## 2 Materials and Methods
### Data Analysis  
Each heatmap could be interpreted as a two-dimensional probability function, which mapped an (x, y) pair to the likelihood that a player with this expression was positioned here during a match.  
We compared these 2D distributions using a variant of the Kolmogorov-Smirnov test adapted to higher dimensions, as previously used in astronomy and climate research [36; 37]. Additionally, we projected the probability map to just x or y portions, respectively, and performed a conventional KS analysis (cf. Figure 4).  
Figure 3: Heatmap comparison for the player types differentiated for right- vs. left-handed players, offensive vs. defensive players and shakehand vs. penholder grip players. For example, a purple color (purple = 60%) indicates that the player had been in the area (purple or lighter) 60% of the time. The lighter the color (light yellow), the more often the players had been in that area.  
Using the interpretation of each heatmap as a probability distribution, we could determine confidence intervals for the locations, i.e., the portion of the area around the table that the players spent 95% of the overall playtime in. The confidence interval was set to 95%. The displayed values were averages of overall position data.  
A heatmap was created for each player expression (cf. Figure 3). The heatmap represented the density function of the different positions in the table tennis match. In each heatmap, the table tennis half was marked with a green line. The coordinate system could also be seen here. The zero point (0, 0) was exactly in the middle of the table, so a value of y = 0 m meant at the height of the net. Because the total length of a table tennis table is 2.74m, and thus the baseline of the table has a value of y = \(-\)1.37m on the y-coordinate, a value of y = \(-\)1.90m meant that a player positioned himself 53 cm from the baseline. The  
Figure 4: The probability rate of player positions on the x and y coordinates differentiated by right-handed vs. left-handed, offensive vs. defensive and shakehand vs. penholder grip players. Kolmogorov–Smirnov test analysis for the projected x and y distributions.  
center line of the table represented the zero point on the x coordinate. If an x value was positive, it meant that the player was positioned to the right of the center line, and if the x value was negative, it meant that the player was positioned to the left of the center line. The colors used in the heatmap represented the frequency of a position and were labeled by percentiles. For example, a color in the middle of the spectrum, purple = 60%, meant that the players spent 60% of the overall time at a location that was purple or brighter. The lighter the color (light yellow), the more often that players were in that area.  
To determine the significant differences, the two-dimensional Kolmogorov-Smirnov test was calculated and implemented in Python programming language syntactically equivalent to the nature paper by [PERSON] et al. (2021) [PERSON] et al. (2021). Significant differences in 2D distributions were found for the right/left pair (D = 0.5712, \(p\) = 0.005). The analyses for the projected x and y distributions of the player types are shown in Figure 4. Comparisons were shown between the expressions of the three attributes (right/left, offensive/defensive, shakehand/penholder). Whereas the heatmaps in Figure 3 display the probability as the color at a certain 2D location, these plots showed the x (left) and y (right) coordinates on the abscissa and the probability that a player was at this point on the ordinate.  
The 1-dimensional KS test yielded significant differences for the x coordinate of the right/left (D = 0.5663, \(p\) < 0.001).