Integrating physical and tactical factors in football using positional data: a systematic review

Background Positional data have been used to capture physical and tactical factors in football, however current research is now looking to apply spatiotemporal parameters from an integrative perspective. Thus, the aim of this article was to systematically review the published articles that integrate physical and tactical variables in football using positional data. Methods and Materials Following the Preferred Reporting Item for Systematic Reviews and Meta-analyses (PRISMA), a systematic search of relevant English-language articles was performed from earliest record to August 2021. The methodological quality of the studies was evaluated using the modified Downs and Black Quality Index (observational and cross-sectional studies) and the Physiotherapy Evidence Database (PEDro) scale (intervention studies). Results The literature search returned 982 articles (WoS = 495; PubMed = 232 and SportDiscus = 255). After screening, 26 full-text articles met the inclusion criteria and data extraction was conducted. All studies considered the integration of physical and tactical variables in football using positional data (n = 26). Other dimensions were also reported, such as psychophysiological and technical factors, however the results of these approaches were not the focus of the analysis (n = 5). Quasi-experimental approaches considered training sets (n = 20) and match contexts (n = 6). One study analysed both training and play insights. Small sided-games (SSG) were the most common training task formats in the reviewed studies, with only three articles addressing medium-sided (MSG) (n = 1) and large-sided games (LSG) (n = 2), respectively. Conclusions Among the current systematic review, the physical data can be integrated by player’s movement speed. Positional datasets can be computed by spatial movement, complex indexes, playing areas, intra-team and inter-team dyads. Futures researches should consider applying positional data in women’s football environments and explore the representativeness of the MSG and LSG.

[1]  F. Clemente,et al.  Integrating notational and positional analysis to investigate tactical behavior in offensive and defensive phases of football matches , 2022, Proceedings of the Institution of Mechanical Engineers, Part P: Journal of Sports Engineering and Technology.

[2]  J. Castellano,et al.  Effects on collective behaviour and locomotor and neuromuscular response in young players by varying the length of the pitch in 11-a-side football , 2022, International Journal of Sports Science & Coaching.

[3]  S. Ibáñez,et al.  Applying Different Strategies of Task Constraint Manipulation in Small-Sided and Conditioned Games: How Do They Impact Physical and Tactical Demands? , 2022, Sensors.

[4]  A. M. Monteiro,et al.  Effects of Chronological Age, Relative Age, and Maturation Status on Accumulated Training Load and Perceived Exertion in Young Sub-Elite Football Players , 2022, Frontiers in Physiology.

[5]  J. Sampaio,et al.  The effects of individual and collective variability on youth players' movement behaviours during football small-sided games. , 2022, Research in sports medicine.

[6]  Ferran Vidal-Codina,et al.  Automatic event detection in football using tracking data , 2022, Sports Engineering.

[7]  J. Sampaio,et al.  Amplifying perceptual demands: How changes in the colour vests affect youth players performance during medium-sided games , 2022, PloS one.

[8]  Jaime Sampaio,et al.  The diagonal positioning of the goals modifies the external training load and the tactical behaviour of young football players , 2021, Biology of sport.

[9]  J. Castellano,et al.  Reference values for collective tactical behaviours based on positional data in professional football matches: a systematic review , 2021, Biology of sport.

[10]  Felipe Arruda Moura,et al.  Progression to the target vs. regular rules in Soccer small-sided Games , 2021, Science & medicine in football.

[11]  Sérgio Matos,et al.  Field-based Tests for Soccer Players: Methodological Concerns and Applications , 2022, SpringerBriefs in Applied Sciences and Technology.

[12]  D. Memmert Match Analysis , 2021 .

[13]  J. Sampaio,et al.  Exploring how limiting the number of ball touches during small-sided games affects youth football players’ performance across different age groups , 2021, International Journal of Sports Science & Coaching.

[14]  Tiago M. Barbosa,et al.  Effects of Match Location, Quality of Opposition and Match Outcome on Match Running Performance in a Portuguese Professional Football Team , 2021, Entropy.

[15]  Igor Junio de Oliveira Custódio,et al.  The impact of match venue on performance indicators and tactical behaviour in youth soccer players , 2021, International Journal of Performance Analysis in Sport.

[16]  K. Davids,et al.  How football team composition constrains emergent individual and collective tactical behaviours: Effects of player roles in creating different landscapes for shared affordances in small-sided and conditioned games , 2021, International Journal of Sports Science & Coaching.

[17]  Tiago M. Barbosa,et al.  Quantifying Sub-Elite Youth Football Weekly Training Load and Recovery Variation , 2021, Applied Sciences.

[18]  M. Marques,et al.  5-a-Side Game as a Tool for the Coach in Soccer Training , 2021, Strength & Conditioning Journal.

[19]  N. Leite,et al.  The effects of maturity matched and un-matched opposition on physical performance and spatial exploration behavior during youth basketball matches , 2021, PloS one.

[20]  A. M. Monteiro,et al.  Monitoring Accumulated Training and Match Load in Football: A Systematic Review , 2021, International journal of environmental research and public health.

[21]  E. Mayo-Wilson,et al.  The PRISMA 2020 statement: an updated guideline for reporting systematic reviews , 2021, BMJ.

[22]  D. Marinho,et al.  Effects of Different Recovery Times on Internal and External Load During Small-Sided Games in Soccer , 2021, Sports health.

[23]  H. Sarmento,et al.  Small-sided games: An umbrella review of systematic reviews and meta-analyses , 2021, PloS one.

[24]  Keith Davids,et al.  Capturing and Quantifying Tactical Behaviors in Small-Sided and Conditioned Games in Soccer: A Systematic Review , 2020, Research quarterly for exercise and sport.

[25]  D. Barreira,et al.  Tactical Behaviour of Youth Soccer Players: Differences Depending on Task Constraint Modification, Age and Skill Level , 2020, Journal of human kinetics.

[26]  José Pino-Ortega,et al.  A comparison between UWB and GPS devices in the measurement of external load and collective tactical behaviour variables during a professional official match , 2020 .

[27]  A. Tong,et al.  Evaluation of the Cochrane Consumers and Communication Group’s systematic review priority-setting project , 2020, Health Research Policy and Systems.

[28]  Pedro Figueiredo,et al.  Using Optical Tracking System Data to Measure Team Synergic Behavior: Synchronization of Player-Ball-Goal Angles in a Football Match , 2020, Sensors.

[29]  I. Couzin,et al.  Collective movement analysis reveals coordination tactics of team players in football matches , 2020 .

[30]  J. Pino-Ortega,et al.  Accelerometry as a method for external workload monitoring in invasion team sports. A systematic review , 2020, PloS one.

[31]  R. Hristovski,et al.  Training or Synergizing? Complex Systems Principles Change the Understanding of Sport Processes , 2020, Sports Medicine - Open.

[32]  J. Sampaio,et al.  Effects of Knowing the Task’s Duration on Soccer Players’ Positioning and Pacing Behaviour during Small-Sided Games , 2020, International journal of environmental research and public health.

[33]  H. Sarmento,et al.  The effects of small-sided soccer games on tactical behavior and collective dynamics: A systematic review , 2020 .

[34]  M. Reis,et al.  The role of somatic maturation in the tactical effectiveness, efficiency and variability of young soccer players , 2020 .

[35]  B. Travassos,et al.  Comparison between Continuous and Fractionated Game Format on Internal and External Load in Small-Sided Games in Soccer , 2020, International journal of environmental research and public health.

[36]  M Ranjitha,et al.  Artificial Intelligence Algorithms and Techniques in the computation of Player-Adaptive Games , 2020, Journal of Physics: Conference Series.

[37]  Daniel Memmert,et al.  A Systematic Review of Collective Tactical Behaviours in Football Using Positional Data , 2019, Sports Medicine.

[38]  Hugo Folgado,et al.  Different Marks in the Pitch Constraint Youth Players’ Performances During Football Small-sided Games , 2020, Research quarterly for exercise and sport.

[39]  Peter Krustrup,et al.  Methods to collect and interpret external training load using microtechnology incorporating GPS in professional football: a systematic review , 2019, Research in sports medicine.

[40]  M. Anguera,et al.  Observational Studies in Male Elite Football: A Systematic Mixed Study Review , 2019, Front. Psychol..

[41]  Daniel Rojas-Valverde,et al.  From big data mining to technical sport reports: the case of inertial measurement units , 2019, BMJ Open Sport & Exercise Medicine.

[42]  Jaime Sampaio,et al.  Extracting spatial-temporal features that describe a team match demands when considering the effects of the quality of opposition in elite football , 2019, PloS one.

[43]  Pilar Sainz de Baranda,et al.  Physical and Tactical Demands of the Goalkeeper in Football in Different Small-Sided Games , 2019, Sensors.

[44]  Paulo Pereira,et al.  Towards the use of multidimensional performance indicators in football small-sided games: the effects of pitch orientation , 2018, Journal of sports sciences.

[45]  Jaime Sampaio,et al.  Effects of the pitch configuration design on players’ physical performance and movement behaviour during soccer small-sided games , 2018, Research in sports medicine.

[46]  F. García-Pinillos,et al.  A systematic review on small-sided games in football players: Acute and chronic adaptations , 2018, Journal of sports sciences.

[47]  Jaime Sampaio,et al.  Effects of pitch spatial references on players’ positioning and physical performances during football small-sided games , 2018, Journal of sports sciences.

[48]  Anthony S Leicht,et al.  Comparison of the movement patterns between small- and large-sided game training and competition in professional soccer players. , 2018, The Journal of sports medicine and physical fitness.

[49]  Antonio Dello Iacono,et al.  The Validity and Between-Unit Variability of GNSS Units (STATSports Apex 10 and 18 Hz) for Measuring Distance and Peak Speed in Team Sports , 2018, Front. Physiol..

[50]  Hugo Folgado,et al.  Speed synchronization, physical workload and match-to-match performance variation of elite football players , 2018, PloS one.

[51]  Martin Lames,et al.  Validation of electronic performance and tracking systems EPTS under field conditions , 2018, PloS one.

[52]  K. Lemmink,et al.  Match-derived relative pitch area changes the physical and team tactical performance of elite soccer players in small-sided soccer games , 2018, Journal of sports sciences.

[53]  Fernando Manuel Lourenço Martins,et al.  The effects of large-sided soccer training games and pitch size manipulation on time–motion profile, spatial exploration and surface area: Tactical opportunities , 2018 .

[54]  J. Sampaio,et al.  Changes in Effective Playing Space when Considering Sub-Groups of 3 to 10 Players in Professional Soccer Matches , 2018, Journal of human kinetics.

[55]  Paul S. Bradley,et al.  Are Current Physical Match Performance Metrics in Elite Soccer Fit for Purpose or Is the Adoption of an Integrated Approach Needed? , 2018, International journal of sports physiology and performance.

[56]  Keith Davids,et al.  How manipulating task constraints in small-sided and conditioned games shapes emergence of individual and collective tactical behaviours in football: A systematic review , 2018 .

[57]  Jürgen Freiwald,et al.  Validity and reliability of GPS and LPS for measuring distances covered and sprint mechanical properties in team sports , 2018, PloS one.

[58]  Aida Mustapha,et al.  Measurement of the Pitch Exploration Amongst Elite Professional Soccer Players: Official Match Analysis , 2018, SCDM.

[59]  D. Marinho,et al.  Pacing behaviour of players in team sports: Influence of match status manipulation and task duration knowledge , 2018, PloS one.

[60]  Jorge Baptista,et al.  Exploring the effects of playing formations on tactical behaviour and external workload during football small-sided games. , 2018, Journal of strength and conditioning research.

[61]  Hugo Folgado,et al.  Positional synchronization affects physical and physiological responses to preseason in professional football (soccer) , 2018, Research in sports medicine.

[62]  Jaime Sampaio,et al.  Effects of knowing the task duration on players’ pacing patterns during soccer small-sided games , 2018, Journal of sports sciences.

[63]  Jaime Sampaio,et al.  Differential Learning as a Key Training Approach to Improve Creative and Tactical Behavior in Soccer , 2018, Research quarterly for exercise and sport.

[64]  J. Sampaio,et al.  Exploring how playing football with different age groups affects tactical behaviour and physical performance , 2017, Biology of sport.

[65]  M. Jamil,et al.  Intra-system reliability of SICS: video-tracking system (Digital.Stadium®) for performance analysis in soccer. , 2017, The Journal of sports medicine and physical fitness.

[66]  K. Davids,et al.  What Performance Analysts Need to Know About Research Trends in Association Football (2012–2016): A Systematic Review , 2018, Sports Medicine.

[67]  Caleb D. Bazyler,et al.  Current Research and Statistical Practices in Sport Science and a Need for Change , 2017, Sports.

[68]  Bruno Travassos,et al.  Mental Fatigue and Spatial References Impair Soccer Players' Physical and Tactical Performances , 2017, Front. Psychol..

[69]  Hugo Folgado,et al.  Effects of Pitch Area-Restrictions on Tactical Behavior, Physical, and Physiological Performances in Soccer Large-Sided Games , 2017, Journal of strength and conditioning research.

[70]  Bruno Gonçalves,et al.  Dynamics of tactical behaviour in association football when manipulating players' space of interaction , 2017, PloS one.

[71]  Jos J de Koning,et al.  Monitoring Training Loads: The Past, the Present, and the Future. , 2017, International journal of sports physiology and performance.

[72]  F. García-Pinillos,et al.  How does high-intensity intermittent training affect recreational endurance runners? Acute and chronic adaptations: A systematic review , 2016, Journal of sport and health science.

[73]  Jaime Sampaio,et al.  Soft-assembled Multilevel Dynamics of Tactical Behaviors in Soccer , 2016, Front. Psychol..

[74]  Mark Russell,et al.  Changes in Acceleration and Deceleration Capacity Throughout Professional Soccer Match-Play , 2016, Journal of strength and conditioning research.

[75]  Daniel Memmert,et al.  Big data and tactical analysis in elite soccer: future challenges and opportunities for sports science , 2016, SpringerPlus.

[76]  Bruno Travassos,et al.  Application of entropy measures to analysis of performance in team sports , 2016 .

[77]  Kevin Norton,et al.  Game style in soccer: what is it and can we quantify it? , 2016 .

[78]  Keith Davids,et al.  Practice effects on intra-team synergies in football teams. , 2016, Human movement science.

[79]  Jaime Sampaio,et al.  Technical performance and match-to-match variation in elite football teams , 2016, Journal of sports sciences.

[80]  Hugo Folgado,et al.  Influence of additional players on collective tactical behavior in small-sided soccer games , 2016 .

[81]  R. Marcelino,et al.  Effects of emphasising opposition and cooperation on collective movement behaviour during football small-sided games , 2016, Journal of sports sciences.

[82]  Pedro Silva,et al.  Sports teams as complex adaptive systems: manipulating player numbers shapes behaviours during football small-sided games , 2016, SpringerPlus.

[83]  Terje Dalen,et al.  Player Load, Acceleration, and Deceleration During Forty-Five Competitive Matches of Elite Soccer , 2016, Journal of strength and conditioning research.

[84]  Richard E.A. van Emmerik,et al.  Multiscale entropy: A tool for understanding the complexity of postural control , 2016, Journal of sport and health science.

[85]  Jaime Sampaio,et al.  Timescales for exploratory tactical behaviour in football small-sided games , 2016, Journal of sports sciences.

[86]  Daniel Memmert,et al.  Current Approaches to Tactical Performance Analyses in Soccer Using Position Data , 2016, Sports Medicine.

[87]  Javier Mallo,et al.  Physical Demands of Top-Class Soccer Friendly Matches in Relation to a Playing Position Using Global Positioning System Technology , 2015, Journal of human kinetics.

[88]  L. Suarez-Arrones,et al.  Relationships between rating-of-perceived-exertion- and heart-rate-derived internal training load in professional soccer players: a comparison of on-field integrated training sessions. , 2015, International journal of sports physiology and performance.

[89]  Darren J Paul,et al.  Factors affecting match running performance of elite soccer players: shedding some light on the complexity. , 2015, International journal of sports physiology and performance.

[90]  Alan H. Welsh,et al.  “Magnitude-based Inference”: A Statistical Review , 2015, Medicine and science in sports and exercise.

[91]  Hugo Folgado,et al.  The effects of congested fixtures period on tactical and physical performance in elite football , 2015, Journal of sports sciences.

[92]  Heita Goto,et al.  Motion analysis of U11 to U16 elite English Premier League Academy players , 2015, Journal of sports sciences.

[93]  Adam Allen,et al.  Integrating different tracking systems in football: multiple camera semi-automatic system, local position measurement and GPS technologies , 2014, Journal of sports sciences.

[94]  Ricardo Monteiro,et al.  How perceiving additional targets modifies teams' tactical behavior during football small-sided games. , 2014, Human movement science.

[95]  Hugo Folgado,et al.  Competing with Lower Level Opponents Decreases Intra-Team Movement Synchronization and Time-Motion Demands during Pre-Season Soccer Matches , 2014, PloS one.

[96]  J. Sampaio,et al.  Time-motion and physiological profile of football training sessions performed by under-15, under-17 and under-19 elite Portuguese players. , 2014, International journal of sports physiology and performance.

[97]  C. Castagna,et al.  Variability of Objective and Subjective Intensities During Ball Drills in Youth Soccer Players , 2014, Journal of strength and conditioning research.

[98]  Jaime E Sampaio,et al.  Effects of pacing, status and unbalance in time motion variables, heart rate and tactical behaviour when playing 5-a-side football small-sided games. , 2014, Journal of science and medicine in sport.

[99]  Paul S. Bradley,et al.  Evaluation of Research Using Computerised Tracking Systems (Amisco® and Prozone®) to Analyse Physical Performance in Elite Soccer: A Systematic Review , 2014, Sports Medicine.

[100]  Kevin Thomas,et al.  Time-motion analysis of acceleration demands of 4v4 small-sided soccer games played on different pitch sizes. , 2014, Human movement science.

[101]  Jaime Sampaio,et al.  Effect of player position on movement behaviour, physical and physiological performances during an 11-a-side football game , 2014, Journal of sports sciences.

[102]  Craig Wright,et al.  Comment on ‘Performance analysis in football: A critical review and implications for future research’ , 2014, Journal of sports sciences.

[103]  Keith Davids,et al.  Interpersonal coordination tendencies supporting the creation/prevention of goal scoring opportunities in futsal , 2014, European journal of sport science.

[104]  Wouter Frencken,et al.  Length, width and centroid distance as measures of teams tactical performance in youth football , 2014, European journal of sport science.

[105]  Micael S. Couceiro,et al.  Measuring Tactical Behaviour Using Technological Metrics: Case Study of a Football Game , 2013 .

[106]  M. Anguera,et al.  Observational methodology in sport sciences , 2013 .

[107]  E. Flanagan The Effect Size Statistic—Applications for the Strength and Conditioning Coach , 2013 .

[108]  Keith Davids,et al.  Competing together: Assessing the dynamics of team-team and player-team synchrony in professional association football. , 2013, Human movement science.

[109]  Keith Davids,et al.  How Small-Sided and Conditioned Games Enhance Acquisition of Movement and Decision-Making Skills , 2013, Exercise and sport sciences reviews.

[110]  Keith Davids,et al.  Performance analysis in team sports: Advances from an Ecological Dynamics approach , 2013 .

[111]  Keith Davids,et al.  Capturing complex, non-linear team behaviours during competitive football performance , 2013, Journal of Systems Science and Complexity.

[112]  Christian Collet,et al.  The possession game? A comparative analysis of ball retention and team success in European and international football, 2007–2010 , 2013, Journal of sports sciences.

[113]  Ludovic Seifert,et al.  Key Properties of Expert Movement Systems in Sport , 2013, Sports Medicine.

[114]  Nathaniel H. Hunt,et al.  The Appropriate Use of Approximate Entropy and Sample Entropy with Short Data Sets , 2012, Annals of Biomedical Engineering.

[115]  Keith Davids,et al.  Sports Teams as Superorganisms , 2012, Sports Medicine.

[116]  Bruno Travassos,et al.  Spatial dynamics of team sports exposed by Voronoi diagrams. , 2012, Human movement science.

[117]  Keith Davids,et al.  Intra- and inter-group coordination patterns reveal collective behaviors of football players near the scoring zone. , 2012, Human movement science.

[118]  Arnold Baca,et al.  Accuracy of the LPM tracking system considering dynamic position changes , 2012, Journal of sports sciences.

[119]  Wouter Frencken,et al.  Variability of inter-team distances associated with match events in elite-standard soccer , 2012, Journal of sports sciences.

[120]  Keith Davids,et al.  Interpersonal coordination tendencies shape 1-vs-1 sub-phase performance outcomes in youth soccer , 2012, Journal of sports sciences.

[121]  J. Sampaio,et al.  Measuring Tactical Behaviour in Football , 2012, International Journal of Sports Medicine.

[122]  Oleguer Camerino,et al.  Lince: Multiplatform Sport Analysis Software , 2012 .

[123]  D. Araújo,et al.  Interpersonal coordination and ball dynamics in futsal (indoor football). , 2011, Human movement science.

[124]  Arnold Baca,et al.  Local Positioning Systems in (Game) Sports , 2011, Sensors.

[125]  Wouter Frencken,et al.  Oscillations of centroid position and surface area of soccer teams in small-sided games , 2011 .

[126]  Pablo Juan Greco,et al.  System of tactical assessment in Soccer (FUT-SAT): Development and preliminary validation , 2011 .

[127]  Jamie A Harley,et al.  The validity and reliability of 1-Hz and 5-Hz global positioning systems for linear, multidirectional, and soccer-specific activities. , 2010, International journal of sports physiology and performance.

[128]  Renato Rodano,et al.  Motor variability in sports: A non-linear analysis of race walking , 2010, Journal of sports sciences.

[129]  Ben Wisbey,et al.  Quantifying movement demands of AFL football using GPS tracking. , 2010, Journal of science and medicine in sport.

[130]  Peter O’Donoghue,et al.  Research Methods for Sports Performance Analysis , 2010 .

[131]  Tim McGarry,et al.  Space–time coordination dynamics in basketball: Part 2. The interaction between the two teams , 2010, Journal of sports sciences.

[132]  Aaron J. Coutts,et al.  Validity and reliability of GPS devices for measuring movement demands of team sports. , 2010, Journal of science and medicine in sport.

[133]  Grant Abt,et al.  The use of individualized speed and intensity thresholds for determining the distance run at high-intensity in professional soccer , 2009, Journal of sports sciences.

[134]  Nicholas Stergiou,et al.  Movement Variability and the Use of Nonlinear Tools: Principles to Guide Physical Therapist Practice , 2009, Physical Therapy.

[135]  Carlo Castagna,et al.  Technical performance during soccer matches of the Italian Serie A league: effect of fatigue and competitive level. , 2009, Journal of science and medicine in sport.

[136]  Brian Dawson,et al.  The reproducibility of physiological responses and performance profiles of youth soccer players in small-sided games. , 2008, International journal of sports physiology and performance.

[137]  R. S. Mendes,et al.  Statistics of football dynamics , 2007, 0706.1758.

[138]  Rhys Thatcher,et al.  A modified TRIMP to quantify the in-season training load of team sport players , 2007, Journal of sports sciences.

[139]  Di Salvo Valter,et al.  Validation of Prozone ®: A new video-based performance analysis system , 2006 .

[140]  Pier-Giorgio Zanone,et al.  A dynamical analysis of tennis: Concepts and data , 2005, Journal of sports sciences.

[141]  Madalena Costa,et al.  Multiscale entropy analysis of biological signals. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[142]  Catherine Sherrington,et al.  Reliability of the PEDro scale for rating quality of randomized controlled trials. , 2003, Physical therapy.

[143]  A. Jeukendrup,et al.  Heart Rate Monitoring , 2003, Sports medicine.

[144]  Ian M Franks,et al.  Sport competition as a dynamical self-organizing system , 2002, Journal of sports sciences.

[145]  J. Richman,et al.  Physiological time-series analysis using approximate entropy and sample entropy. , 2000, American journal of physiology. Heart and circulatory physiology.

[146]  N. Black,et al.  The feasibility of creating a checklist for the assessment of the methodological quality both of randomised and non-randomised studies of health care interventions. , 1998, Journal of epidemiology and community health.

[147]  J F Gréhaigne,et al.  Dynamic-system analysis of opponent relationships in collective actions in soccer. , 1997, Journal of sports sciences.

[148]  M. Saxton Anomalous diffusion due to binding: a Monte Carlo study. , 1996, Biophysical journal.

[149]  R. Balescu Equilibrium and Nonequilibrium Statistical Mechanics , 1991 .

[150]  S M Pincus,et al.  Approximate entropy as a measure of system complexity. , 1991, Proceedings of the National Academy of Sciences of the United States of America.

[151]  Kathryn A. Lee,et al.  Validity and reliability of a scale to assess fatigue , 1991, Psychiatry Research.

[152]  R. S. Yuill The Standard Deviational Ellipse; An Updated Tool for Spatial Description , 1971 .

[153]  D. Welty Lefever,et al.  Measuring Geographic Concentration by Means of the Standard Deviational Ellipse , 1926, American Journal of Sociology.