## 3 Results  
Figure 1 shows the typical eye movements evoked by a repeated motion of a visual target in a basketball player across the five target speeds. In good agreement with our previous findings [12], the participants could visually track the target even at 100 deg/s. Although the amplitudes of eye movements decreased with increasing target speed, they maintained the same repetitive motion pattern as the visual target, with only a minor bilateral deviation due to convergence eye movements. To compare the eye movements of basketball players and non-athlete students, we calculated the rho max between the eye movements and target trajectories for both groups [12] (Figure 2). At the highest visual target speed (100 deg/s), the horizontal eye movements mainly consisted of saccades (Figure 3). The visual target traversed from 20\({}^{\circ}\) to the left to 20\({}^{\circ}\) to the right; thus, the total amplitude would be 40\({}^{\circ}\) if exact saccades occurred. Figure 4 displays the total amplitude for each cycle of the basketball group and non-athlete group, with a mean total amplitude of 37.96 \(\pm\) 0.82 and 27.74 \(\pm\) 2.55 deg, respectively, which were significantly different based on [PERSON]'s two-sample \(t\)-test (\(p\) = 0.0047) (Figure 5). There was also a significant difference in the variance of the trial-wise variances across the eight subjects (F test, \(p\) = 0.0020). This suggests that compared to the non-athlete subjects, basketball players executed more accurate and consistent eye movements in response to the regularly repeating movements of the visual target. Figure 1: Eye positions were assessed during horizontal eye movements at various target speeds. The trajectory of the visual target is denoted by the black line, while the right and left eye positions are illustrated by the pink and blue lines, respectively. Positive values signify a gaze directed to the right. Figure 2: Comparison of rho max between the basketball player group and the non-athlete group. The red and black lines show the results for the basketball player group and the non-athlete group, respectively. The pale colors indicates individual results, while the dark colors indicates mean values and standard deviations. The time lag and frequency of saccades are presented in Figure 6, while Figure 7 depicts the integrated results of saccades during rightward and leftward gazes shown in Figure 6. Kurtosis was calculated for the time lag of saccade occurrence. At a target speed of 100 deg/s, the saccades of the basketball player group were concentrated at specific timings, exhibited high kurtosis, and displayed a non-normal distribution (kurtosis = 8.50, \(p\) = 0.0050). In contrast, in the non-athlete group, saccades were not concentrated at specific timings, showed low kurtosis, and were normally distributed (kurtosis = 4.11, \(p\) = 0.2110). Concerning the variance of lag during saccades, the variance in the basketball group was significantly smaller (F test, \(p\) = 0.0499). This result indicates that in the basketball player group, the timing of saccades is more concentrated than in the non-athlete group. Figure 3: An example of eye position and eye velocity during measurement at a target speed of 100 deg/s. (**Upper**) Continuous waveforms of horizontal eye movements over 20 s are overlaid on a single back-and-forth cycle of the target motion. (**Lower**) Eye velocity corresponding to the upper panel. The black line represents the (upper) position or (lower) velocity of the visual target, while the pink and blue lines depict those of the right and left eyes, respectively. Figure 4: All data for the total amplitude of each subject. Since the target moves 20\({}^{\circ}\) to the left and right directions, if the subject makes an appropriate saccade, it will be plotted at 40\({}^{\circ}\). The dotted line indicates the average value for each subject. Figure 5: Comparison of the total amplitude between the basketball player group and the non-athlete group.