# Influence of the Slope and Gate Offset on Movement Variability and Performance in Slalom Skiing
## 1 Introduction  
Alpine ski racing is a technical sport, which requires great coordinative ability from the skiers [1]. One of the main challenges of alpine skiing is the unpredictability of the descents. This is due to the high degree of uncertainty that arises when interacting with the environment at high speed [2]. When competing, the skier must be prepared to deal with variations in the terrain such as the steepness of the slope [3, 4, 5], and with variations in the course setting, such as the horizontal gate offset, that will regulate the amount that a course will be turned [6, 7]. Therefore, in order to adjust to all types of terrain changes and course configurations, the central and peripheral nervous system of alpine skiers must workquickly and efficiently at every moment of the race [2, 8]. Adaptability to the unpredictable and changing environments is clearly a key aspect that elite skiers possess. In recent years, several studies have analyzed the coordinative aspects of different motor actions via the assessment of human movement variability (MV) [9, 10, 11, 12, 13]. MV is inherent within all biological systems and can be defined as the natural variations that typically occur during the execution of motor tasks when repeated multiple times [14, 15, 16, 17, 18], also known as execution variability [19] that assesses movement reproducibility [17]. In that context, research suggests that MV might be reduced as a function of practice [20, 21] and experience [22, 23]. The degree of mastery or adaptation to a task decreases the system's degrees of freedom and makes it highly predictable. Thus, experienced athletes are able to reproduce more consistently the same technical gesture, even in changing circumstances [10, 17, 24, 25]. However, when athletes face new or complex situations, a technical gesture becomes less reproducible. The central nervous system of athletes is forced to find an optimized motor solution and must explore the full range of movement possibilities, which causes an increase in the degrees of freedom and thus in MV [26]. This increase in MV is what enables motor adaptation to a changing environment. Thus, MV should be considered a tool to stimulate learning [27, 28, 29]. In this regard, to ensure that exercise continues to provide an optimal stimulus for athlete development, it would be desirable to introduce different variations to the tasks that induce an increase in MV [10]. These variations become important in sports, especially in situation sports, such as alpine skiing, characterized by unpredictable and changing environments [30]. These athletes must continuously perceive and interpret external and internal information to adjust their actions and obtain effective and efficient solutions [31]. In addition, the application of different stimulus on-snow training such as a different steepness of the slope and variations in course settings, such as a different gate offset between gates, could produce a destabilizing effect on the body that would cause an increase in MV. MV could be measured through the use of linear measurements such as standard deviation in the time evolution of a variable [32]. The standard deviation is useful to characterize the amount of variability present in the perceptual-motor system, as it quantifies the mean amount of dispersion around an averaged value. However, in some cases, different time series can exhibit the same standard deviation even if they do not share the same structure in time [33, 34]. This limitation can be addressed with the use of non-linear tools, such as entropy, since it quantifies the amount of regularity and unpredictability of point-to-point fluctuations in large sets of time-series data and it is suitable for dealing with the complexity of biological systems [34, 35, 36, 37]. Sample entropy (SampEn), Multiscale entropy (MSE), and Approximate entropy (ApEn) are the most popular methods for assessing data regularity in health and sports sciences [9, 35, 38, 39].