Michael Stöckl

On the use of continuous relative phase: Review of current approaches and outline for a new standard

BACKGROUND In this paper we review applications of continuous relative phase and commonly reported methods for calculating the phase angle. Signals with known properties as well as empirical data were used to compare methods for calculating the phase angle. FINDINGS Our results suggest that the most valid, robust and intuitive results are obtained from the following steps: 1) centering the amplitude of the original signals around zero, 2) creating analytic signals from the original signals using the Hilbert transform, 3) calculating the phase angle using the analytic signal and 4) calculating the continuous relative phase. INTERPRETATIONS The resulting continuous relative phase values are free of frequency artifacts, a problem associated with most normalization techniques, and the interpretation remains intuitive. We propose these methods for future research using continuous relative phase in studies and analyses of human movement coordination.

A topography of free kicks in soccer

ABSTRACT This study investigates the spatial relationship of performance variables for soccer free kicks. In order to suggest ways in which players might optimise their performance, we collected data from free kicks (<35 m to goal line) of two German Bundesliga seasons (2013/14, 2014/15) (n = 1624). In the analysis, we applied the ISO-map approach using colour gradients to visualise the mean values of a variable on a 2D-map of the pitch. Additionally, variograms were used to describe the degree of spatial dependence of the free kick variables. Results show that DENSITY, TYPE OF PLAY, PLAYERS IN WALL, DISTANCE TO WALL and RULE VIOLATION were strongly spatially dependent. Centrality and proximity to the goal increased the variables PLAYERS IN WALL, RULE VIOLATIONS and INTERRUPTION TIME, and the ratio of goals scored increased from 5.9% (central far) to 10.9% (central near). In 70.9% of the shots, players preferred a switched laterality, which did not result in a higher success rate. Furthermore, there was no statistical advantage for the defensive team when DISTANCE TO WALL was below 9.15 m or when there was a RULE VIOLATION. Crosses had a success rate (i.e., first controlled ball contact after the cross) of 20.8%. Played with natural laterality, they were 5% more successful than with switched laterality. Crosses from the right side outside the penalty box were 10% more successful than from the left side. Therefore, it might be worthwhile practising the defence of balls coming from this side.

Modelling game sports as complex systems – application of recurrence analysis to golf and soccer

ABSTRACT Analyses of game sports or of performances shown in them require appropriate models. Many game sports can be modelled as complex, dynamic systems. This study investigated how recurrence plots (RPs) – a method to analyse complex systems – and the analyses of RPs can be applied to the game sports golf and soccer. A golfer is treated as a complex system with many unknown components. The scalar variable Shots Saved can describe his/her behaviour. Phase space reconstruction is needed to unfold hidden facets of a golfer’s behaviour. Results indicate that golfers’ performances do not approach a stable state, but seem rather unpredictable. A soccer match can also be treated as a complex system. Some components – the players – and their respective behaviour represented by movement trajectories are known and can be used to describe the system’s behaviour. We propose that no embedding is needed for the RP construction in this case. Results indicate that the more goal shots there are in a game, the more unstructured it is. Furthermore, if several golfers or soccer matches are investigated, we recommend using the same RP parameters to achieve comparable results.

Visualization and Analysis of Spatial Characteristics of Attacks in Field Hockey

In field hockey players are only allowed to move the ball with the flattened side of a right-handed stick, and consequently it is easier for players to move the ball or retain ball possession on the right side of a player’s body. This study investigated the characteristics of ball possession, passing, and attacking behaviour of world-class teams using association rule mining techniques and a visualization technique based on the ISOPAR method. We analysed the women’s preliminary round matches of Pool A of the 2008 Olympic Games. The results reveal a) that teams tend to carry the ball on the right side of the pitch, and b) that ball possession that resulted in goal shots were more likely to be neutral or left side, although left sided plays were less frequent overall.

Performance analysis in golf using the ISOPAR method

Performance analysis in golf has been hindered by a lack of valid performance indicators available. This paper presents an application of the ISOPAR method (Stöckl et al., 2011) to performance analysis in golf for two tournaments at the Golfclub Augsburg in Germany. The method involves characterising golf holes using ball locations and the number of shots required to hole out from each respective ball location. Using these data, ISOPAR maps can be created to visualise the difficulty of the hole. Areas on the greens which provide putts with the least difficulty were shown on the ISOPAR maps. Shots played to hole locations on elevated areas of the green may be considered more influential in the outcome (score) of the hole. A new performance indicator Shot Quality is also demonstrated in this paper. The quality of individual shots was highly correlated (Rd 1, ρ = -0.749; Rd 2, ρ = -0.441; Rd 3, ρ = -0.429) with hole score yet showed almost no relationship with round score. The correlation with tournament ranking was higher than expected (ρ = 0.221) considering the lack of correlation with Shot Quality and round score. In this study, only putting data were collected but future research will extend the method to include entire holes.

Gait Stability During Shod and Barefoot Walking and Running on a Treadmill Assessed by Correlation Entropy

This study tests correlation entropy, \(K_2\), as a measure of stability for gait analysis. An average of 13 strides from 10 participants in each combination of one footwear (barefoot vs shod) condition and one gait mode (walking vs running) were collected during treadmill walking and running. Sagittal plane ankle, knee and hip angular displacement and velocity data were used for analysis. Two-way repeated measures ANOVA showed a main effect for gait mode (\(p=.03\)) – running had lower \(K_2\) than walking, indicating higher stability. Although the sample of strides and participants was small, we speculate that the greater inertia for running helped stabilize movement control, making the running coordination pattern more resilient against small stride-to-stride perturbations.

Modelling the Tactical Difficulty of Passes in Soccer

A pass is an important action in soccer. Amongst other things, it allows moving the ball across the pitch quickly to create scoring opportunities and score goals. Passing performances are usually analyzed using descriptive measures such as number of passes or passing accuracy, however, neglecting the game context. This paper provides an approach to assess passes with respect to the tactical behavior of the participating teams. Results illustrate the application of the model by analyzing the passes played by players of different playing positions. Depending on the game context the players on different playing positions face different environments and, therefore, play passes of different tactical difficulty.