# Influence of the Slope and Gate Offset on Movement Variability and Performance in Slalom Skiing
## 3 Results  
The effect of different slopes and gate offsets on MV was investigated using SampEn, as shown in Figure 3. SampEn was higher on the steeper slope (21\({}^{\circ}\): ST and SS courses) than on the flatter slope (12\({}^{\circ}\): FT and FS courses). Concretely, differences at the 5% level were found between ST and FS courses (ST: 0.094 \(\pm\) 0.015 a.u. vs. FS: 0.074 \(\pm\) 0.008 a.u.). Differences at the 10% level were found between ST and FT (ST: 0.094 \(\pm\) 0.015 a.u. vs. FT: 0.082 \(\pm\) 0.007 a.u.) and between SS and FS courses (SS: 0.088 \(\pm\) 0.008 a.u. vs. FS: 0.074 \(\pm\) 0.008 a.u.) (Table 1). Additionally, a trend was observed in which turned courses had greater SampEn values than straight courses, consistent across all comparisons, i.e., ST had higher entropy values than SS and FT had higher entropy values than FS. Figure 3 also shows the deviation of each skier from the mean SampEn in each SL course. On the FT course, skiers 1, 4, and 5 exceeded the mean entropy (0.082) by 1.83%, 1.62%, and 1.97%, respectively. The mean SampEn on the FS course was 0.074, and all skiers had a lower entropy on this run except skier 4, who had exceeded this value by 6.55%. The ST course had the highest mean SampEn (0.094), and skiers 2 and 5 had even higher entropies on this course, exceeding the mean by 8.29% and 7.85%, respectively. The mean SampEn on the SS course was 0.088, and skier 5 exceeded the mean on this SL by 4.72%. Differences in descent times between SLs were also plotted (Figure 4). Turned courses (gate offset of 4 m: FT and ST) had the longest descent times (7.712 \(\pm\) 0.245 s and 7.857 \(\pm\) 0.146 s, respectively). The FS course had been the one with the shortest descent time (6.934 \(\pm\) 0.168 s), followed by the SS course (7.335 \(\pm\) 0.145 s). There were differences at the 5% level between all the SL courses, except for FT vs. ST courses (Table 1). Figure 4 also illustrates the deviation of each skier's descent time from the mean for each SL course. Skiers 4 and 5 consistently exceeded the mean descent time on all course settings. On theFT course, skiers 4 and 5 were 4.39% and 1.58% slower than the mean group, respectively. Similarly, on the FS course, skier 4 exceeded the mean descent time by 3.13%, and skier 5 by 0.32%. This trend repeated on the ST course, where skier 4 exceeded the mean time by 2.30% and skier 5 by 1.64%. Finally, on the SS course, skier 4 surpassed the mean descent time by 1.78%, and skier 5 by 1.52%. Additionally, in Table 2, a two-way ANOVA was employed to evaluate the significance of two key explanatory variables: the steepness of the slope and the gate offset. Both had a significant impact on MV and performance of the skiers with large (\(\eta^{2}\)P \(>\) 0.14) effects. There was no interaction between the explanatory variables in any of the response variables. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Conditions**} & \multicolumn{2}{c}{**Mean Differences**} & \(p\) & \multicolumn{2}{c}{**95\% CI**} \\ \cline{5-6}  & & FS & 0.008 & 0.339 & \(-\)0.006 & 0.022 \\  & FT & ST & \(-\)0.012 & 0.078 * & \(-\)0.025 & 0.001 \\ \multirow{3}{*}{SampEn (a.u.)} & & SS & \(-\)0.006 & 0.598 & \(-\)0.020 & 0.008 \\  & FS & ST & \(-\)0.020 & 0.004 ** & \(-\)0.034 & \(-\)0.006 \\  & ST & SS & \(-\)0.014 & 0.055 * & \(-\)0.029 & 0.000 \\ \multirow{3}{*}{Time (s)} & & FS & 0.006 & 0.611 & \(-\)0.008 & 0.020 \\ \cline{3-6}  & & FS & 0.778 & 0.0001 ** & 0.419 & 1.136 \\ \multirow{3}{*}{Time (s)} & FT & ST & \(-\)0.146 & 0.605 & \(-\)0.484 & 0.192 \\  & & SS & 0.377 & 0.038 ** & 0.018 & 0.735 \\ \cline{1-1}  & & ST & \(-\)0.923 & \(<\)0.0001 ** & \(-\)1.282 & \(-\)0.565 \\ \cline{1-1}  & FS & SS & \(-\)0.401 & 0.036 ** & \(-\)0.779 & \(-\)0.023 \\ \cline{1-1}  & ST & SS & 0.522 & 0.004 ** & 0.164 & 0.880 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Differences between SL course settings in SampEn and Time. Figure 3: Bar plots illustrating the Sample entropy (SampEn) for individual skiers on each SL.