Sport Informatics and Analytics/Performance Monitoring

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Race time


Overview

Performance monitoring is presented as Theme 3 in this course. This is a time of rapid change on the quantification of one's own as well as others' performances.

This theme:

  • Provides a background to performance monitoring.
  • Discusses the development of wearable technologies to monitor performance.
  • Explores motion and video tracking technologies.

In addition to this introduction, the course includes these topics as part of this theme:

It contains a discussion of the Expected Goals (xG) metric too.

Video signpost

In this video, Jocelyn Mara discusses how she monitors athlete performance. Jocelyn is a graduate of the University of Canberra and was a Teaching Fellow in the Department of Sport and Exercise at the University in 2015. She became a full time member of staff at the University of Canberra in 2016. She has been a postgraduate scholar in performance analysis at the Australian Institute of Sport. Her PhD research included working with the Canberra United football team to identify the physical and physiological characteristics of elite female soccer players[1]. For examples of her research, see: the periodisation and physical performance in elite female soccer players (2015)[2]; the acceleration and deceleration profiles of elite female soccer players during competitive matches (2017a)[3]; quantifying the high-speed running and sprinting profiles of elite female soccer players during competitive matches (2017b)[4]; the accuracy and reliability of a new optical player tracking system for measuring displacement of soccer players (2017c)[5].

Jocelyn Mara - Monitoring Performance


Resources

Wearable Technologies

Since this course started in 2015, there has been an enormous change in wearable technologies. In a review paper, titled Wearables for Integrative Performance and Tactic Analyses: Opportunities, Challenges, and Future Directions Jonas Lutz (2019) and his colleagues [6] examine the use of micro-electromechanical systems that "enable the capture of relevant physiological and tactical information in individual and team sports". Jonas and his colleagues focus in their paper on reliability and validity, challenges, and future directions.

Mike Butler and Paul Luebbers (2018)[7] provide a summary of developments in health and fitness wearables.

André Henriksen and his colleagues (2018)[8] report on the use of fitness trackers and smartwatches to measure physical activity. The The objective of their study was to examine the availability of wrist-worn fitness wearables and analyze availability of relevant fitness sensors from 2011 to 2017. Lynne Feehan and her colleagues (2018)[9] investigate the accuracy of Fitbit devices in their paper. They conclude:

Other than for measures of steps in adults with no limitations in mobility, discretion should be used when considering the use of Fitbit devices as an outcome measurement tool in research or to inform health care decisions, as there are seemingly a limited number of situations where the device is likely to provide accurate measurement.

An introduction to performance monitoring

Heidi Thornton and her colleagues (2019)[10] note:

Within professional team sports, the collection and analysis of athlete monitoring data is common practice in the aim of assessing fatigue and subsequent adaptation responses, examining performance potential as well as minimizing the risk of injury and/or illness.

As you read the material shared here, you might like to consider Heidi and her colleagues' observation:

Athlete monitoring systems should be underpinned by appropriate data analysis and interpretation, in order to enable the rapid reporting of simplistic and scientifically valid feedback. Using the correct scientific and statistical approaches can improve the confidence of decisions made from athlete monitoring data.[11]

Matt Taberner and his colleagues (2019)[12] provided an example of the issues raised by Heidi and her colleagues. Matt and his colleagues conclude:

In the present study augmented GPS technology (GPS-2) and the TRACAB camera system provided interchangeable measures of positional tracking metrics to allow concurrent assessment and monitoring of training and competition in football players. However, we recommend practitioners evaluate their own systems to identify where errors exist, calculate and apply the regression equations to confidently interchange data.

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Monitoring performance at training camps

Anna Saw, Shona Halson and Inigo Mujika (2018)[13] have provided an introduction to the process of monitoring performance in training camps for cyclists and swimmers.

The purpose of their paper was:

To provide insight into the typical measurements and responses observed from monitoring elite road cyclist and swimmers during training camps, and translate these observations to practical strategies for other practitioners to employ. Twenty-nine male professional cyclists, 12 male and 19 female international swimmers participated in up to three of the eight 4–19 day training camps, held early in the season or leading into major competitions, at sea-level or moderate altitude. Monitoring included body mass and composition, subjective sleep, urinary specific gravity (USG), resting heart rate (HR) and peripheral oxygen saturation (SpO2) at altitude. (2018:63)

We recommend that you read this open access paper to get a sense of the process of monitoring performance by three very experienced sport scientists and to explore their retrospective analysis of the data shared as an insight into what is usually unpublished, privileged information.

What evidence does the paper present to support the authors' conclusions that:

Elite athletes experienced shifts in body composition during training camps, likely in line with individual performance goals and possibly aided by altitude. The stability of other monitored measures suggests athletes managed themselves appropriately, with the assistance of coaching and sport science support.



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Running faster?

The training camp paper[14] you have read in this introduction to performance monitoring mentioned "shifts ... likely in line with individual performance goals". We hope to extend your thinking about performance by recommending you read an article in the New York Times (Kevin Quealy and Josh Katz, 2018) [15] about the impact of a shoe design on running performance. The article uses secondary data, analyses these data and visualises them in ways that resonate with the themes of this course. It is an excellent example of data journalism that demonstrates how your work in sport informatics and analytics might progress. In passing, you might also consider some of the ethical issues raised in the article.



Case studies

We present sixteen case studies, from eleven sports, here to exemplify the range of approaches taken to monitor performance in sport contexts. Our first case study (association football) indicates the level of detail that can be used to discuss performance monitoring.

Association football

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Predicting variation in match performance

Robbie Wilson and his colleagues (2017)[16] present an evolutionary biology approach to consider whether skill or athleticism predict individual variation in football match performance. They report a study of thirty-two football players (at the University of Queensland) that measured:

  • morphology
    • upper and lower limb lengths
    • total height
    • torso-length
    • maximum circumference of leg and arm muscles
    • mass
  • maximum athletic performance
    • maximum speed over 1500 m
    • total squat time
    • maximum jumping distance
    • fastest sprint speed over 40 m
    • fastest speed through an agility circuit
  • motor skill function
    • maximum dribbling speed
    • average keep-up juggling ability of a size 1 football
    • static-ball passing accuracy
    • volley-kick accuracy
    • heading accuracy
  • static balance
    • average of three trials (for each leg) of total time taken to lose balance when standing on high-density foam with eyes closed and non-standing leg flexed at the knee at a right angle
  • individual ability in football-game scenarios
    • performance in a 1v1 football tennis tournament
    • performance in 11v11 football games (challenging, dribbling, intercepting, passing, shooting)[17].

The research team used social network analysis "to quantify individual player performance and connectedness within a team"[18]. Seven measures of connectedness were calculated for each player in the 11v11 games. The researchers share the networks for each game analysed (n=10). Robbie and his colleagues concluded:

We found that individuals with greater skill were more likely to perform well in soccer-tennis games and 11-a-side matches. Furthermore, skill was also the best predictor of an individual's contribution to the success of a team, based on a social network analysis of ball movement.[19]

We recommend that you take some time to review this research. The range of methods used and the analysis of performance presented raise some important issues for how a team of researchers or support staff in a football club might work together. The evolutionary biology approach taken in the research builds upon earlier work by Robbie Wilson and colleagues in predicting movement speeds of animals (including humans) in natural environments.[20]



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Centroids

Hugo Folgado and his colleagues (2017)[21] aimed to identify how tactical collective behaviour varies with age in different small-sided football game formats. They used the concept of a centroid to help them with their analysis of small-sided games. Robert Rein and Daniel Memmert (2016)[22] provide a comprehensive view of the centroid literature. Zengyuan Yue and colleagues (2008)[23] shared a mathematical background to the conceptual use of centroids in game analysis. Their paper calculated "geometrical centers, radii, expansion speeds, possession functions of the two teams" and were expressed as functions of time.[24]

Wouter Frencken and Lemmink (2008)[25] presented their work on centroids at the Fifth World Congress on Science and Football. They analysed a 4v4 game. In their paper, the centroid was defined as the average position of all of the outfield players on a team. Three measures were derived from the centroid:

  • the x-distance (in metres) to indicate representing longitudinal displacement
  • the y-distance (in metres) to indicate representing lateral displacement
  • the radial distance (in metres) that comprised longitudinal and lateral displacements.



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Football Analytics: Now and Beyond

Barça Innovation Hub has published Football Analytics: Now and Beyond.[26] It is a comprehensive discussion of analytics in association football. We suggest this is essential reading as you explore the place of analytics in sport. It includes a discussion of prospects for the next decade and aims to encourage conversations between practitioners as well as data scientists.



Australian rules football

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Interface of performance monitoring and pattern recognition

Sam McIntosh, Stephanie Kovalchik and Sam Robertson (2018)[27] sought to validate an Australian Football League player ratings system. They investigated also the extent to which "the distribution of points across the 13 rating subcategories could explain Australian Football League match outcome". Their paper illustrates the connections between performance monitoring and pattern recognition. We suggest you read their study to learn more about their approach and their identification of seven rules "capable of determining the extent to which relative contributions of rating subcategories explain Win/Loss at an accuracy of 79.3%".[28]



Basketball

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An ideal talent distribution for an NBA roster?

Todd Whitehead (2017)[29] has examined the history of NBA teams since 1980 in search of "the ideal talent distribution for a championship roster". His question was "Given a certain level of overall team quality, what is the most effective way to distribute talent within a roster?" His analysis raises some important issues that might distinguish a champion team[30] from a team of champions. These issues are fundamental to performance monitoring processes.



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Assessing shooting performance in NBA and NCAA basketball

Todd Schneider (2018)[31] reported the development of an open-source app, NBA Shots DB, that used the NBA Stats API "to populate a database with all 4.5 million shots attempted in NBA games since 1996". The NBA Shots DB processes a dataset provided by Sportradar of NCAA men’s shot attempts since 2013 into a format that can be merged with the NBA data.



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Refereeing behaviour in the last two minutes of NBA games

Russell Goldenberg (2018)[32] has analysed the data the NBA has made available about officiating the last two minutes of close games. Russell notes:

Since March 2015, the NBA has reviewed 20,798 plays from 1,208 games. In those 3,561 minutes of action, the officials have missed or incorrectly called 1,854 plays, or about 8.9% of all calls reviewed. This amounts to 1.53 wrong decisions in the final minutes of each close game.[33]

We recommend you read Russell's post to explore the use made of an open data set. Note that his post is updated automatically from new data made available by the NBA.



Cricket

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Assessing game performance

Steven Stern (2017)[34] has investigated performance in the Australian T20 cricket competition. His approach to monitoring performance is based on 'resources' ("The more efficiently players and teams use the resources available (120 deliveries and 10 wickets per team in a Twenty20 match), the more they advance their chance of victory". He suggests:

To appreciate the impact of a player we need a metric based not on how many runs are scored or wickets taken, but when and under what circumstances.[35]

He adds:

As this measurement is calculated in the same units for both batsmen and bowlers, it provides a means to compare performances across the two disciplines, as well as assess the performance of all-rounders (players who can competently bat and bowl).[36]

We suggest you look at Steven's methodology as an approach to combining quantitative and qualitative data to monitor and assess player performance in cricket in particular but more generally as a performance monitoring strategy.



Cross-country skiing

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Training characteristics of an Olympic and world champion

Guro Solli, Espen Tønnessen and Øyvind Sandbakk (2017)[37] investigated the training characteristics of an Olympic and world champion female cross-country skier (6 gold medals at the Olympic Games, 18 gold medals at the World Championship, and 110 World Cup victories). They analysed her day-to-day training diary data, interview data, and physiological tests:

Training data was systemized by training form (endurance, strength, and speed), intensity [low, moderate, and high-intensity training], and mode (running, cycling, and skiing/roller skiing), followed by a division into different periodization phases. Specific sessions utilized in the various periodization periods and the day-to-day periodization of training, in connection with altitude camps and tapering toward major championships[38]

We recommend that you read Guro, Espen and Øyvind's paper to appreciate the granular detail that can be applied to performance monitoring of an Olympic and world champion athlete over an extended period of time.



Cycling

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Optimal road cycling strategies

Stefan Wolf and Dietmar Saupe (2017)[39] investigated how two road cyclists might work together to optimise their performance in a 5km simulation. They report:

significant improvements in the total race time are achieved if two riders cooperate in an optimal way. The improvement of the total race time of about 10% for two equally strong riders is explained by exploiting slipstream effects.[40]

Stefan and Dietmar's discussion of optimal strategies in road racing raise some interesting questions about strategies in other sports. How might these be applied to other sports in which cooperative behaviour might be possible?



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BikeNet

Shane Eisenman and his colleagues (2009)[41] reported on their development of BikeNet. They share their insights into the development of "an extensible mobile sensing system for cyclist experience map-ping leveraging opportunistic sensor networking principles and techniques".

In this paper, we design and implement the prototype of a system not only to give context to the cyclist performance as part of a user-targeted application (e.g., health and safety), but also to collect environmental data as part of communal projects (e.g., pollution monitoring/mapping). We quantify aspects of cycling performance and environmental conditions that the mainstream recreational cyclist can appreciate and afford ...[42]



Marathon running

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Pacing

Eric Allen and his colleagues (2016)[43] use a large dataset of marathon finishing times (n= 9,524,071) to explore the bunching of performances (reference-dependent preferences) in the context of round numbers (for example, a four-hour marathon). They have made their dataset available online. (Note that the csv file for the dataset is 1.15 gigabytes. A smaller sample of data (n = 873,674) is 119.8 megabytes). We suggest you have a look at their article and consider how the authors reconcile 'clock time' and RFID 'chip time' to account for finishing times and identify reference-dependent preferences.

Derek Breen and his colleagues (2017)[44] added to the discussion of pacing in marathons with their analysis of data from the 2015 New York City Marathon for masters athletes (n=31,762).

Chris Dick (2019)[45] explored how to pace the London marathon and paid specific attention to weather conditions at the marathon.



Performance profiling

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Anti-doping

Sergei Iljukov and Yorck Schumacher (2017)[46] and Paolo Menaspà and Chris Abbiss (2017)[47] contributed to Frontiers in Physiology's discussions about performance profiling in anti-doping. Sergei and Yorck discussed the use of performance profiling. Paolo and Chris discussed the use of cycling performance metrics and their integration in an athlete's biological passport. We recommend that you look at both these papers to get a feel for how performance monitoring can be used in anti-doping contexts.



Rowing

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Investigating pair performance

Meddi R'Kiouak and his colleagues (2016[48], 2017[49]) report on their work with two expert rowers who had not practiced together. They concluded:

joint action training in rowing might imply an increase in the joint sense-making activities, probably associated with a change from an inter-personal to an extra-personal meaningful mode of co-regulation of the joint action.[50]

We suggest you look at this paper to get a sense of how the authors used a mixed methods approach to performance monitoring.



Rugby Union

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In-match physical demands

Hayato Yamamoto and his colleagues (2020)[51] investigated the in-match physical demands on elite Japanese rugby union players using a global positioning system. Their aim "was to quantify the physical demands of elite rugby union players by each position as a step towards designing position-specific training programme using a Global Positioning System/accelerometer system". They concluded "by clarifying the physical demands according to the positions, it will be possible to create optimised position-specific training programmes".



Sailing

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Sydney-Hobart Yacht Race

Each year, GPS data are shared from the home page of the Sydney-Hobart Yacht Race.[52]

Included on the race's website is a list of yachts entered, along with a photograph and description of each boat. The site has "a crew list, and the boat's performance data, predicted finishing time and standing for both Line Honours and Handicap Division which is updated every ten minutes". [53]

There are archival data that includes the results of previous races since 1945, "the weather they encountered; historical reports and statistical information".[54]

Basil Hess and his colleauges (2012)[55] have looked at the use of smartphones with GPS sailing data. They conclude:

Our results lead to guidelines relevant for GIS: tracking performance measurement, mobile platform and device selection, tracking application development and operation.



Swimming

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Endurance profiles of German elite swimmers over three decades

Christine Hoffmann and Martin Lames (2017)[56] investigated the use of an incremental test protocol[57] over three decades. They note:

At the German Swimming Association (DSV), the Pansold-step-test has been established as a standardized procedure since the 1980s. Every national DSV squad member has periodically to undergo this multi-stage test in water.[58]

Christine and Martin accessed data held by the DSV from the three decades in order to compare the data for sprinters and long distance swimmers. They investigated gender differences too.

We recommend you read this paper to learn how longitudinal data collected with a standardised protocol can be analysed to comment on changes in performance profiles. Their paper includes a critical reflection on the limitations of using longitudinal data. They conclude:

Drawing conclusions from our results for training of contemporary top level swimmers should only be done with caution. Derivations from means are not directly applicable for individuals. The variation of individuals can be greater than variation over years. To give meaningful recommendations, the inclusion of comprehensive training documentation would be necessary.[59]


Tennis

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Competition schedules, fatigue and injury

Stephanie Kovalchik (2018)[60] discussed injuries and absence from tennis tournaments. Stephanie shared the data she used for her analysis on Github. We suggest you look at Stephanie's analysis of Andy Murray's performance of how longitudinal data can be used to monitor current trends.



Athlete management systems

In recent years, there has been a growth in the literature about athlete monitoring systems.[61][62][63][64][65][66]

Aaron Coutts, Stephen Crowcroft and Tom Kempton (2018)[67] provide an overview of this literature in their discussion of the theory and practice of athlete monitoring. Their discussion includes a note of caution:

despite a growing body of applied work in high-performance sport, there is still a relatively poor understanding of the most appropriate tools and methods that can be used to assess how individuals are coping with training.

In a study of fourteen nationally competitive swimmers, Stephen Crowcroft and his colleagues (2017) observed:

Many monitoring variables are sensitive to changes in fitness and fatigue. However, no single monitoring variable could discriminate performance change. As such the use of a multidimensional system that may be able to better account for variations in fitness and fatigue should be considered.[68]

We suggest that you have a look at a presentation by Todd Ryall and Ian Morrow (2018)[69] that provides an example of the implementation of an an athlete management system over a five year period in collaboration with an industry partner[70] in order to reflect on the relationship between theory and practice in athlete data management.

Two examples of proprietary system documentation illustrate the role athlete management systems are playing in sport. KangaTech reported their use analytics dashboards to identify risk factors in athlete preparation and maintenance. Catapult shared their observations about the process of athlete monitoring (August 2018).

A number of presentations from the 2018 Human Performance Summit were shared online as video presentations including overviews by Simon Harries (rugby union) and Lisa Alexander (netball).

Emma Neuport, Stewart Cotterill and Simona Jobson (2019)[71] discussed the adherence of 9 female sprint water sport athletes to a training monitoring system and noted "perceptions of opaque or unfair decision making on training-program modifications and insufficient feedback were the primary causes for poor athlete adherence".

ePortfolio questions

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Questions about this theme

As you work your way through this theme and compile your ePortfolio, you might like to consider these six questions.

Q13. What aspects of this topic are of particular interest to you?

Q14. What criteria would you use to decide which wearable technologies to use?

Q15. Were there any aspects of the work of universities, centres, and sport you found informative?

Q16. Have you used any video tracking technology or video monitoring data?

Q17. Do you have any concerns about the validity and reliability of data gathered from wearable technologies or video tracking?

Q18. Are there any ethical issues involved in monitoring data collected in the ways discussed in this theme?



ePortfolio task

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Your advice is required

An academic department in a local university has heard about a decision to regulate female track athletes with elevated levels of testosterone in some races (Jeré Longman, 2019)[72]. You are invited to explore this issue and report back to the university within a month. You have a short brief to investigate this topic that includes a newspaper article and a link to Stéphane Bermon and Pierre-Yves Garnier's (2017)[73] paper on serum androgen levels and their relation to performance in track and field. You are tasked to: check the data and methods in the 2017 paper; identify what methods might be used to distinguish between female athletes competing in 800m, 1500m and one mile events; advise the university about engagement in other sports including Australian rules football[74]. The report format is your choice but you must include an executive summary and a list of recommendations that might guide the university's policy.



References

  1. ↑ Mara, Jocelyn (2016). "The physical and physiological characteristics of elite female soccer players" (PhD). University of Canberra. http://webpac.canberra.edu.au/record=b1901130. Retrieved 9 January 2018.
  2. ↑ Mara, Jocelyn; Thompson, Kevin; Pumpa, Kate; Ball, Nick (2015). "Periodization and physical performance in elite female soccer players". International journal of sports physiology and performance 10(5): 664-669.
  3. ↑ Mara, Jocelyn; Thompson, Kevin; Pumpa, Kate; Morgan, Stuart (2017). "The acceleration and deceleration profiles of elite female soccer players during competitive matches". Journal of Science and Medicine in Sport http://dx.doi.org/10.1016/j.jsams.2016.12.078.
  4. ↑ Mara, Jocelyn; Thompson, Kevin; Pumpa, Kate; Morgan, Stuart (2017). "Quantifying the High-Speed Running and Sprinting Profiles of Elite Female Soccer Players During Competitive Matches Using an Optical Player Tracking System". Journal of Strength & Conditioning Research 31(6): 1500-1508.
  5. ↑ Mara, Jocelyn; Morgan, Stuart; Pumpa, Kate; Thompson, Kevin (2017). "The Accuracy and Reliability of a New Optical Player Tracking System for Measuring Displacement of Soccer Players". International Journal of Computer Science in Sport 16(3): 175-184.
  6. ↑ Lutz, Jonas (2020). "Wearables for Integrative Performance and Tactic Analyses: Opportunities, Challenges, and Future Directions". Journal of Statistical Software 17(1): 59.
  7. ↑ Butler, Mike (2018). "Health and Fitness Wearables". Wearable Technologies: Concepts, Methodologies, Tools, and Applications: 30-50.
  8. ↑ Henriksen, André et al (March 2018). "Using Fitness Trackers and Smartwatches to Measure Physical Activity in Research: Analysis of Consumer Wrist-Worn Wearables". Journal of Medical Internet Research 20(3).
  9. ↑ Feehan, Lynne et al (2018). "Accuracy of Fitbit devices: systematic review and narrative syntheses of quantitative data.". MIR mHealth and uHealth 6(8): e10527.
  10. ↑ Thornton, Heidi; Delaney, Jace; Duthie, Grant; Dascombe, Ben (2019). "Developing Athlete Monitoring Systems in Team-Sports: Data Analysis and Visualization". International journal of sports physiology and performance https://doi.org/10.1123/ijspp.2018-0169.
  11. ↑ Thornton, Heidi et al (2019). "Developing Athlete Monitoring Systems in Team-Sports: Data Analysis and Visualization". International journal of sports physiology and performance https://doi.org/10.1123/ijspp.2018-0169.
  12. ↑ Taberner, Matt et al (2019). "Interchangeability of position tracking technologies; can we merge the data?". Journal of Science and Medicine in Football https://doi.org/10.1080/24733938.2019.1634279.
  13. ↑ Saw, Anna; Halson, Shona; Mujika, Inigo (2018). "Monitoring Athletes during Training Camps: Observations and Translatable Strategies from Elite Road Cyclists and Swimmers". Sports 6(3): 63.
  14. ↑ Saw, Anna; Halson, Shona; Mujika, Inigo (2018). "Monitoring Athletes during Training Camps: Observations and Translatable Strategies from Elite Road Cyclists and Swimmers". Sports 6(3): 63.
  15. ↑ Quealy, Kevin; Katz, Josh (18 July 2018). "Nike Says Its $250 Running Shoes Will Make You Run Much Faster. What if That’s Actually True?". https://www.nytimes.com/interactive/2018/07/18/upshot/nike-vaporfly-shoe-strava.html. Retrieved 25 July 2018.
  16. ↑ Wilson, Robbie et al (2017). "Skill not athleticism predicts individual variation in match performance of soccer players". Proceedings of the Royal Society B Biological Sciences 284(1869).
  17. ↑ Wilson, Robbie et al (2017). "Skill not athleticism predicts individual variation in match performance of soccer players". Proceedings of the Royal Society B Biological Sciences 284(1869).
  18. ↑ Wilson, Robbie et al (2017). "Skill not athleticism predicts individual variation in match performance of soccer players". Proceedings of the Royal Society B Biological Sciences 284(1869).
  19. ↑ Wilson, Robbie et al (2017). "Skill not athleticism predicts individual variation in match performance of soccer players". Proceedings of the Royal Society B Biological Sciences 284(1869).
  20. ↑ Wilson, Robbie; Husak, Jerry; Halsey, Lewis; Clemente, Christofer (2015). "Predicting the Movement Speeds of Animals in Natural Environments". SpringerPlus 5(1): 1410.
  21. ↑ Folgado, Hugo et al (2012). "Length, width and centroid distance as measures of teams tactical performance in youth football". European Journal of Sport Science 14(sup1), S487-S492.
  22. ↑ Rein, Robert; Memmert, Daniel (2016). "Big data and tactical analysis in elite soccer: future challenges and opportunities for sports science". Integrative and Comparative Biology 55(6): 1125-1141.
  23. ↑ Yue, Zengyuan et al (2008). "Mathematical Analysis of a Soccer Game. Part I: Individual and Collective Behaviors". Studies in Applied Mathematics https://doi.org/10.1111/j.1467-9590.2008.00413.x.
  24. ↑ Yue, Zengyuan et al (2008). "Mathematical Analysis of a Soccer Game. Part I: Individual and Collective Behaviors". Studies in Applied Mathematics https://doi.org/10.1111/j.1467-9590.2008.00413.x.
  25. ↑ Frencken, Wouter; Lemmink. Science and football VI: 27 Team kinematics of small-sided soccer games. London: Routledge. p. 161.
    ISBN 0-203-89368-9
    .
  26. ↑ Lyons, Keith (3 January 2020). "Football Analytics: Now and Beyond".
  27. ↑ McIntosh, Sam; Kovalchik, Stephanie (2018). "Validation of the Australian Football League Player Ratings". International Journal of Sports Science & Coaching https://doi.org/10.1177/1747954118758000.
  28. ↑ McIntosh, Sam; Kovalchik, Stephanie (2018). "Validation of the Australian Football League Player Ratings". International Journal of Sports Science & Coaching https://doi.org/10.1177/1747954118758000.
  29. ↑ Whitehead, Todd. "In search of the ideal talent distribution for an NBA roster". https://fansided.com/2017/07/18/celtics-talent-distribution-gordon-hayward-nba-championship/. Retrieved 18 October 2017.
  30. ↑ Hodge, Ken; Henry, Graham; Smith, Wayne (2014). "A Case Study of Excellence in Elite Sport: Motivational Climate in a World Champion Team". The Sport Psychologist 28(1): 60-74.
  31. ↑ Schneider, Todd (2 April 2018). "Assessing Shooting Performance in NBA and NCAA Basketball". http://toddwschneider.com/posts/nba-vs-ncaa-basketball-shooting-performance/. Retrieved 4 April 2018.
  32. ↑ Goldenberg, Russell (3 January 2018). "NBA last two minute report". https://pudding.cool/2017/02/two-minute-report. Retrieved 4 January 2018.
  33. ↑ Goldenberg, Russell (3 January 2018). "NBA last two minute report". https://pudding.cool/2017/02/two-minute-report. Retrieved 4 January 2018.
  34. ↑ Stern, Steven. "What data tells us about the best cricket players". https://theconversation.com/what-data-tells-us-about-the-best-cricket-players-87000. Retrieved 28 December 2017.
  35. ↑ Stern, Steven. "What data tells us about the best cricket players". https://theconversation.com/what-data-tells-us-about-the-best-cricket-players-87000. Retrieved 28 December 2017.
  36. ↑ Stern, Steven. "What data tells us about the best cricket players". https://theconversation.com/what-data-tells-us-about-the-best-cricket-players-87000. Retrieved 28 December 2017.
  37. ↑ Solli, Guro; Tønnessen, Espen; Sandbakk, Øyvind (2017). "The Training Characteristics of the World's Most Successful Female Cross-Country Skier". Frontiers in Physiology https://doi.org/10.3389/fphys.2017.01069.
  38. ↑ Solli, Guro; Tønnessen, Espen; Sandbakk, Øyvind (2017). "The Training Characteristics of the World's Most Successful Female Cross-Country Skier". Frontiers in Physiology https://doi.org/10.3389/fphys.2017.01069.
  39. ↑ Wolf, Stefan; Saupe, Dietmar (2017). "How to Stay Ahead of the Pack: Optimal Road Cycling Strategies for two Cooperating Riders". International Journal of Computer Science in Sport 16(2): 88-100.
  40. ↑ Wolf, Stefan; Saupe, Dietmar (2017). "How to Stay Ahead of the Pack: Optimal Road Cycling Strategies for two Cooperating Riders". International Journal of Computer Science in Sport 16(2): 97.
  41. ↑ Eisenman et al, Shane (2009). "BikeNet: A mobile sensing system for cyclist experience mapping". ACM Transactions on Sensor Networks 6(1): 6.
  42. ↑ Eisenman et al, Shane (2009). "BikeNet: A mobile sensing system for cyclist experience mapping". ACM Transactions on Sensor Networks 6(1): 6.
  43. ↑ Allen, Eric et al (2016). "Reference-Dependent Preferences: Evidence from Marathon Runners". Management Science 63(6): 1657-1672.
  44. ↑ Breen, Derek et al (2017). "Marathon pace control in masters athletes". International journal of sports physiology and performance doi: 10.1123/ijspp.2016-0730.
  45. ↑ Dick, Chris (30 January 2019). "Fuelled by Data: How to Pace the London Marathon". https://towardsdatascience.com/how-to-pace-the-london-marathon-fuelled-by-data-8c62efa50054. Retrieved 9 February 2019.
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