**4. Discussion**

The major novel finding here was confirmation of the hypothesis that asymmetries in technique and ground reaction forces are associated with asymmetries in the performance of elite, competitive slalom skiers. More specifically, (i) asymmetries in instantaneous and sectional performance were associated with the largest predictor coe fficients for asymmetry in the angle of the shank and hip flexion on the outside leg; and (ii) asymmetry in turning radius demonstrated the largest predictor coe fficients for asymmetry in the angle of the shank and GRF on the entire foot of the outside leg.

Our descriptive statistics showed that, on average, these elite alpine skiers performed left and right turns quite symmetrically (Tables 1 and 2), with the only statistically significant di fference between these turns being the GRF on the entire foot of the inside leg. In particular, the average mean values for performance were almost identical for the left and right turns (Table 2). Furthermore, the symmetrical indices (SI) were all above 84% (sectional performance), except for instantaneous performance (70%).

This symmetry, which in light of the very small di fferences in performance of elite alpine skiers [9,29,30] was not unexpected, confirmed that our experimental setup was well suited for observing di fferences between left and right turns. Previously, the di fferences in the GRF and temporal parameters associated with left and right slalom turns by highly skilled ski instructors were also reported to be non-significant [23]. Similarly, the mean di fference in strength between the dominant and non-dominant legs of elite Austrian alpine skiers was also small [31].

In the present case, the only SI that was markedly lower concerned instantaneous performance (70.6%). Overall, sectional and instantaneous performance demonstrated the most pronounced asymmetries, which was the initial rationale for employing these as measures of alpine skiing performance [5,7,30]. In giant slalom as well, utilization of energy-based performance over an entire section was found to be a valuable measure of performance [9].

However, the Jaccard indices (JI) revealed much more pronounced asymmetry between left and right turns, with the lowest value being only 28.6% (for flexion of the outside knee) and the highest 71.3% (for the overall GRF) (Table 1). The lowest individual JI value for the angle of the outside shank was only 14% (Skier I, Figure 4) and during the steering phase, a di fference between left and right turns by this skier was clearly visible. This same skier exhibited the lowest JI for instantaneous performance (Figure 6) and the second lowest for turning radius (Figure 5). At the same time for Skier G, the largest JI for the angle of the outside shank (Figure 4) was associated with the largest JI values for both turning radius (Figure 5) and instantaneous performance (Figure 6). The dependence of sectional and instantaneous performance on the SI for the angles of both the inside and outside shank received further support from the multivariable regression analysis (Models #10–13, Table 3). Similarly, the JI for turning radius proved to be dependent on the corresponding value for the angle of the outside shank (Model #4, Table 3), an observation which in itself clearly demonstrates that asymmetry in technique is associated with asymmetry in performance. Such a relationship is not entirely unexpected, since according to the theory of carving skiing, the inclination of the ski is related to turning radius [32] and, moreover, in the case of slalom skiing, turning radius is related to instantaneous performance [5].

The SI for turning radius was not dependent on the SI for the angle of the outside shank. This independence demonstrates that the mean turn values taken into consideration when calculating SI did not take the profound turn cycle information into account as was the case with JI values in Model #4 (Table 3). The SI for turning radius was negatively correlated with the JI for flexion of the outside hip (predictor coe fficient −0.10, Model #5, Table 3). This negative association means that less pronounced asymmetry in flexion of the outside hip should correspond to more asymmetry in the turning radius, an observation that we were unable to explain at present.

The predictor coe fficients for JI and SI for the GRF acting on the entire foot of the outside leg were also relatively large in connection with the JI and SI for the turning radius (Models #4 and 5, Table 3). This finding can be explained by the action of radial forces, whose basic biomechanical modeling has shown to be dependent on the turning radius [32,33]. In this context, it is important to emphasize that only the GRF acting on the outside leg, not the overall GRF, was a predictor in the multivariable

models. Indeed, in a previous study [5], this overall GRF did not di ffer between better and poorer slalom skiers. However, in the present investigation, the SI for average velocity was dependent on the corresponding value for the overall GRF in combination with several other "less important" variables with small predictor coe fficients (Models #6–9, Table 3). This particularly interesting finding reveals that despite the virtually identical average velocity and overall GRF associated with left and right turns by our elite skiers, the asymmetries in these variables were actually large enough to demonstrate related dependency in the multivariable models (Tables 1 and 2).

The largest predictor coe fficients observed in our multivariable models concerned the dependence of the SI for instantaneous performance on the combination of the SI values for the angle of the inside shank and flexion of the outside hip (Model #12, Table 3). The only apparent explanation for this dependency is the speculation that skiing technique influenced how smoothly the skis glide, (e.g., the attack angle defined as the angle between the longitudinal axis of the ski and the ski's center point's velocity vector projected onto a plane parallel to the surface of the snow) [14]) and/or the distribution of pressure under the ski and thereby the ski–snow interaction [34]. Either or both of these influences could exert an impact on energy dissipation.

Finally, some of the symmetry indices (SI) observed here, such as those for turning time, turn length and sectional performance, were dependent on various parameters related to the asymmetry of the inside leg (Models #1–3 and 13). This indicates that asymmetries in performance were also associated with the behavior of the inside leg, which has earlier been suggested to only play a role in maintaining stability while skiing [35]. Ski coaches already pay special attention to the inside leg in connection with training to optimize performance, but our findings provide the first experimental evidence that this is a valid concern.

Although the current investigation was extensive, assessing the full-body three-dimensional kinematics and GRF in connection with 720 slalom turns, like all studies, has certain limitations. Although some researchers question the reliability of inertial measurement systems and GNSS and/or pressure insoles, their reliability for in-field measurements on alpine skiers has already been demonstrated [23–25,35–39] and, moreover, we utilized state-of-the-art technology in this respect, i.e., one of the most up-to-date and accurate Leica Geosystems RTK GNSS systems and the latest version of the Xsens inertial motion capture hardware. However, since it was not possible to install an inertial sensor on a foot in a ski boot, we were unable to monitor flexion of the ankle joint. It would have been possible to measure bending of the ski boot, but this does not entirely reflect the more complicated three-dimensional behavior of the ankle joint (i.e., technique).

In addition, although GRF can certainly be measured most accurately with dynamometers/ force-plates [40], the size and weight of these devices disturb the skiing equipment and, thereby, the performance of the skier. To avoid this, we used pressure insoles here, which do not always indicate the magnitude of GRF accurately [41]. On the other hand, direct measurement of the pressure on the soles, an important parameter when skiing [23,35], is especially useful for dealing with asymmetries in pressure on di fferent parts of the foot. To assess a more precise magnitude of the GRF, we performed biomechanical modeling of this parameter based on the acceleration of the center of mass monitored by three-dimensional kinematics, as in our previous studies [11,42].

As is true of virtually all studies on alpine skiing, generalization of our present results, despite the relatively large size of our study population, is not straightforward. The snow, terrain and weather were nearly ideal during our testing and similar studies under varying conditions are now required.
