Movement variability and skills monitoring in sports

Citation for published version: Preatoni, E, Hamill, J, Harrison, AJ, Hayes, K, Van Emmerik, REA, Wilson, C & Rodano, R 2013, 'Movement variability and skills monitoring in sports', Sports Biomechanics, vol. 12, no. 2, pp. 69-92. https://doi.org/10.1080/14763141.2012.738700 DOI: 10.1080/14763141.2012.738700 Publication date: 2013 Document Version Early version, also known as pre-print Link to publication This is an Author's Original Manuscript of an article submitted for consideration in the Sports Biomechanics, copyright Taylor & Francis; Sports Biomechanics is available online at http://www.tandfonline.com/doi/abs/10.1080/14763141.2012.738700 University of Bath General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. Take down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Download date: 10. Jun. 2020 1 TITLE PAGE 2 TITLE 3 Movement variability and skills monitoring in sports 4 KEYWORDS 5 Biomechanics, experimental methods, injury, performance, reliability 6 AUTHOR LIST 7 Ezio Preatoni(a,b,c), Joseph Hamill(d), Andrew J. Harrison(e), Kevin Hayes(e), 8 Richard E. A. Van Emmerik(d), Cassie Wilson(a), Renato Rodano(b) 9 AFFILIATIONS 10 (a) Sport, Health and Exercise Science, Department for Health, University of Bath, UK 11 (b) Dipartimento di Bioingegneria, Politecnico di Milano, Milano, Italy 12 (c) 13 Politecnico di Milano, Milano, Italy 14 (d) Department of Kinesiology, University of Massachusetts, Amherst, MA, USA 15 (e) Department of Physical Education and Sports Sciences, University of Limerick, 16 Ireland 17 CONTACT INFORMATION OF THE CONTACT AUTHOR 18 Ezio Preatoni 19 [email protected] 20 +44 (0)1225 383959 Dipartimento di Industrial Design, Arti, Comunicazione e Moda (INDACO), 21 Sport, Health & Exercise Science 22 Department for Health 23 University of Bath 24 Applied Biomechanics Suite, 1.305 25 Claverton Down 26 BATH (UK) 27 BA2 7AY 28 29 TITLE 30 Movement variability and skills monitoring in sports 31 ABSTRACT 32 The aim of this paper is to present a review on the role that movement variability 33 plays in the analysis of sports movement and in the monitoring of the athlete’s skills. 34 Movement variability has been traditionally considered an unwanted noise to be 35 reduced, but recent studies have re-evaluated its role and have tried to understand 36 whether it may contain important information about the neuro-musculo-skeletal 37 organisation. Issues concerning both views of movement variability, different 38 approaches for analysing it and future perspectives are discussed. 39 Information regarding the nature of the movement variability is vital in the analysis of 40 sports movements/motor skills and the way in which these movements are analysed 41 and the movement variability subsequently quantified is dependent on the movement 42 in question and the issues the researcher is trying to address. In dealing with a 43 number of issues regarding movement variability, this paper has also raised a 44 number of questions which are still to be addressed. 45 46 INTRODUCTION 47 Movement variability is pervasive throughout the multiple levels of movement 48 organization and occurs not only between but also within individuals (Bartlett, Wheat, 49 & Robins, 2007; Bartlett, 1997; Bates, 1996; Hatze, 1986; James, 2004; Müller & 50 Sternad, 2004; Newell, Deutsch, Sosnoff, & Mayer-Kress, 2006). Every time we 51 replicate the same movement a certain amount of change may be recorded between 52 its subsequent repetitions, regardless of how good or familiar we are in performing it 53 ( 54 Figure 1). 55 56 **** Figure 1 about here **** 57 58 The study of movement variability has been gaining increasing interest in the sports 59 biomechanics community. In the last six years, for example, three “Geoffrey Dyson” 60 lectures (Bartlett, 2005; Bates, 2010; Hamill, 2006), several keynote talks (e.g. 61 Bartlett, 2004; Hamill, Haddad, & Van Emmerik, 2005; Preatoni, 2010; Wilson, 2009), 62 and an applied session at the annual conference of the International Society of 63 Biomechanics in Sports (ISBS 2009 hosted by the University of Limerick), have 64 demonstrated the importance of movement variability (MV) and coordination 65 variability (CV) in the analysis of sports movements. 66 Movement Variability in Sports Biomechanics 67 Sports biomechanics possesses distinctive peculiarities compared with other 68 branches of the study of human motion such as clinical biomechanics or ergonomics. 69 While clinical biomechanics is generally devoted to describing average behaviours 70 and to comparing pathological patterns to a physiological range, the sports context 71 should not be centred on the idea of average subject and normality. Rather, sports 72 biomechanics usually aims at enhancing the individual capabilities, in terms of 73 performance, technique proficiency and consistency of results. At the same time, it 74 should also pursue injury prevention and wellness, given the increased (in some 75 cases maximal) and repetitive biomechanical demands the athlete receives. 76 Details concerning movement organisation and performance may be fundamental in 77 sports, and the higher the level of performance the greater their importance. Elite 78 athletes possess an outstanding mastery of their movements and their motor 79 outcomes often appear very repeatable and stereotyped. However subtle differences 80 may distinguish one from another, or small changes may develop over time as a 81 consequence of environmental changes, training procedures, learning phenomena, 82 latent pathologies or incomplete recoveries. These underlying factors may be easily 83 masked by the presence of variability. 84 Therefore the study of movement variability in sports deserves particular attention. It 85 should not be addressed only in terms of reliability and appropriate experimental 86 procedures, which are still essential, but it should also be considered as a potential 87 source of information in the process of analysing and monitoring the athlete’s 88 biomechanical qualities. 89 Monitoring Sports Skills 90 Motor skills represent the ability of obtaining a predetermined outcome with a high 91 degree of certainty and maximum proficiency (Newell & Ranganathan, 2009; Schmidt 92 & Lee, 2005). Hence, the process of learning or improving sports skills involves the 93 capability of producing a stable performance under different conditions: only repeated 94 motor performance reflects mastery in carrying out a desired task. 95 The process of monitoring the athlete’s capabilities may be schematised like a 96 feedback loop (Preatoni, 2007; Preatoni, La Torre, Santambrogio, & Rodano, 2010b) 97 ( 98 99 Figure 2), where the starting point is the athlete executing a motor task and the end 100 point is the same athlete who gets back information concerning his/her performance 101 directly or through the coach’s mediation. 102 103 **** Figure 2 about here **** 104 105 Three intermediate phases are identifiable. Phase I addresses the issue of motor 106 performance depiction. Phase II deals with the definition of references that provide 107 the criterion to which measures from Phase I are compared and through which the 108 individual skills are assessed. The interpretation of biomechanical data and the 109 determination of references may be carried out on multiple levels, like, for example: 110 using coaches’ anecdotal indications, creating a record of individual changes over 111 time, modelling optimal behaviour through a purely theoretical approach and/or 112 simulation. Phase III involves the need for returning data to the athlete/coach, after 113 translating biomechanical observations into information that is suitable for both the 114 end users’ needs and their know-how. This cyclic flow of information provides 115 athletes and coaches with a tool to monitor motor skill trends, to check on possible 116 anomalies, to plan and control training programs and rehabilitative procedures. 117 Sports Skills and the Dual Nature of Movement Variability 118 In light of the framework presented in 119 120 Figure 2, MV may emerge as an unwanted source of error that should be eliminated 121 or reduced (Fitts, 1954; Fitts & Posner, 1967; Harris & Wolpert, 1998; Schmidt, 122 Zelaznik, Hawkins, Frank, & Quinn Jr, 1979; Van Beers, Baraduc, & Wolpert, 2002). 123 When trying to capture the biomechanics of individual technique, research should 124 depict the core strategy that governs the movement, regardless of the variations that 125 emerge across repetitions. 126 However, MV always occurs when the same action is repeated and even the elite 127 athlete cannot reproduce identical motor patterns (Bartlett, et al., 2007). MV is 128 inherently present in motor performance and may be associated with the extreme 129 complexity of the neuro-musculo-skeletal system and with the redundancy of its 130 degrees of freedom (e.g. Bartlett, et al., 2007; Bernstein, 1967; Hamill, et al., 2005; 131 James, 2004; Newell, et al., 2006; Riley & Turvey, 2002). While MV has been 132 associated with a reduction in performance due to a lack of consistency (Dierks & 133 Davis, 2007; Knudson & Blackwell, 2005; Salo & Grimshaw, 1998), it may not 134 correspond only to randomness but also to functional changes whose investigation 135 might unveil information about the system health, about its evolutions, and about its 136 flexibility and adaptability to variable external conditions (Bartlett, et al., 2007; Glazier 137 & Davids, 2009; Hamill, Van Emmerik, Heiderscheit, &Li, 1999). 138 Therefore MV may possess a dual connotation: (1) It is an unwanted error which 139 impedes a simple description of the actual individual status through standard 140 approaches. Moreover, it hinders the detection of the small inter-individual 141 differences or intra-individual changes that often characterise the sports domain. At 142 the same time, (2) MV reflects the inherent functional features of the neuromuscular 143 system and may contain important information that should not be neglected. 144 Aims of the Paper 145 Despite the efforts of researchers, many issues concerning the variability of human 146 motion are still to be thoroughly addressed and/or are waiting for comprehensive 147 explanations. These issues include: the magnitude of movement variability and the 148 subsequent need for appropriate experimental design and data processing; the 149 meaning of MV; the information MV may provide and the possible relationship 150 between MV and performance, MV and the acquisition/development of motor skills, 151 and/or MV and injury factors. Furthermore, MV needs to be considered during the 152 selection of the experimental design and may influence the validity of the obtained 153 results. Currently, however, there are no universally agreed guidelines for 154 practitioners regarding the treatment of variability within experiments. The lack of 155 such information becomes more serious when the focus of investigations is shifted 156 from basic movements such as walking or running to the multiplicity of more complex 157 sports movements. 158 Therefore, the aim of this paper is to present a review of the role and the potential 159 that movement variability and coordination variability may have in the process of 160 monitoring the athlete’s motor patterns. The review will endeavour to address (i) how 161 much MV is present in sports movements, (ii) how the human system copes with MV 162 and (iii) the purpose of MV. We will report practical indications about how MV should 163 be treated, present the different approaches that may be used to study MV in sports 164 and we will emphasise their limits and potential applications. In addition, we will 165 report possible developments and ideas for future research in MV. 166 THE TRADITIONAL APPROACH: MOVEMENT VARIABILITY 167 AS NOISE 168 There is a growing need to develop methodologies that enable investigators to 169 capture and effectively analyse individual motor skills and their change over time 170 independent of the variability that emerges with repetition of the same movement. 171 Many studies have revealed changes inherent to human motion and have suggested, 172 whenever possible, the use of experimental protocol in which multiple trials are 173 recorded for the subject (Chau, Young, & Redekop, 2005; Hamill & Mcniven, 1990; 174 James, 2004; Preatoni, 2007; Preatoni, et al., 2010b; Rodano & Squadrone, 2002; 175 Winter, 1984) given that the analysis of a single trial can often lead to erroneous 176 conclusion (Bates, Dufek, & Davis, 1992) particularly in the study of individual motor 177 skills. Variability in motor skills stabilises within certain ranges (James, 2004) and this 178 may be dependent on the subject, the variable and on the experimental procedures 179 for data collection. 180 According to the conventional control theory approach, movement variability is made 181 equal to noise (Equation [1]) that prevents the final output from matching the planned 182 program (Bartlett, et al., 2007; Bays & Wolpert, 2007; Fitts, 1954; Harris & Wolpert, 183 1998; James, 2004; Müller & Sternad, 2004; Newell, et al., 2006; Van Beers, et al., 184 2002). In this approach, outcome variability (i.e. variability in ‘what’ has been 185 achieved) and performance variability (i.e. variability in ‘how’ it has been obtained) 186 are equally read as poor achievement: both of them come from noise that may 187 corrupt the different levels of motor organisation (Veb, i.e. errors in the sensory 188 information and in the motor output commands) and may be caused by the 189 changeable environmental conditions (Vee) or by measuring and data processing 190 procedures (Vem). 191 [1] 192 This view of MV has important implications for the investigation of sports skills and 193 highlights the need for proper experimental designs and data reduction procedures 194 (Bartlett, et al., 2007; Comyns, Harrison, Hennessy, & Jensen, 2007; Dona, Preatoni, 195 Cobelli, Rodano, & Harrison, 2009; Preatoni, 2007; Preatoni, et al., 2010b). The 196 quantification, synthesis and meaning of MV are very important in depicting the 197 athlete’s status and can influence the practical decisions made in sport. 198 In the investigation of sports skills a crucial element is a consistent description of the 199 actual motor skills of the athlete. This may involve the extraction of either discrete or 200 continuous variables which describe the athlete’s kinematic and kinetic patterns. 201 Discrete Measures Variability 202 Quantitative biomechanical analysis often involves the extraction of parameters from 203 kinematic and kinetic curves. The assessment of discrete measures is commonly 204 used to to understand the characteristics of a particular motor task and to outline the 205 differences between different populations. In addition, discrete parameters have been 206 used for performance evaluation (Bartlett, 2005; Vamos & Dowling, 1993) or 207 enhancement and injury prevention (Granata, Marras, & Davis, 1999; James, Dufek, 208 & Bates, 2000; Nigg & Bobbert, 1990). 209 While several researchers have investigated the reliability of normal walking 210 variables (Benedetti, Catani, Leardini, Pignotti, & Giannini, 1998; Chau, et al., 2005; 211 Dingwell & Cavanagh, 2001; Growney, Meglan, Johnson, Cahalan, & An, 1997; 212 Kadaba, Ramakrishnan, & Wootten, 1990; Kadaba et al., 1989; Steinwender et al., Ve = Veb + Vee+ Vem 213 2000; Stolze, Kuhtz-Buschbeck, Mondwurf, Jöhnk, & Friege, 1998; Winter, 1984), 214 relatively few studies have been conducted to assess the variability of kinematic and 215 kinetic variables during sports movements. This lack of research is compounded 216 further by the wide variety of motor tasks that are performed by athletes in many 217 different sports disciplines. Jumping (James, et al., 2000; Rodano & Squadrone, 218 2002) and running (Bates, Osternig, Sawhill, & James, 1983; Devita & Bates, 1988; 219 Diss, 2001; Ferber, Mcclay Davis, Williams, & Laughton, 2002; Lees & Bouracier, 220 1994; Queen, Gross, & Liu, 2006) are the most frequently studied movements and 221 more recently the sprint start (Bradshaw, Maulder, & Keogh, 2007) and race walking 222 (Preatoni, 2007; Preatoni, et al., 2010b) have been investigated. 223 When analysing any sporting movement we need to be careful not to confuse 224 variability present within ‘global parameters’ (parameters which define the output of 225 the whole system) with variability that is present within kinetic and kinematic 226 (technique parameters). Low variability in the outcome measure does not necessarily 227 indicate a low variability in technique parameters describing the movement. This has 228 previously been demonstrated in reaching movements whereby variability in discrete 229 kinematic variables did not correspond to the endpoint variability (Messier & Kalaska, 230 1999). In gait analysis, (Karamanidis, Arampatzis, & Bruggemann, 2003) reported 231 that variability within kinematic data is primarily determined by the specific parameter 232 under investigation. Further to this, Van Emmerik et al. (1999) reported lower levels 233 of variability in joint kinematics between individuals with Parkinson’s disease and 234 healthy controls but not for basic gait parameters. They concluded that variability of 235 stride characteristics offers a less sensitive measure of differences between groups 236 than does variability of joint characteristics. Additionally, Preatoni (2007) and 237 Preatoni et al. (2010b) showed that skilled race walkers produced intra-individual 238 coefficient of variation that were very low (less than 3%) for ‘global parameters’ such 239 stance duration, step length and progression speed, but may become fairly high 240 (greater than 10%) for kinematic/kinetic parameters related to movement execution 241 and technique. 242 Many different methods have been proposed for estimating the variability within 243 kinematic and kinetic parameters. The use of standard deviation (Kao, Ringenbach, 244 & Martin, 2003; Owings & Grabiner, 2004) and coefficient of variation (Bradshaw, et 245 al., 2007; Queen, et al., 2006) as spread estimators is common within quantitative 246 motion analysis. However, the use of these methods relies on the assumption that 247 the data being analysed are normally distributed and this is not always the case or 248 may be not easily assessed. 249 Non-parametric measures, such as the inter-quartile range (IQR) or the median 250 absolute deviation (MAD) have been indicated as more robust estimates of variability 251 (Chau & Parker, 2004; Chau, et al., 2005). In support of this view, Preatoni (2007) 252 and Preatoni et al. (2010b) analysed race walking data and concluded that 253 summarising the variability of discrete variables should not be addressed using 254 parametric estimates indiscriminately. The use of either standard deviation or 255 coefficient of variation could inflate variability assessment thus diminishing the 256 chances of detecting significant differences when they do in fact exist (Chau, et al., 257 2005). However, MAD and IQR also manifested statistically significant changes due 258 to contaminants in nearly 50% of the considered kinetic/kinematic parameters 259 (Preatoni, 2007). Therefore, the use of non-parametric estimators of spread, 260 combined with the collection of a “proper” number of trials and the identification and 261 elimination of atypical occurrences appear to be the most advisable solution (Chau, 262 et al., 2005). 263 Unfortunately, the identification of how many repetitions may be considered 264 appropriate is not straightforward, due to multiple causes. Universally recognised 265 references are not always available, or are available for a limited number of sports 266 movements, and no proposed standards exist on how this estimation should be 267 made, especially when more than one single measure is included in the analysis. 268 The sequential estimation procedure (Hamill & Mcniven, 1990) is a technique used to 269 determine the number of consecutive trials that are necessary to obtain a stable 270 mean for each considered variable, subject and movement, whereby a value is 271 generated for the cumulative mean by adding one trial at a time. Stability is 272 recognised when the successive mean deviations fall within a range around the 273 overall average. The specific criterion to obtain a stable mean (i.e. the bandwidth) is 274 based on the need to obtain a stable result while attempting to keep the total of trials 275 as low as possible (Hamill & Mcniven, 1990). The number of trials required to depict 276 a stable performance is therefore a consequence of the activity, the subject and the 277 variable under investigation (Preatoni, 2007; Preatoni, et al., 2010b). In the analysis 278 of running the number of trials required to provide reliable estimates of the ground 279 reaction force (GRF) data variables has been identified to be as few as 8 (Bates, et 280 al., 1983) and as many as 25 (Devita & Bates, 1988). In walking the minimum 281 number of trials required has been shown to be 10 (Hamill & Mcniven, 1990). When 282 looking at joint kinetic data (moments and powers) during vertical jumping, Rodano 283 and Squadrone (2002) concluded that a 12-trial protocol was needed to obtain a 284 stable estimate. Preatoni et al. (2010b) observed a number of kinematic parameters 285 depicting race walking technique in a group of elite athletes, and suggested that as 286 many as 15 trials were necessary to obtain stability of average values. 287 In order to be able to determine how to successfully treat movement variability and 288 the conclusions that can be drawn when investigating a wide variety of sports skills it 289 is necessary to create a database of what has previously been identified. 290 Continuous Measures Variability 291 The use of discrete variables in the analysis of human movement is powerful but may 292 not be sufficient to provide an exhaustive description of the observed movement. 293 When a single measurement is extracted from a continuous variable, a large amount 294 of data are discarded and potentially useful information may be unaccounted for 295 (Queen, et al., 2006; Ryan, Harrison, & Hayes, 2006; Sutherland, Kaufman, 296 Campbell, Ambrosini, & Wyatt, 1996). Indeed, the shape of kinematic/kinetic curves 297 is often a good indicator of “how” a motor task is accomplished and may help either 298 physicians in classifying the patient’s behaviour as physiological or pathological, or 299 coaches in identifying the athlete’s characteristics and their change over time. When 300 repeating the same movement many times, an individual does not generate 301 kinematic/kinetic patterns that perfectly overlap, but produces a family of curves that 302 may differ from each other in magnitudes and timings. 303 The issue of variability across curves is considered by practitioners when attempting 304 to depict the individual motor patterns, but the analysis typically stops at summarising 305 the general characteristics of a group of curves through the estimation of confidence 306 bands (e.g. mean curves ± a multiple of the standard deviation). Previous research 307 on the variability within continuous variables is even less prevalent than research on 308 discrete parameters. Some authors have investigated the reproducibility of gait 309 variables but have generally focussed on the influence of methodological factors on 310 data repeatability (Growney, et al., 1997; Kadaba, et al., 1989) or on the differences 311 between normal and pathological subjects (Steinwender, et al., 2000). 312 The two estimators that have been commonly used to assess repeatability in 313 continuous variables are the coefficient of multiple correlation (CMC) (Kadaba, et al., 314 1989) and the intra-class correlation coefficient (ICC) (Duhamel et al., 2004; Ferber, 315 et al., 2002). Both indeces may range between 0, for extremely poor repeatability, 316 and 1, for perfect reproducibility. The CMC requires experimental designs with 317 multiple testing sessions, even if intra-session variability is the only aim of the 318 analysis. For example, Growney et al. (1997) used 3 trials collected on each of 3 319 separate days; Queen et al. (2006) adopted two separate testing sessions with as 320 many as six trials each. Alternatively, the ICC can be calculated also when data from 321 a single testing session are available, and may be considered as the “proportion of 322 variance due to the time-to-time variability in the total variance” (Duhamel, et al., 323 2004). 324 Within-day, between-day and overall variability of continuous variables have mainly 325 been assessed during walking (Growney, et al., 1997; Kadaba, et al., 1989; 326 Steinwender, et al., 2000) and running activities (Queen, et al., 2006). Results 327 showed that lower limb kinematics and kinetics have better reproducibility in the 328 sagittal plane, while reliability on secondary planes of motion is less effective. Hence, 329 the authors have concluded that repeatability for sagittal plane variables is good 330 enough for their use in clinical examinations, provided that operators are very careful 331 with marker placement and in the control of experimental settings. 332 Unfortunately and similarly observations on discrete measures analysis, there are 333 neither standard guidelines to be followed, nor agreement about what should be set 334 as a threshold settings for good reliability. Shrout (1998) proposed categories of 335 agreement based on ICC of discrete variables, and set “substantial” reliability for 336 values greater than 0.80. However, other authors (Atkinson & Nevill, 1998; Duhamel, 337 et al., 2004) have underpinned the need for more research to identify appropriate 338 reference values and argued that each motion variable, experimental objective and 339 population may involve different limits above which repeatability can be considered 340 good. 341 Moreover, there is lack of such investigations in sports movements, and in cohorts of 342 high-level athletes in particular. Preatoni (2007) analysed 15 continuous variables in 343 a group of very skilled race walkers, including joint angles, moments and powers, 344 and ground reaction forces. Results concurred with previous findings, reporting better 345 reliability for ground reaction forces and angles in the sagittal plane, but also showed 346 that the values of ICCs were lower than the ones reported for walking (Duhamel, et 347 al., 2004), and that the level of intra-individual variability was substantially subject- 348 and variable-dependent. Preatoni also suggested an iterative procedure (Figure 3) 349 based on the calculation of the ICC, which may be used to iteratively identify and 350 discard the most unrepresentative curves of a subject, until the remaining ones have 351 a repeatability that is equal or greater than a pre-determined threshold. 352 353 **** Figure 3 about here **** 354 355 However, much more effort is required to define standard guidelines for addressing 356 continuous measures variability in sports and to create reference databases that 357 could help in the analysis of data on performance and on its consistency and 358 evolution over time. The list of open issues that still deserve attention is long and 359 would also include, for instance: (i) the selection of the best statistical methods for 360 summarising and comparing families of intra-individual curves (Chau, et al., 2005; 361 Duhamel, et al., 2004; Lenhoff et al., 1999; Olshen, Biden, Wyatt, & Sutherland, 362 1989; Sutherland, et al., 1996), especially when the aim of the study is the detection 363 of the subtle individual changes of the athlete (Hopkins, 2000; Hopkins, Hawley, & 364 Burke, 1999), and not a patient’s classification that should be free from type II errors 365 (Olshen, et al., 1989; Sutherland, et al., 1996); (ii) the definition of proper 366 experimental protocols and selection of a representative number of trials, based on 367 continuous measures variability; (iii) sensitivity analysis about the effect of time- 368 normalisation of curves and the possible need for curve registration (Chau, et al., 369 2005; Sadeghi et al., 2000; Sadeghi, Mathieu, Sadeghi, & Labelle, 2003). 370 371 As already stated movement variability has traditionally been considered to be noise 372 and therefore an aspect of human motion that we are trying to eliminate. However, 373 this is not possible and therefore it must be taken into consideration when 374 investigating sports movements. Within sports biomechanics we have the additional 375 constraint of often being limited by the number of trials we are able to collect, 376 especially if collected within a competition setting. Furthermore, the additional factors 377 encountered during competition in comparison to training may also influence both the 378 movement itself and the variability present and this therefore also needs to be taken 379 into consideration. 380 381 MOVEMENT VARIABILITY AS INFORMATION: NEW 382 APPROACHES 383 Recent investigations and experimental evidence have shown that outcome and 384 performance variability should not be read in the same way. While outcome variability 385 is by definition an unwanted deviation from the pursued objective, performance 386 variability is not necessarily bad. Several researchers have supported the idea that 387 inter-trial variability (Vtot) does not correspond to noise only but is a combination 388 (Equation [2]) of artefact of noise in the neuro-musculo-skeletal system (i.e. Ve in 389 Equation [1]) and functional changes that may be associated with its proprieties (Vnl) 390 (Bartlett, et al., 2007; Glazier & Davids, 2009; Hamill, et al., 1999; James, 2004): 391 [2] 392 Vnl is an integral part of the biological signal and may be interpreted as the flexibility 393 of the system to explore different strategies to find the most effective one among the 394 many available. This adaptability allows for learning a new movement or adjusting 395 the already known one by gradually selecting the most appropriate pattern for the 396 actual task (Deutsch & Newell, 2003; Dingwell & Cusumano, 2000; Dingwell, 397 Cusumano, Cavanagh, & Sternad, 2001; Dingwell, Cusumano, Sternad, & 398 Cavanagh, 2000; Hamill, et al., 2005; Hausdorff, 2005; James, 2004; Müller & 399 Sternad, 2004; Newell, Broderick, Deutsch, & Slifkin, 2003; Newell, Challis, & 400 Morrison, 2000; Newell, et al., 2006; Riley & Turvey, 2002). The subject is thus able 401 to gradually release the degrees of freedom that have been initially frozen to achieve 402 a greater control over an unfamiliar situation. Changes in the contributions of Ve and 403 Vnl to the total variability may be related to changes in motor strategies and may thus 404 reveal the effects of adaptations, pathologies and skills learning (e.g. Bartlett, et al., Vtot = Ve + Vnl 405 2007; Dingwell, et al., 2001; Wilson, Simpson, Van Emmerik, & Hamill, 2008). It 406 should be noted here that what we are referring to in this paper is biological 407 variability, which is not noise resulting from measuring and data processing 408 procedures, but is internal to the movement signal and cannot be removed from the 409 signal. Non-biological noise (Vee and Vem in Equation [1]) on the other hand is a high 410 frequency component which can be attenuated by data conditioning (Kantz & 411 Schreiber, 1997) . 412 The conventional approaches to MV can only quantify the overall variability, and they 413 rely on assumptions and procedures that do not allow examination of its features and 414 structure. They cannot, for example, assess the extent to which Ve (or, more 415 specifically, Veb) and Vnl participate in the generation of MV, and therefore they are 416 not effective in evaluating the possible information MV conveys. The use of nonlinear 417 dynamics tools (e.g. entropy measures), the analysis of coordinative features (e.g. 418 continuous relative phase) or the use of functional data analysis represent alternative 419 instruments to explore the nature of motion variability and its relation with 420 performances, skills development or injury factors. Only recently and only few 421 authors have used these methods to investigate MV in sports and in elite athletes in 422 particular. 423 An Example of Nonlinear Methods: Entropy Measures 424 A number of nonlinear methods, such as the Lyapunov exponent (Abarbanel, Brown, 425 Sidorowich, & Tsimring, 1993), and entropy measures (Pincus, 1995; Pincus, 1991; 426 Richman & Moorman, 2000), have been proposed as tools for investigating the 427 nature of variability in biological systems. Nonlinear methods do not consider the 428 subsequent repetitions of the same motor task as a bunch of similar but independent 429 events that need to be summarised through statistics (e.g. average pattern and 430 confidence band). Rather, they look at the repeated cycles of the movement as a 431 continuous pseudo-periodic time-series and try to evaluate the dynamics that govern 432 the changes occurring between the cycles. Some authors have recently applied 433 nonlinear analysis in the study of neuro-motor pathologies (Dingwell & Cusumano, 434 2000; Dingwell, et al., 2000; Morrison & Newell, 2000; Newell, et al., 2006; Smith, N. 435 Stergiou, & B.D. Ulrich, 2010; Vaillancourt & Newell, 2000; Vaillancourt, Slifkin, & 436 Newell, 2001) or in the characterisation of movement development, posture and 437 locomotion (Dingwell, et al., 2001; Lamoth & Van Heuvelen, 2012; Newell, et al., 438 2003; Newell, et al., 2000; Newell, et al., 2006), but the number of studies concerning 439 sports movements is extremely limited (Preatoni, Ferrario, Dona, Hamill, & Rodano, 440 2010a). This lack of research may be mainly due to the computational procedures of 441 these techniques, which require a relatively large amount of data (i.e. number of data 442 points= number of trials x duration x sampling frequency), and which consequently 443 make the experimental procedure be difficult to be implemented in a sports context 444 where typically a limited number of repetitions can be collected. 445 Among the different nonlinear methods, entropy measures such as Approximate 446 Entropy (ApEn) (Pincus, 1995; Pincus, 1991) or Sample Entropy (SampEn) 447 (Richman & Moorman, 2000) can be considered particularly appropriate for the study 448 of sports movements, where variability is likely to have both a deterministic and a 449 stochastic origin, and where data set are typically small and may be affected by 450 outliers (Preatoni, et al., 2010a). Entropy indices quantify the regularity of a time- 451 series (e.g. a kinematic or kinetic measure) that contains a sequence of repetitions of 452 the same movement (Figure 4a). ApEn and SampEn measure the probability that 453 similar sequences of m points in the time-series, remain similar within a tolerance 454 level (r) when a point is added to the sequence (m+1 sequences) (Pincus, 1995; 455 Richman & Moorman, 2000). That is, in more simplistic terms, a count of how many 456 similar patches of m points are replicated in the time-series, carried out for each 457 sequence of m points in the signal, and divided by the same count carried out for a 458 patch m+1 points long. ApEn and SampEn range from 0, for regular or periodical 459 time series, to positive values, for which the higher the entropy, the less regular and 460 predictable the time series (Pincus, 1995; Richman & Moorman, 2000). Since 461 regularity is related to the complexity of the system that produces the signal (Pincus, 462 1995), an increase in regularity may indicate a loss of complexity of the system and 463 has often been associated to pathological conditions (Vaillancourt & Newell, 2000; 464 Vaillancourt, et al., 2001). Furthermore, differences in the predictability of movement 465 patterns may also reflect underlying changes in motor strategies whereby the effects 466 of adaptations, and skills learning may be revealed (Bartlett, et al., 2007), which may 467 be particularly beneficial in sports movement analysis when subtle changes in 468 performance are hidden by the magnitude of MV. 469 470 **** Figure 4 about here **** 471 472 Preatoni (2007) and Preatoni et al. (2010a) studied the nature of MV in sports by 473 measuring sample entropy in kinematic and kinetic variables during race walking. 474 They analysed the influence of the different sources of variability (i.e. Ve and Vnl in 475 Equation [2]) over movement repeatability by comparing entropy values of the 476 original time-series (made up of 20 gait cycles) with the ones of their surrogate 477 counterparts. Surrogation is a method for generating new time-series, which 478 maintains original data and its large-scale behaviour (periodicity, mean, variance and 479 spectrum) but eliminates its possible small-scale structure (chaotic, linear/nonlinear- 480 deterministic) (Figure 4b). Therefore, if SampEn significantly increases after 481 surrogation, then it is very likely that the variability between trials (periods) is not, or 482 not only, the outcome of random processes. The study of race walking reported a 483 significant increase of SampEn after surrogation in the range between 16% and 59%, 484 depending on the analysed variable. Their results confirmed that MV is not only noise 485 but also contains functional information concerning the organisation of the neuro- 486 musculo-skeletal system. Results comparing entropy content in the first and last half 487 of trials also suggested that the structure of variability appears invariant and no 488 adaptation effects emerge when a proper experimental protocol is followed. 489 Finally, the same authors showed how entropy measure might have a potential for a 490 fine discrimination between skill levels. While traditional analysis had failed in 491 distinguishing between good athletes and elite ones in a group of apparently similar 492 individuals, SampEn evidenced significant differences with less skilled race walkers 493 showing increased regularity and therefore an increased control over those joints that 494 in race walking mainly compensate for the locked position of the knee. Conversely, in 495 line with the interpretation that higher values of entropy may be read as a better 496 flexibility and adaptability to unpredictable environmental changes (Newell, et al., 497 2006; Vaillancourt, et al., 2001) subjects with an outstanding ability reported a less 498 rigid control over their body’s degrees of freedom. 499 Dynamic Systems Theory Approach 500 Non-linear tools such as entropy measures are computing-intensive procedures that 501 give a concise and powerful measure/assessment of the nature of movement 502 variability and of the extent of its being functional. However, they are not particularly 503 effective in depicting how MV can be functional because they address multiple 504 movement cycles as a whole, they do not look into its constitutive phases, and 505 typically they do not observe the relationships between the multiple elements that 506 concur in coordination and movement execution. 507 From a dynamical systems approach, in systems with multiple degrees of freedom, 508 variability in performance is a necessary condition for optimality and adaptability. 509 Variability patterns in gait parameters such as stride length and stride frequency, 510 therefore, may not reflect variability patterns in segmental coordination. This has 511 been demonstrated in studies on Parkinson’s disease (Van Emmerik, et al., 1999). In 512 biomechanical research on running injuries, several studies have now demonstrated 513 an association between reduced coordination variability and orthopaedic disorders 514 (Hamill, 2006; Hamill, Haddad, Heiderscheit, Van Emmerik, & Li, 2006). 515 Coordination variability can be defined as the range of coordinative patterns the 516 organism exhibits while performing a movement. It is often quantified as the between 517 trial (i.e. between gait cycle) standard deviation of the movement trials. Multiple 518 studies have reported that a certain amount of variability appears to be a signature of 519 healthy, pain-free movement (e.g. Hamill, et al., 1999; Heiderscheit, Hamill, & Van 520 Emmerik, 2002; Miller, Meardon, Derrick, & Gillette, 2008). These authors suggest 521 that this finding is indicative of a narrow range of coordination patterns that allowed 522 for pain-free running. However, since all of these studies were retrospective in 523 nature, a causal relationship between variability and pathology could not be 524 ascertained. Prospective studies on coordination variability and injury development 525 are needed to assess this relationship. 526 From a dynamical systems perspective, variability is not inherently good or bad, but 527 indicates the range of coordination patterns that can be used to complete the motor 528 task. This offers a different view in comparison to the more traditional ‘variability is 529 bad’ perspective. In contrast, dynamical systems theory suggests that there is a 530 functional role for variability that expresses the range of possible patterns and 531 transitions between patterns of movement that a system can accomplish. It should be 532 noted that abnormally low or high levels of variability may be detrimental to the 533 system. 534 In a dynamical systems approach, the reconstruction of the so-called state space is 535 essential in identifying the important features of the behaviour of a system. The state 536 space is a representation of the relevant variables that help identify the features of 537 the system. Two methods for representing the state space of a system are typically 538 used: 1) the angle-angle plot; and 2) position-velocity plot. An ‘angle-angle’ (e.g. 539 sagittal plane knee angle versus ankle angle) plot can reveal regions were 540 coordination changes take place as well as parts of the gait cycle where there is 541 relative invariance in coordination patterns. These coordinative changes in the angle- 542 angle plots can be further quantified by vector coding techniques (see Heiderscheit, 543 et al., 2002). The other form of state space is where the position and velocity of a 544 joint or segment are plotted relative to each other. This state space representation is 545 also often referred to as the phase plane. The phase plane representation is a first 546 and critical step in the quantification of coordination using continuous relative phase 547 techniques (see Hamill, et al., 1999). 548 The relative motion between the angular time series of two joints or segments has 549 been used to distinguish changes in coordination in sport as a function of expertise 550 (see Wheat & Glazier, 2006). Various techniques have been developed over time to 551 quantify the relative motion patterns and variability in angle-angle diagrams. These 552 methods include chain encoding method developed by Freeman (see Whiting & 553 Zernicke, 1982) and vector coding (Tepavac, 2001). In a modified version of vector 554 coding (Heiderscheit, et al., 2002), the relative motion between the two segments is 555 quantified by a coupling angle, an angle subtended from a vector adjoining two 556 successive time points relative to the right horizontal. Since these angles are 557 directional and obtained from polar distributions (0-360), taking the arithmetic mean 558 of a series of angles can result in errors in the average value not representing the 559 true orientation of the vectors. Therefore, mean coupling and standard deviation of 560 the angles must be computed using circular statistics (Batschelet, 1981; Fisher, 561 1996). 562 The vector coding analysis can also provide a measure of coordination variability. 563 Coordination variability measures can be obtained as averages across the gait cycle 564 of between-cycle variation (a global variability measure), or more locally at key points 565 or intervals across the cycle (such as early stance, mid stance, swing, etc.). 566 Continuous relative phase (CRP) is often considered a higher order measure of the 567 coordination between two segments or two joints Figure 5. This higher order 568 emerges from the derivation of CRP from the movement dynamics in the phase 569 plane of the two joints or segments. CRP analysis has been used to characterize 570 joint or segmental coordination during gait (Hamill, et al., 1999; Van Emmerik, et al., 571 1999). While CRP may seem to be relatively easy to implement, there are several 572 key concepts regarding the methodology and the interpretation that must be 573 addressed. First, CRP is not a higher resolution form of discrete relative phase 574 (Peters, Haddad, Heiderscheit, Van Emmerik, & Hamill, 2003). CRP quantifies the 575 coordination between two oscillators based on the difference in their phase plane 576 angles. It should be understood that the motion of the segments and joints are not 577 physical oscillators but are modelled behaviourally as oscillators. 578 579 **** Figure 5 about here **** 580 581 A particularly important step in the CRP procedure involves normalizing the angular 582 position and angular velocity profiles. Normalization of the two signals (i.e. position 583 and velocity) that make up the phase plane is necessary to account for the amplitude 584 and frequency differences in the signals. For a complete description of the necessity 585 of normalizing these signals see Peters, et al. (2003). The phase plane is constructed 586 by plotting the angular position versus angular velocity for each of the oscillators (i.e. 587 joints or segments). For each of the oscillators, the phase angle is obtained by 588 calculating the four-quadrant arctangent angle relative to the right horizontal at each 589 instant in the cycle. To determine the CRP angle, the phase angle for one oscillator is 590 subtracted from the other. When the CRP(i) angle is 0o, the two oscillators are 591 perfectly in-phase. A CRP(i) angle of 180o indicates that the oscillators are perfectly 592 anti-phase. Any CRP(i) angle between 0o and 180o indicates that the oscillators are 593 out-of phase, but could be relatively in-phase (closer to 0o) or anti-phase (closer to 594 180o). It is often tempting to use the CRP angle to discuss which oscillator is leading 595 and which is lagging relative to the other oscillator. Since the phase angle of one 596 oscillator is subtracted from the phase angle of another, the lead-lag interpretation is 597 often assumed. However, the calculation of CRP described above does not allow for 598 such an interpretation. 599 The CRP time series can also be used to obtain a measure of coordination variability. 600 For a proper assessment of coordination variability, the following two key aspects 601 need to be addressed: (1) average variability measures should not be obtained 602 directly from CRP time series that vary systematically throughout the movement 603 (stride) cycle, and (2) variability measures can only be obtained from data that do not 604 contain discontinuities. To obtain a measure of variability, we typically calculate the 605 standard deviation with respect to the average CRP in the data. 606 Principal Component Analysis and Functional Principal Component 607 Analysis 608 Principal Component Analysis (PCA) is a statistical technique, which is ideally suited 609 to dimension reduction and examination of the modes of variation in experimental 610 data. Traditionally PCA has been used to examine and interpret data sets that are 611 discrete in nature, rather than continuous time series or curves. PCA reduces the 612 dimensionality of an experimental problem by converting a large number of measures 613 into a smaller number of uncorrelated, independent variables called principal 614 components (PCs) that explain the modes of variation in the experimental data. 615 More recently PCA techniques have been adapted and used in biomechanics 616 research to analyse temporal waveform data in various applications including gait 617 (Landry, Mckean, Hubley-Kozey, Stanish, & Deluzio, 2007; Muniz & Nadal, 2009), 618 balance (Pinter, Van Swigchem, Van Soest, & Rozendaal, 2008) ergonomics 619 (Wrigley, Albert, Deluzio, & Stevenson, 2006), surface electromyography (Hubley- 620 Kozey, Deluzio, Landry, Mcnutt, & Stanish, 2006; Perez & Nussbaum, 2003). 621 Currently two distinct approaches have been used to apply PCA to the analysis of 622 biomechanical data sets where the data appear as families of curves or waveforms. 623 These approaches are: PCA of waveforms (Deluzio & Astephen, 2007; Deluzio, 624 Wyss, Costigan, Sorbie, & Zee, 1999) or functional PCA (f-PCA) which is generally 625 categorised as part of a larger analysis process, functional data analysis (FDA) 626 originally introduced by (Ramsay & Dalzell, 1991). 627 In PCA of waveforms, the original curves are re-sampled to ensure equal numbers of 628 records on every waveform and then entered into a large matrix where a Principal 629 Component Score (PC) is derived for each data point on the waveform. While this 630 procedure is relatively easy to implement using proprietary software applications 631 such as IBM® SPSS® (IBM, New York, USA) or Minitab (Pennsylvania, USA), it has 632 some deficiencies. Firstly, creating data sets of equal length may result in distortion 633 of the time series. Secondly the smoothing and calculation of derivatives is carried 634 out separately from PCA procedures resulting in unknown and potentially unwanted 635 sources of variation entering the PCA. Thirdly and most importantly, in PCA of 636 waveforms, the data points on the curve are assumed to be independent of each 637 other, but in reality we know that any point on a curve is correlated to the data points 638 that precede and follow that point. As a result of these deficiencies it may be difficult 639 to relate the waveforms described by each PC to specific subjects in the 640 experimental population. 641 FDA and f-PCA were devised by Ramsey and Dalzell (1991) in an attempt to rectify 642 some of the limitations of other approaches. The distinctive feature of functional data 643 analysis (FDA) is that the entire sequence of measurements for a measurement is 644 considered as a single entity or function rather than a series of individual data points 645 (Ryan, et al., 2006). The term Functional in FDA and f-PCA refers to our attention to 646 the intrinsic nature of measurements we frequently obtain in biomechanics 647 experiments. While biomechanical data are obtained at various regularly spaced time 648 points, these measurements can be assumed to be generated by some underlying 649 function which we can denote as the function: x(t). A further characteristic of the 650 functional data is that of smoothness. In practise, the smoothing and derivation of 651 functions are generally linked processes and the decision on the choice of 652 appropriate basis functions is dependent on the nature of the data being analysed. 653 For example, if the observed data are periodic, then a Fourier basis may be 654 appropriate. Alternatively, if the observed functions are locally smooth and non- 655 periodic, then B-splines may be appropriate; if the observed data are noisy but 656 contain informative “spikes” that need to avoid the effect of severe smoothing, then a 657 wavelet basis may be appropriate. The final choice of basic functions should provide 658 the best approximation using a relatively small number of functions. 659 B-splines have been shown to be useful basis functions for smoothing kinematic data 660 because their structure is designed to provide the smooth function with the capacity 661 to accommodate changing local behaviour (Coffey, Harrison, Donoghue, & Hayes, 662 2011). B-splines consist of polynomial pieces joined at certain values of x (t), called 663 knots. (Eilers & Marx, 1996) outlined the general properties of a B-spline basis. Once 664 the knots are known it is relatively easy to compute the B-splines using the recursive 665 algorithm of de Boor (2001). 666 The functional form of a PCA (f-PCA) has previously been used to distinguish 667 differences in kinematic jumping patterns and coordination in groups of children at 668 various stages of development (Harrison, Ryan, & Hayes, 2007; Ryan, et al., 2006). 669 The analysis of these data showed that at the early stages of development in the 670 vertical jump, most subjects’ movement patterns were characterised by the first f-PC 671 in 672 Figure 6 and therefore displayed higher levels of variability than found in the later 673 stages of development. The high scorers in f-PC3 were typically described as more 674 mature performers and these were subjects who displayed a smoother and quicker 675 counter-movement which is typical of a more effective stretch-shortening cycle 676 performance. 677 678 **** Figure 6 about here **** 679 680 Dona’ et al. (2009) applied f-PCA bilaterally to sagittal knee angle and net moment 681 data in race-walkers of national and international level and found that scatterplots of 682 f-PC scores provided evidence of technical differences and asymmetries between the 683 subjects even when traditional analysis (mean ±s curves) was not effective. They 684 concluded that f-PCA was sensitive enough to detect potentially important technical 685 differences between higher and lower skilled athletes and therefore f-PCA might 686 represent a useful and sensitive aid for the analysis of sports movements, if 687 consistently applied to performance monitoring. f-PCA was also used by Donoghue 688 et al. (2008) to examine the effects of in-shoe orthoses on the kinematics of the lower 689 limb in subjects with previous Achilles tendon injury compared to uninjured controls. 690 Donoghue et al. (2008) provided evidence using f-PCA that in-shoe orthoses 691 appeared to constrain some movement patterns but restored some aspects of 692 variability in other movements. Coffey et al. (2011) took this analysis further using an 693 extension of f-PCA which they called Common f-PCA. This technique is better suited 694 to analysis of families of curves where repeated measures designs are used. Using 695 Common f-PCA, Coffey et al. (2011) provided evidence that control subjects had 696 greater levels of variability in lower limb movement patterns than injured subjects. 697 All of the above studies highlight the importance of treating variability in the data as a 698 real, biological phenomenon that has a structure which can be separated from the 699 noise or error information generated by data acquisition. In this respect f-PCA 700 appears to be a very useful to aid the investigation of biological variability in 701 biomechanical studies. 702 703 CONCLUSION 704 This paper has briefly examined the “dual” role that motion variability plays in the 705 analysis of sports movement, being concurrently a limitation, both in terms of its 706 function and the way we deal with it, as well as a potentiality. Regardless of the point 707 of view from which we consider MV, more research is needed to gain a thorough 708 insight into this issue. For example, there is still lack of: (i) reference values and 709 database, that could help in the interpretation of movement and coordination 710 variability in sports; (ii) knowledge of the relationship between causes (e.g. 711 detrimental behaviours, motor learning) and effects (e.g. changes in the analysed 712 variables or indices) (Bartlett, et al., 2007; Hamill, et al., 2005; Preatoni, 2007; 713 Preatoni, et al., 2010a); (iii) integration of the outcomes of the different methods of 714 investigation; and, (iv) ability in translating complex approaches and results into 715 suitable information that may be easily read as feedback and thus applied on the 716 field. 717 Previous studies investigating MV have looked at functional motor skills such as 718 walking (e.g. Chau, et al., 2005), whilst other authors have focused their attention on 719 injury factors (e.g. Hamill, et al., 2005; Hamill, et al., 1999) or on coordinative 720 patterns (e.g. Seay, Haddad, Van Emmerik, & Hamill, 2006), by studying the 721 variability in phasing relationships between different elements of the locomotor 722 system (body segments or joints). Fewer works have concentrated their attention on 723 the relation between sports skills and MV/CV, with practical implications for 724 performance monitoring and training purposes. Wilson et al. (2008) studied how 725 coordination variability changes in relation with skills development in the triple jump. 726 Preatoni (2007) and Preatoni et al. (2010a) reported different levels of entropy, in 727 selected variables, between elite and high-level race walkers. Furthermore, Preatoni 728 (2007, 2010), Preatoni et al. (2010a) and Donà et al. (2009) presented evidence 729 relating to how advanced methodologies may be an important means for finely 730 investigating individual peculiarities – e.g. subtle changes over time that may be due 731 to 732 ( 733 Figure 7) – when no apparent changes occur at a macroscopic level. 734 735 736 **** Figure 7 about here **** underlying pathologies 737 This paper has considered five methods of analysis of sport movements which are 738 able to address MV. Discrete and continuous measures of variability have 739 traditionally viewed variability as an unwanted source of error which is detrimental to 740 performance. These measures allow the quantification of MV in a way which is not 741 computationally complex and which does not rely on a very large sample size. In 742 addition these measures provide information which is easy to interpret and 743 understand by the end user (athlete or coach). However, similar performances in 744 sporting events are often the result of different motor strategies, both within and 745 between individuals and these subtle discrepancies are typically less detectable than 746 the ones that emerge in clinical studies, and are often concealed by the presence of 747 invariance. Hence, the conventional use of discrete variables or continuous curves 748 may be ineffective. When a movement is performed repetitively, the motions of the 749 body’s segments will exhibit some variability, even for a cyclical motion like running. 750 A common assumption in many locomotion studies is that increased variability in gait 751 parameters such as stride length and stride frequency is associated with instability. 752 Although increased variability in these spatio-temporal patterns of footfalls may 753 indicate potential gait problems, an understanding regarding the mechanisms 754 underlying instability requires insight into the dynamics of segmental coordination in 755 the upper and lower body. DST provides an approach to quantifying variability which 756 considers a higher order measure of coordinative variability and therefore allows the 757 potential for analysing subtle differences between individuals/performances and the 758 possibility of analysing across functional phases of the movement in question. 759 Unfortunately DST requires the use of large numbers of trials and, maybe as a result 760 of this, there is currently a lack of research applied to the analysis of sports skills. 761 Entropy has many of the benefits and drawbacks of DST but unlike DST cannot 762 provide information regarding the way through which movement variability is 763 functional. However what entropy can add is the potential for analysing the content or 764 nature of the MV present in the system and therefore potentially the ability for fine 765 discrimination between skills. Finally, f-PCA supplements DST and entropy by 766 creating a function that describes the complete movement, and by giving a tool both 767 for data reduction and for the interpretation of performance and skills learning factors. 768 The considerations which need to be taken when quantifying and treating MV have 769 been discussed in addition to what conclusions we can draw when investigating 770 sports skills. How a particular movement or motor skill is analysed and the MV 771 quantified is dependent on the movement in question and the issues the researcher 772 is trying to address. 773 774 The implications of the issues discussed in this paper are wide reaching. Movement 775 variability should not simply be treated as noise which needs be eliminated. Equally it 776 should not be viewed as a solely function element of human movement. 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Example of the outcoming variability in a well mastered motor task like 1117 writing. Repeatedly fast-writing the same word generates traces that do not perfectly 1118 overlap. 1119 1120 1121 Figure 2. The athlete’s monitoring scheme. Three key issues may be identified in the 1122 monitoring process: (I) the robust description of motor characteristics; (II) the 1123 interpretation of 1124 biomechanical analyses into readily comprehensible information for application on 1125 the field. 1126 biomechanical measures; (III) the translation of complex 1127 1128 Figure 3. Algorithm for the iterative identification and discard of unrepresentative 1129 curves through the use of ICC (left) and an example of its application (right) when 1130 multiple repetitions of race walking stance are taken into account and the threshold 1131 for good repeatability is set at ICCmin= 0.80. 1132 1133 1134 Figure 4. Example of a time-series made up of multiple repetitions of the same tasks 1135 (a) and its corresponding surrogate counterpart (b). Surrogation was here carried out 1136 by applying the pseudo-periodic surrogate algorithm (Miller, Stergiou, & Kurz, 2006; 1137 Small, Yu, & Harrison, 2001). 1138 1139 1140 Figure 5. Example of CRP calculation based on data from a race walker’s hip and 1141 knee joint motion. Normalised (Hamill, et al., 1999) phase plane plots concerning the 1142 hip (a) and the knee (b) angles are used to calculate the respective phase patterns (c 1143 and d). (d) is then subtracted from (c) to obtain the CRP plot (e). The deviation phase 1144 (time-to-time standard deviation of the CRP) is reported in (f). Data are normalised to 1145 100 points, with gait cycles identified by two subsequent toe-offs (TO1 and TO2). HS= 1146 heel-strike; V= instant when the support leg passes through the projection of the 1147 centre of mass; U= instant when the knee is unlocked. Bold lines represent mean 1148 and standard deviation. 1149 1150 1151 Figure 6. The first three Functional Principal Components (f-PCs) on unregistered 1152 data for knee joint function during vertical jump in children The graphs show mean 1153 ensemble curve with the high scorers for each f-PC being represented by +signs and 1154 the low scorers for the f-PC represented by – signs. 1155 1156 1157 Figure 7. Example showing the potential of advanced studies of movement and 1158 coordination variability in evidencing underlying changes due to injury. The phase 1159 plane plots of the hip (a-left) and knee (a-right) joints concerning multiple race 1160 walking gait cycles pre- (red) and post-injury (green) are here reported, together with 1161 the outcoming CRP variables (b) (see Figure 5 for annotations). The athlete was 1162 considered clinically recovered and reported no significant changes in terms of: 1163 duration of the movement, speed, step length, antero-posterior and vertical ground 1164 reaction force. However, both entropy measures and phasing relations between joint 1165 angles manifested a decrease of regularity/variability between the two testing 1166 session, evidencing that something had changed in the neuro-muscular organisation 1167 of movements. Only the availability of proper reference values may help in 1168 interpreting whether the increased variability in the pre-injury test was a detrimental 1169 factor or whether the higher regularity in the post-injury test was a sign of excessive 1170 control resulting from the pathology. 1171