \(\omega_{z}\). This means that the game will not only slow down, but also diagonal play with longer reaction times for the opponent will get more important than fast parallel balls. One can also  
Figure 15: Cluster center coordinates of side spin component \(\omega_{z}\) versus topspin component \(\omega_{y}\) of the normalized spin vector for the four clusters for the different cases.  
expect from this longer and more attractive rallies. However, the characteristics of the game will change strongly, because the possibilities for successful trajectories are limiting technical and tactical alternatives, reducing especially the influence of service.  
Modifications of basic rules of table tennis, such as ball size and net height, can reduce the maximum velocities; however, such modifications will be linked to severe changes in the characteristics of table tennis: dynamics, technique, and strategy will change strongly. The question is if a possible gain in attractiveness of table tennis for TV upon implementing such changes is worth the loss of key elements of existing table tennis.